Explanation:

To solve this problem, we need to determine the cost price of the toy given the marked price, discount, and profit percentage.

1. Given information:

The marked price (MP) of the toy is Rs. 770.

A discount of 10\% is given on the marked price.

After the discount, the person still makes a 10\% gain on the cost price (CP).

2. Calculate the selling price (SP) after the discount:

A 10% discount on the marked price of Rs. 770 is calculated as:

$$
\text{Discount} = 10\% \text{ of } 770 = \frac{10}{100} \times 770 = 77 \, \text{Rs.}
$$

The selling price (SP) after the discount is:

$$
\text{SP} = \text{MP} – \text{Discount} = 770 – 77 = 693 \, \text{Rs.}
$$

3. Relate the selling price to the cost price:

The person makes a 10\% gain on the cost price. The gain percentage formula is:
$$
\text{Gain Percentage} = \frac{\text{SP} – \text{CP}}{\text{CP}} \times 100
$$

Given that the gain percentage is 10\%, we can set up the equation:
$$
10 = \frac{693 – \text{CP}}{\text{CP}} \times 100
$$

4. Solve for the cost price (CP):

Rearrange the equation to solve for CP:

$$
\frac{693 – \text{CP}}{\text{CP}} = \frac{10}{100} = 0.10
$$
$$
693 – \text{CP} = 0.10 \times \text{CP}
$$
$$
693 = 0.10 \times \text{CP} + \text{CP}
$$
$$
693 = 1.10 \times \text{CP}
$$
$$
\text{CP} = \frac{693}{1.10}
$$

Calculate CP:
$$
\text{CP} = \frac{693}{1.10} = 630 \, \text{Rs.}
$$

Therefore, the cost price of the toy is Rs. 630.

The correct answer is (c) Rs. 630.

Explanation:

To solve this problem, we need to calculate the probability that an arrow falls in the red region of the archery target. The probability is determined by the ratio of the area of the red region to the total area of the target.

1. Determine the total area of the archery target:

The diameter of the target is 1 meter, so the radius $R$ is:

$$
R = \frac{1}{2} = 0.5 \, \text{meters}
$$

The area $A_{\text{total}}$ of the circular target is given by the formula for the area of a circle:

$$
A_{\text{total}} = \pi R^2 = \pi (0.5)^2 = \pi \times 0.25 = 0.25\pi \, \text{square meters}
$$

2. Calculate the area of the red region:

The radius of the red region $r_{\text{red}}$ is 0.20 meters.

The area $A_{\text{red}}$ of the red region is:

$$
A_{\text{red}} = \pi (r_{\text{red}})^2 = \pi (0.20)^2 = \pi \times 0.04 = 0.04\pi \, \text{square meters}
$$

3. Calculate the probability of hitting the red region:

The probability $P$ that an arrow falls in the red region is the ratio of the area of the red region to the total area of the target:

$$
P = \frac{A_{\text{red}}}{A_{\text{total}}} = \frac{0.04\pi}{0.25\pi} = \frac{0.04}{0.25}
$$

Simplify the fraction:

$$
P = \frac{0.04}{0.25} = 0.16
$$

Therefore, the probability that the arrows fall in the red region of the archery target is 0.16.

The correct answer is (c) 0.16.

Explanation:

To solve this problem, we need to calculate the total distance the competitor runs while collecting all six apples and dropping them into the bucket. The apples are placed in a straight line, with specific distances between them, and the competitor can only carry one apple at a time to the bucket.

1. Understand the placement of apples and the bucket:

The bucket is placed at the starting point (0 meters).

The first apple is 5 meters away from the bucket.

Each subsequent apple is placed 3 meters apart from the previous one.

2. Determine the positions of the apples:

The first apple is at 5 meters.

The second apple is at $5 + 3 = 8$ meters.

The third apple is at $5 + 3 \times 2 = 11$ meters.

The fourth apple is at $5 + 3 \times 3 = 14$ meters.

The fifth apple is at $5 + 3 \times 4 = 17$ meters.

The sixth apple is at $5 + 3 \times 5 = 20$ meters.

3. Calculate the total distance for each apple:

Since the competitor picks up one apple at a time and returns to the bucket after picking each apple, the distance covered for each apple is twice the distance from the bucket.

For the 1st apple:

$$
\text{Distance} = 2 \times 5 = 10 \text{ meters}
$$

For the 2nd apple:

$$
\text{Distance} = 2 \times 8 = 16 \text{ meters}
$$

For the 3rd apple:

$$
\text{Distance} = 2 \times 11 = 22 \text{ meters}
$$

For the 4th apple:

$$
\text{Distance} = 2 \times 14 = 28 \text{ meters}
$$

For the 5th apple:

$$
\text{Distance} = 2 \times 17 = 34 \text{ meters}
$$

For the 6th apple:

$$
\text{Distance} = 2 \times 20 = 40 \text{ meters}
$$

4. Calculate the total distance run by the competitor:

Add all the distances calculated for each apple:

$$
\text{Total distance} = 10 + 16 + 22 + 28 + 34 + 40 = 150 \text{ meters}
$$

Therefore, the total distance that the competitor has to run to collect all the apples and drop them in the bucket is 150 meters.

The correct answer is (c) 150 m.

Explanation:

To determine who will complete the work first, we need to calculate the total time each person takes to complete the entire work based on the partial work they can complete in a given number of days.

1. Calculate the total time required for each person to complete the work:

W can do 25% of the work in 30 days:

Since 25% of the work is $\frac{1}{4}$ of the work, we can find the total time W takes to complete the work by setting up a proportion:
$$
\text{Total time for W} = \frac{30 \text{ days}}{\frac{1}{4}} = 30 \times 4 = 120 \text{ days}
$$

X can do $\frac{1}{4}$ of the work in 10 days:

The total time X takes to complete the work is:

$$
\text{Total time for X} = \frac{10 \text{ days}}{\frac{1}{4}} = 10 \times 4 = 40 \text{ days}
$$

Y can do 40% of the work in 40 days:

Since 40% of the work is $\frac{40}{100} = \frac{2}{5}$ of the work, the total time Y takes to complete the work is:

$$
\text{Total time for Y} = \frac{40 \text{ days}}{\frac{2}{5}} = 40 \times \frac{5}{2} = 40 \times 2.5 = 100 \text{ days}
$$

Z can do $\frac{1}{3}$ of the work in 13 days:

The total time Z takes to complete the work is:
$$
\text{Total time for Z} = \frac{13 \text{ days}}{\frac{1}{3}} = 13 \times 3 = 39 \text{ days}
$$

2. Compare the total time for each person:

W: 120 days

X: 40 days

Y: 100 days

Z: 39 days

3. Determine who will complete the work first:

The person who completes the work in the least amount of time is Z, who takes 39 days.

Thus, Z will complete the work first.

The correct answer is (d) Z.

Explanation:

To solve this problem, we need to determine how many times A and B cross each other when walking around a circular park in opposite directions from 8:00 a.m. to 9:30 a.m.

1. Understand the given information:

A and B start at the same point at 8:00 a.m.

A walks at a speed of 2 rounds per hour.

B walks at a speed of 3 rounds per hour.

They walk in opposite directions.

We need to find the number of times they cross each other from 8:00 a.m. to 9:30 a.m.

2. Calculate the relative speed:

Since A and B walk in opposite directions, their relative speed is the sum of their individual speeds:

$$
\text{Relative speed} = 2 + 3 = 5 \text{ rounds per hour}
$$

3. Determine the total time interval:

The time from 8:00 a.m. to 9:30 a.m. is 1.5 hours.

4. Calculate the total distance covered due to relative speed:

In 1 hour, their relative distance covered is 5 rounds.

In 1.5 hours, the total distance covered due to their relative speed is:

$$
\text{Total relative distance} = 5 \times 1.5 = 7.5 \text{ rounds}
$$

5. Determine the number of times they cross each other:

A and B cross each other once for every full round covered by the relative distance.

The number of times they cross each other in 1.5 hours is equal to the integer part of 7.5:

$$
\text{Number of crossings} = \lfloor 7.5 \rfloor = 7
$$

Therefore, A and B will cross each other 7 times between 8:00 a.m. and 9:30 a.m.

The correct answer is (a) 7.

Explanation:

To solve this problem, we need to find out how many boys are ranked after Kamal in a class of 60 students where the number of girls is twice that of boys.

1. Determine the number of boys and girls:

Let the number of boys be $b$.

The number of girls is twice the number of boys, so the number of girls is $2b$.

Given that the total number of students is 60:

$$
b + 2b = 60
$$
$$
3b = 60
$$
$$
b = \frac{60}{3} = 20
$$

Therefore, there are 20 boys and $2b = 40$ girls in the class.

2. Determine Kamal’s position:

Kamal is ranked seventeenth from the top.

There are 9 girls ahead of Kamal.

3. Determine the number of boys ahead of Kamal:

Since Kamal is ranked seventeenth and there are 9 girls ahead of him, the number of boys ahead of him is:

$$
\text{Number of boys ahead of Kamal} = 17 – 9 – 1 = 7
$$

This subtraction accounts for the 9 girls ahead of him and Kamal himself, a boy.

4. Determine the number of boys after Kamal:

The total number of boys in the class is 20.

The number of boys after Kamal can be calculated by subtracting the number of boys ahead of Kamal (7) and Kamal himself (1) from the total number of boys:

$$
\text{Number of boys after Kamal} = 20 – 7 – 1 = 12
$$

Thus, the number of boys in rank after Kamal is 12.

The correct answer is (b) 12.

Explanation:

To solve this problem, we need to calculate the volume of water in both the overhead cylindrical tank and the underground rectangular tank. Then, we can determine how much of the underground tank remains filled with water after filling the overhead tank completely.

1. Calculate the volume of the overhead cylindrical tank:

The formula for the volume of a cylinder is given by:
$$
V = \pi r^2 h
$$
where $r$ is the radius and $h$ is the height of the cylinder.

Radius $r = 2 \, \text{m}$

Height $h = 7 \, \text{m}$

Therefore, the volume of the overhead tank is:
$$
V_{\text{cylinder}} = \pi (2)^2 (7) = 28\pi \, \text{m}^3
$$

2. Calculate the volume of the underground rectangular tank:

The formula for the volume of a rectangular tank is given by:
$$
V = l \times w \times h
$$
where $l$ is the length, $w$ is the width, and $h$ is the height of the rectangular tank.

Length $l = 5.5 \, \text{m}$

Width $w = 4 \, \text{m}$

Height $h = 6 \, \text{m}$

Therefore, the volume of the underground tank is:
$$
V_{\text{rectangular}} = 5.5 \times 4 \times 6 = 132 \, \text{m}^3
$$

3. Calculate the remaining volume of water in the underground tank:

When the overhead tank is filled, the volume of water transferred from the underground tank is $28\pi \, \text{m}^3$.

The remaining volume of water in the underground tank is:

$$
V_{\text{remaining}} = V_{\text{rectangular}} – V_{\text{cylinder}}
$$

Substituting the values:

$$
V_{\text{remaining}} = 132 – 28\pi \, \text{m}^3
$$

4. Calculate the portion of the underground tank still filled with water:

To find the fraction of the underground tank that is still filled with water, we divide the remaining volume by the total volume of the underground tank:
$$
\text{Fraction filled} = \frac{V_{\text{remaining}}}{V_{\text{rectangular}}} = \frac{132 – 28\pi}{132}
$$

5. Simplify the expression:

We know that $\pi \approx 3.14$, so:
$$
28\pi \approx 28 \times 3.14 = 87.92
$$
Substituting this value:
$$
V_{\text{remaining}} = 132 – 87.92 = 44.08 \, \text{m}^3
$$
The fraction filled is:
$$
\text{Fraction filled} = \frac{44.08}{132} \approx \frac{1}{3}
$$

Thus, after filling the overhead tank completely, approximately $\frac{1}{3}$ of the underground tank is still filled with water.

The correct answer is (a) $\frac{1}{3}$.

Explanation:

To solve this problem, we need to count the numbers between 100 and 300 that either begin with 2 or end with 2.

1. Numbers that begin with 2:

Numbers that begin with 2 are in the range from 200 to 299.

This includes all the numbers from 200 to 299.

The total number of such numbers is:

$$
299 – 200 + 1 = 100 \text{ numbers}
$$

2. Numbers that end with 2:

Numbers between 100 and 300 that end with 2 are: 102, 112, 122, …, 292.

These numbers form an arithmetic sequence where the first term is 102, and the common difference is 10.

3. Calculate the total numbers that end with 2:

– To find the number of terms in this sequence, we can use the formula for the $n$-th term of an arithmetic sequence:
$$
a_n = a_1 + (n – 1)d
$$
where $a_n$ is the $n$-th term, $a_1 = 102$ is the first term, and $d = 10$ is the common difference. We need to find $n$ such that $a_n = 292$:

$$
292 = 102 + (n – 1) \times 10
$$

Solving for $n$:
$$
292 = 102 + 10n – 10
$$
$$
292 = 92 + 10n
$$
$$
200 = 10n
$$
$$
n = \frac{200}{10} = 20
$$

So, there are 20 numbers that end with 2.

4. Subtract the overlap:

Numbers between 200 and 299 that end with 2 are: 202, 212, 222, …, 292.

These numbers also form an arithmetic sequence where the first term is 202 and the common difference is 10.

The last term is 292, and using the same formula for $n$:

$$
292 = 202 + (n – 1) \times 10
$$

Solving for $n$:

$$
292 = 202 + 10n – 10
$$
$$
292 = 192 + 10n
$$
$$
100 = 10n
$$
$$
n = \frac{100}{10} = 10
$$

So, there are 10 numbers between 200 and 299 that end with 2.

5. Calculate the total unique numbers:

– To find the total count of numbers either beginning with or ending with 2, we add the two groups and subtract the overlap:
$$
\text{Total} = \text{Numbers beginning with 2} + \text{Numbers ending with 2} – \text{Overlap}
$$
$$
\text{Total} = 100 + 20 – 10 = 110
$$

Therefore, the total number of numbers between 100 and 300 that either begin with or end with 2 is 110

The correct answer is (a) 110.

Explanation:

To solve this problem, we need to analyze each statement about integers $R$ and $S$ that are divisible by 5, and determine which statement is not necessarily true.

1. Given:

$R$ and $S$ are different integers both divisible by 5.

This implies that $R = 5m$ and $S = 5n$ for some integers $m$ and $n$.

2. Analyzing each statement:

Option (a): $R – S$ is divisible by 5

\[
R – S = 5m – 5n = 5(m – n)
\]

Since $m – n$ is an integer, $R – S$ is divisible by 5. This statement is true.

Option (b): $R + S$ is divisible by 10

\[
R + S = 5m + 5n = 5(m + n)
\]

$R + S$ is divisible by 5. For it to be divisible by 10, $m + n$ must be even. However, $m$ and $n$ can be both odd, both even, or one odd and one even. Thus, $m + n$ is not necessarily even. Therefore, $R + S$ is not necessarily divisible by 10. This statement is not necessarily true.

Option (c): $R \times S$ is divisible by 25

\[
R \times S = (5m) \times (5n) = 25mn
\]

Since $25mn$ is clearly divisible by 25, this statement is true.

Option (d): $R^2 + S^2$ is divisible by 5

\[
R^2 + S^2 = (5m)^2 + (5n)^2 = 25m^2 + 25n^2 = 25(m^2 + n^2)
\]

Since $25(m^2 + n^2)$ is divisible by 5, this statement is true.

3. Conclusion:

The statement that is not necessarily true is option (b): R + S is divisible by 10.

The correct answer is (b) $R + S$ is divisible by 10.

Explanation:

To solve this problem, we need to find out how many days Ram would take to complete the entire job alone, based on the information about how Ram and Shyam worked together and individually.

1. Define the variables:

Let $R$ be the amount of work Ram can complete in one day.

Let $S$ be the amount of work Shyam can complete in one day.

2. Work completed together:

Ram and Shyam work together for 4 days and complete 60% of the job. The combined daily work rate of Ram and Shyam is $R + S$.

The total work done by both in 4 days is $4(R + S)$.

Given that this work represents 60% of the job, we can write:
$$
4(R + S) = 0.60
$$

3. Calculate $R + S$:

Solve for $R + S$:
$$
R + S = \frac{0.60}{4} = 0.15
$$

Therefore, the combined daily work rate of Ram and Shyam is $R + S = 0.15$.

4. Work completed by Shyam alone:

After Ram takes leave, Shyam works alone for 8 more days to complete the remaining 40% of the job.

The work done by Shyam alone in 8 days is $8S$.

Since this work represents the remaining 40% of the job, we can write:
$$
8S = 0.40
$$

5. Calculate $S$:

Solve for $S$:
$$
S = \frac{0.40}{8} = 0.05
$$

Therefore, Shyam’s daily work rate is $S = 0.05$.

6. Calculate $R$:

Substitute $S = 0.05$ into the equation $R + S = 0.15$:
$$
R + 0.05 = 0.15
$$
$$
R = 0.15 – 0.05 = 0.10
$$

Therefore, Ram’s daily work rate is $R = 0.10$.

7. Determine the number of days Ram would take to complete the entire job alone:

The total job is represented as 1 (or 100%).

To find out how many days Ram would take to complete the entire job alone, we divide the total job by Ram’s daily work rate:
$$
\text{Days} = \frac{1}{R} = \frac{1}{0.10} = 10
$$

Therefore, Ram would take 10 days to complete the entire job alone.

The correct answer is (c) 10 days.

Explanation:

To solve this problem, we need to calculate the net displacement of the person from the starting point after all the movements.

1. Understand the movements:

The person walks 12 km due north.

Then, he walks 15 km due east.

After that, he walks 19 km due west.

Finally, he walks 15 km due south.

2. Calculate the net displacement in the north-south direction:

The person initially walks 12 km north and then 15 km south. The net displacement in the north-south direction is:
$$
\text{Net north-south displacement} = 12 \, \text{km} – 15 \, \text{km} = -3 \, \text{km}
$$

This means the person ends up 3 km south of the starting point.

3. Calculate the net displacement in the east-west direction:

The person walks 15 km east and then 19 km west. The net displacement in the east-west direction is:
$$
\text{Net east-west displacement} = 15 \, \text{km} – 19 \, \text{km} = -4 \, \text{km}
$$

This means the person ends up 4 km west of the starting point.

4. Determine the total displacement from the starting point:

The total displacement is the straight-line distance from the starting point to the final position, which can be calculated using the Pythagorean theorem.

The net displacements form a right-angled triangle where one leg is 3 km (south) and the other leg is 4 km (west).

The total displacement $d$ is given by:

$$
d = \sqrt{(-3)^2 + (-4)^2}
$$

Simplifying this:

$$
d = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{km}
$$

5. Conclusion:

The person is 5 km away from the starting point.

The correct answer is (a) 5 km.

Explanation:

To solve this problem, we need to determine the original height of the tree trunk given that it broke at a certain height and fell to the ground, forming a right-angled triangle.

1. Understand the problem setup:

Let $AB$ be the original height of the tree trunk.

Point $A$ is where the trunk touches the ground.

The trunk broke at point $C$, which is 12 meters above the ground.

The broken part $CB$ is still attached at $C$ and touches the ground at point $D$.

The distance $AD$ is 5 meters.

2. Visualize the geometry:

The situation forms a right-angled triangle $ACD$ where:

$AC$ is the vertical segment of the trunk still standing, which is 12 meters.

$AD$ is the horizontal distance from the base of the tree to where the top of the trunk touches the ground, which is 5 meters.

$CD$ is the hypotenuse of the triangle, representing the length of the broken part of the tree trunk.

3. Apply the Pythagorean theorem:

In right-angled triangle $ACD$, we can use the Pythagorean theorem to find the length of $CD$:

$$
CD = \sqrt{AC^2 + AD^2}
$$

Substituting the given values:

$$
CD = \sqrt{12^2 + 5^2}
$$
$$
CD = \sqrt{144 + 25}
$$
$$
CD = \sqrt{169}
$$
$$
CD = 13 \, \text{meters}
$$

4. Calculate the original height of the tree trunk:

The original height of the tree trunk $AB$ is the sum of the standing part $AC$ and the length of the broken part $CB$. Since $CB = CD = 13$ meters, we have:

$$
AB = AC + CB
$$
$$
AB = 12 + 13 = 25 \, \text{meters}
$$

Thus, the original height of the trunk was 25 meters.

The correct answer is (b) 25 m.

Explanation:

To solve this problem, we need to determine the total number of steps on a ladder given that climbing 4 more steps from the first step brings a person to the middle step.

1. Understand the given information:

The person is initially standing on the first step of the ladder.

After climbing 4 more steps, the person reaches the middle step of the ladder.

2. Define the variables:

Let the total number of steps on the ladder be $n$.

The middle step of the ladder can be found by dividing the total number of steps by 2.

3. Set up the equation:

Since the person is initially on the 1st step and climbs 4 more steps to reach the middle step, the position of the middle step is:

$$
\text{Middle step} = 1 + 4 = 5
$$

This means the 5th step is the middle step of the ladder.

4. Determine the total number of steps:

If the 5th step is the middle step, then the total number of steps, $n$, must be:

$$
n = 2 \times 5 – 1 = 9
$$

This is because for a ladder with an odd number of steps, the middle step is the $\frac{n + 1}{2}$-th step.

5. Conclusion:

Therefore, the ladder has 9 steps.

The correct answer is (b) 9.

Explanation:

To solve this problem, we need to determine the age of the baby based on the given information about the sum of ages in a family over a period of time.

1. Given information:

The sum of the ages of 5 family members 3 years ago was 80 years.

The average age of the family today is the same as it was 3 years ago.

A baby was born during the intervening period.

2. Calculate the sum of ages of the original 5 family members today:

Let the ages of the 5 family members 3 years ago be $a_1, a_2, a_3, a_4,$ and $a_5$.

The sum of their ages 3 years ago was:
$$
a_1 + a_2 + a_3 + a_4 + a_5 = 80
$$

Over the next 3 years, each member would have aged by 3 years. So, the sum of their ages today is:
$$
(a_1 + 3) + (a_2 + 3) + (a_3 + 3) + (a_4 + 3) + (a_5 + 3)
$$

Simplifying, the sum of their ages today becomes:
$$
a_1 + a_2 + a_3 + a_4 + a_5 + 15 = 80 + 15 = 95
$$

Therefore, the sum of the ages of the 5 original members today is 95 years.

3. Determine the total age sum with the baby today:

Let the age of the baby today be $b$.

Including the baby, the sum of the ages of all 6 family members today is:
$$
95 + b
$$

4. Finding the average age today:

The average age of the family today is the same as it was 3 years ago. The average age 3 years ago for the 5 members was:
$$
\text{Average age 3 years ago} = \frac{80}{5} = 16
$$

Therefore, the average age of the 6 members today is also 16. Setting up the equation for the average age today:
$$
\frac{95 + b}{6} = 16
$$

5. Solve for $b$:

Multiply both sides by 6:
$$
95 + b = 96
$$

Subtract 95 from both sides:
$$
b = 1
$$

Therefore, the age of the baby today is 1 year.

The correct answer is (b) 1 year.

Explanation:

To solve this problem, we need to maximize the area of a rectangle with a fixed perimeter. Given that the perimeter condition is $X_1 + X_2 = 40$ meters, we want to find the maximum possible area.

1. Express the area of the rectangle:

The area $A$ of the rectangle can be expressed in terms of its length $X_1$ and breadth $X_2$ as:
$$
A = X_1 \times X_2
$$

2. Given the constraint:

We are given that $X_1 + X_2 = 40$ meters. We can express $X_2$ in terms of $X_1$:
$$
X_2 = 40 – X_1
$$

Substituting this into the area formula gives:
$$
A = X_1 \times (40 – X_1)
$$

3. Rewrite the area equation:

Expanding the equation:
$$
A = 40X_1 – X_1^2
$$

This is a quadratic equation in the form $A = -X_1^2 + 40X_1$.

4. Finding the maximum area:

The quadratic equation $A = -X_1^2 + 40X_1$ represents a parabola that opens downward (because the coefficient of $X_1^2$ is negative). The maximum value of $A$ occurs at the vertex of the parabola.

The $X_1$ value at the vertex can be found using the formula $X_1 = -\frac{b}{2a}$, where $a = -1$ and $b = 40$:
$$
X_1 = -\frac{40}{2 \times (-1)} = 20
$$

5. Calculate the maximum area:

Substituting $X_1 = 20$ back into the equation $X_2 = 40 – X_1$, we get:
$$
X_2 = 40 – 20 = 20
$$

Thus, the maximum area $A$ is:
$$
A = X_1 \times X_2 = 20 \times 20 = 400 \text{ square meters}
$$

Therefore, the maximum area of the agricultural field will not exceed 400 square meters.

The correct answer is (a) 400 sq m.

Explanation:

To solve this problem, we need to calculate the straight-line distance from the starting point $O$ to the final point $B$ after the person has traveled from $O$ to $A$ and then from $A$ to $B$.

1. Understanding the movements:

The person starts at point $O$ and moves to point $A$ in the north-east direction, covering a distance of 5 km.

From point $A$, the person then moves to point $B$ in the north-west direction, covering a distance of 12 km.

2. Analyzing the directions:

Since the person is traveling in straight lines in specific compass directions (north-east and north-west), we can use trigonometry to solve this.

– Moving north-east means traveling 45 degrees from both the north and east directions.
– Moving north-west means traveling 45 degrees from both the north and west directions.

3. Setting up the coordinate system:

Let’s place point $O$ at the origin $(0, 0)$.

– After moving to point $A$ (5 km north-east), the coordinates of $A$ are $(5 \cos 45^\circ, 5 \sin 45^\circ)$.
– Given that $\cos 45^\circ = \sin 45^\circ = \frac{\sqrt{2}}{2}$, the coordinates of $A$ are:
$$
A = \left(5 \times \frac{\sqrt{2}}{2}, 5 \times \frac{\sqrt{2}}{2}\right) = \left(\frac{5\sqrt{2}}{2}, \frac{5\sqrt{2}}{2}\right)
$$

4. Calculating the coordinates of point $B$:

After moving to point $B$ (12 km north-west), point $B$ will have new coordinates:

– Moving 12 km in the north-west direction means moving 45 degrees counterclockwise from the north.
– The north-west direction will change the coordinates by adding 12 km in the north direction and subtracting 12 km in the west direction:

Thus, the coordinates of $B$ can be calculated by first determining the movement in the x and y directions:

$$
\Delta x = -12 \cos 45^\circ = -12 \times \frac{\sqrt{2}}{2} = -6\sqrt{2}
$$
$$
\Delta y = 12 \sin 45^\circ = 12 \times \frac{\sqrt{2}}{2} = 6\sqrt{2}
$$

Adding these changes to the coordinates of $A$:

$$
B = \left(\frac{5\sqrt{2}}{2} – 6\sqrt{2}, \frac{5\sqrt{2}}{2} + 6\sqrt{2}\right)
$$

5. Simplifying the coordinates:

– The coordinates of $B$ can be simplified as:

$$
B = \left(\frac{5\sqrt{2}}{2} – \frac{12\sqrt{2}}{2}, \frac{5\sqrt{2}}{2} + \frac{12\sqrt{2}}{2}\right)
$$

$$
B = \left(\frac{-7\sqrt{2}}{2}, \frac{17\sqrt{2}}{2}\right)
$$

6. Calculating the distance from $O$ to $B$:

Using the distance formula, the distance $OB$ is:

$$
OB = \sqrt{\left(\frac{-7\sqrt{2}}{2}\right)^2 + \left(\frac{17\sqrt{2}}{2}\right)^2}
$$

$$
OB = \sqrt{\left(\frac{49 \times 2}{4}\right) + \left(\frac{289 \times 2}{4}\right)}
$$

$$
OB = \sqrt{\left(\frac{98}{4} + \frac{578}{4}\right)}
$$

$$
OB = \sqrt{\frac{676}{4}} = \sqrt{169} = 13
$$

Thus, the person is 13 km away from the starting point $O$.

The correct answer is (b) 13 km.

Explanation:

To solve this problem, we need to determine the side length of a cube that can be constructed from a rectangular piece of tin with given dimensions.

1. Understand the dimensions of the rectangular piece of tin:

The piece of tin is a rectangle with a length of 12 cm and a width of 8 cm.

2. Calculate the area of the rectangular piece of tin:

The area $A$ of the rectangle is:
$$
A = \text{length} \times \text{width} = 12 \, \text{cm} \times 8 \, \text{cm} = 96 \, \text{cm}^2
$$

3. Determine the surface area of the cube:

A cube has 6 faces, and each face of the cube is a square with side length $s$. The total surface area $S$ of a cube is given by:
$$
S = 6s^2
$$

Since the entire piece of tin is used to construct the cube, the surface area of the cube must be equal to the area of the rectangular tin:
$$
6s^2 = 96
$$

4. Solve for the side length $s$ of the cube:

Divide both sides by 6:
$$
s^2 = \frac{96}{6} = 16
$$

Taking the square root of both sides:
$$
s = \sqrt{16} = 4
$$

5. Conclusion:

The side length of the cube is 4 cm.

The correct answer is (c) 4 cm.

Explanation:

To solve this problem, we need to calculate by what percentage the number $Y$ is less than the number $X$, given that both $X$ and $Y$ are percentages less than a third number $Z$.

1. Express $X$ and $Y$ in terms of $Z$:

$X$ is 20\% less than $Z$. Therefore, $X$ can be expressed as:
$$
X = Z – 0.20Z = 0.80Z
$$

$Y$ is 28\% less than $Z$. Therefore, $Y$ can be expressed as:
$$
Y = Z – 0.28Z = 0.72Z
$$

2. Calculate the difference between $X$ and $Y$:

The difference between $X$ and $Y$ is:
$$
X – Y = 0.80Z – 0.72Z = 0.08Z
$$

3. Determine the percentage by which $Y$ is less than $X$:

The percentage by which $Y$ is less than $X$ can be calculated by dividing the difference by $X$ and then multiplying by 100:
$$
\text{Percentage decrease} = \left(\frac{X – Y}{X}\right) \times 100
$$

Substituting the values of $X$ and $Y$:
$$
\text{Percentage decrease} = \left(\frac{0.80Z – 0.72Z}{0.80Z}\right) \times 100 = \left(\frac{0.08Z}{0.80Z}\right) \times 100
$$

Simplifying:
$$
\text{Percentage decrease} = \left(\frac{0.08}{0.80}\right) \times 100 = 0.1 \times 100 = 10%
$$

Therefore, $Y$ is 10% less than $X$.

The correct answer is (b) 10%.

Explanation:

To solve this problem, we need to find the number of girls in the class based on the given information about the boys and the total number of students.

1. Determine the total number of boys in the class:

We know that 18 very tall boys constitute three-fourths of the total number of boys in the class. Let’s denote the total number of boys by $b$.

Given:
$$
\frac{3}{4}b = 18
$$

Solving for $b$:
$$
b = \frac{18 \times 4}{3} = 24
$$

So, the total number of boys in the class is $24$.

2. Determine the total number of students in the class:

We are given that the total number of boys is two-thirds of the total number of students in the class. Let the total number of students be $S$.

Given:
$$
\frac{2}{3}S = 24
$$

Solving for $S$:
$$
S = \frac{24 \times 3}{2} = 36
$$

So, the total number of students in the class is $36$.

3. Calculate the number of girls in the class:

The number of girls, $g$, can be calculated by subtracting the number of boys from the total number of students:

$$
g = S – b = 36 – 24 = 12
$$

Thus, the number of girls in the class is $12$.

The correct answer is (b) 12.

Explanation:

To solve this problem, we need to calculate the total marks Anita scored in the test and determine how many more questions she would have needed to answer correctly to reach a passing score of 60%.

1. Understanding the structure of the test:

Total problems: 70

Problems in arithmetic: 10

Problems in algebra: 30

Problems in geometry: 30

2. Calculating the number of problems Anita answered correctly:

Arithmetic: She answered 70% of 10 problems correctly.
$$
\text{Correct arithmetic problems} = 0.7 \times 10 = 7
$$

Algebra: She answered 40% of 30 problems correctly.
$$
\text{Correct algebra problems} = 0.4 \times 30 = 12
$$

Geometry: She answered 60% of 30 problems correctly.
$$
\text{Correct geometry problems} = 0.6 \times 30 = 18
$$

3. Calculating the total number of problems answered correctly:

\[
\text{Total correct problems} = 7 + 12 + 18 = 37
\]

4. Calculating the total marks Anita obtained:

Since each problem carries equal marks, the total marks obtained is the number of correct answers:
$$
\text{Marks obtained} = 37
$$

5. Calculating the passing marks:

To pass, Anita needs at least 60% of the total marks:
$$
\text{Passing marks} = 0.6 \times 70 = 42
$$

6. Calculating the additional number of correct answers needed to pass:

Anita currently has 37 marks. To reach 42 marks, she needs:
$$
\text{Additional correct answers needed} = 42 – 37 = 5
$$

Therefore, Anita would need to answer 5 more questions correctly to earn a 60% passing mark.

The correct answer is (b) 5.

Explanation:

To solve this problem, we need to determine the number of students in a class based on the total amount of money collected for charity, given that each student contributes an amount equal to the number of students, with one student contributing an additional Rs. 2.

1. Let the number of students in the class be $n$.

2. Each student contributes $n$ rupees:

Therefore, the total contribution from all students, except the one contributing an additional Rs. 2, is:
$$
n \times n = n^2 \text{ rupees}
$$

3. Including the additional Rs. 2 contribution by one student:

The total collection becomes:
$$
n^2 + 2 \text{ rupees}
$$

4. Given that the total collection is Rs. 443:

We set up the equation:
$$
n^2 + 2 = 443
$$

5. Solve for $n$:

Subtract 2 from both sides:
$$
n^2 = 443 – 2 = 441
$$

Take the square root of both sides:
$$
n = \sqrt{441} = 21
$$

6. Conclusion:

Therefore, the number of students in the class is 21.

The correct answer is (b) 21.

Explanation:

To solve this problem, we need to find how many times all five groups meet on the same day within 180 days. This requires finding the Least Common Multiple (LCM) of the meeting intervals of the five groups.

1. Understanding the meeting intervals:

Gardening group meets every 2 days.

Electronics group meets every 3 days.

Chess group meets every 4 days.

Yachting group meets every 5 days.

Photography group meets every 6 days.

2. Finding the Least Common Multiple (LCM):

We need to find the LCM of 2, 3, 4, 5, and 6 to determine when all groups meet on the same day.

Prime factorization:
\[
2 = 2
\]
\[
3 = 3
\]
\[
4 = 2^2
\]
\[
5 = 5
\]
\[
6 = 2 \times 3
\]

The LCM is the product of the highest powers of all prime factors:
\[
\text{LCM} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60
\]

3. Calculating the number of times all groups meet together in 180 days:

Since the LCM is 60, all groups meet together every 60 days.

To find how many times this happens in 180 days:

\[
\text{Number of times} = \frac{180}{60} = 3
\]

Thus, all five groups meet on the same day 3 times within 180 days.

The correct answer is (d) 3.

Explanation:

To solve this problem, we need to determine the number of days required to produce a total of 19,000 saleable units of a product, given that 5% of the production is unfit for sale.

1. Understanding the production details:

The firm produces 1,000 units of the product per day.

Out of these 1,000 units, 5% are unfit for sale.

2. Calculating the number of saleable units produced per day:

The number of unfit units per day is:
\[
\text{Unfit units per day} = 1000 \times 0.05 = 50
\]

The number of saleable units per day is:
\[
\text{Saleable units per day} = 1000 – 50 = 950
\]

3. Determining the number of days required to complete the order:

The total order quantity is 19,000 saleable units.

The number of days required to produce 19,000 saleable units is:
\[
\text{Number of days} = \frac{19000}{950}
\]

4. Calculating the exact number of days:

\[
\text{Number of days} = \frac{19000}{950} = 20
\]

Thus, the order will be completed in 20 days.

The correct answer is (c) 20.

Explanation:

To solve this problem, we need to determine the route that will bring person X back to the starting point based on his initial movements.

1. Understanding the initial movements:

Let’s assume person X starts at the point $(0, 0)$ on a grid.

First movement: 3 km north. This moves X from $(0, 0)$ to $(0, 3)$.

Second movement: 3 km west. This moves X from $(0, 3)$ to $(-3, 3)$.

Third movement: 4 km south. This moves X from $(-3, 3)$ to $(-3, -1)$.

At this point, X is at $(-3, -1)$.

2. Calculating the distance to return to the starting point $(0, 0)$:

To return to $(0, 0)$ from $(-3, -1)$, X needs to:
– Move 3 km east to change the x-coordinate from $-3$ to $0$.
– Move 1 km north to change the y-coordinate from $-1$ to $0$.

3. Determining the correct route from the options:

We need to find the route from the options that involves moving 3 km east and 1 km north to return to the starting point.

Option (a): 3 km east, then 2 km south.

Moving 3 km east would bring X to $(0, -1)$, and moving 2 km south would bring X to $(0, -3)$.

This does not return X to $(0, 0)$.

Option (b): 3 km east, then 1 km north.

Moving 3 km east would bring X to $(0, -1)$, and moving 1 km north would bring X to $(0, 0)$.

This returns X to $(0, 0)$.

Option (c): 1 km north, then 2 km west.

Moving 1 km north would bring X to $(-3, 0)$, and moving 2 km west would bring X to $(-5, 0)$.

This does not return X to $(0, 0)$.

Option (d): 3 km south, then 1 km north.

Moving 3 km south would bring X to $(-3, -4)$, and moving 1 km north would bring X to $(-3, -3)$.

This does not return X to $(0, 0)$.

4. Conclusion:

The correct route that will bring person X back to the starting point is option (b): 3 km east, then 1 km north.

The correct answer is (b) 3 km east, then 1 km north.

Explanation:

Passage Analysis

The passage discusses the challenge of achieving a balance between demand and supply of food globally and why this issue has gained importance in recent times. Key points include:

1. Demand-Supply Balance: Maintaining a balance between food demand and supply is crucial to preventing hunger and starvation, particularly in underdeveloped countries where purchasing power is low.
2. Challenges in Food Supply: The passage mentions that the quantum and composition of demand for food have been changing and that the capabilities of individual countries to ensure an uninterrupted supply of food have come under strain recently.
3. Global Food Issues: Issues related to food production, marketing, and pricing, especially price affordability for the poor, have become global concerns that require global solutions.

The passage does not explicitly mention population growth or a decline in food production area as reasons for the rising importance of global food supply issues. Instead, it highlights limitations in the ability of countries to sustain food supply chains due to changing demand and production constraints.

Evaluation of Each Statement

Let’s examine each statement to see if it aligns with the passage.

Statement 1: “Overgrowth of the population worldwide”

• The passage does not mention global population growth as a reason for the increased importance of food supply issues. While population growth could contribute to demand, this is not specifically cited in the passage as a primary factor.
• This statement is not supported by the passage.

Statement 2: “Sharp decline in the area of food production”

• The passage does not refer to a decline in the area of food production. It only mentions that the capabilities of individual countries to ensure uninterrupted food supplies have been strained due to changing demand and other factors, but it does not mention a decrease in production area as a specific reason.
• This statement is not supported by the passage.

Statement 3: “Limitation in the capabilities for sustained supply of food”

• This statement is directly supported by the passage. The passage mentions that the capabilities of individual countries to ensure an uninterrupted supply of food have come under strain, which is one of the primary reasons for the increased importance of global food supply issues.
• This statement is correct.

Conclusion

Based on the analysis, only Statement 3 is correct.

The correct answer is: (b) 3 only

Explanation:

Passage Analysis

The passage discusses the biggest challenge to world agriculture, which it identifies as achieving a balance between the demand for and supply of food. Key points include:

1. Demand-Supply Balance: The passage emphasizes that achieving a balance between food demand and supply has historically been the greatest challenge for world agriculture. This balance is particularly critical for closed and populous economies that do not have sufficient agricultural growth and cannot rely on imports.
2. Global Food Distribution: The passage points out that even if there is an adequate global food supply, food does not automatically move from surplus countries to deficit countries if the latter lack purchasing power. This leads to hunger and malnutrition in underdeveloped economies.
3. Global Issues: The passage highlights that food production, marketing, and pricing—especially price affordability for the poor in the developing world—have become global issues requiring global solutions.

The main message is that balancing the global demand and supply of food is essential to addressing hunger and food security issues worldwide.

Evaluation of Each Option

Let’s examine each option to see which one aligns best with the passage.

Option (a): “to find sufficient land for agriculture and to expand food processing industries”

• The passage does not mention finding sufficient land for agriculture or expanding food processing industries as the main challenge. The focus is on balancing food demand and supply, not on expanding agricultural land or food processing facilities.
• This option is incorrect.

Option (b): “to eradicate hunger in underdeveloped countries”

• While eradicating hunger in underdeveloped countries is certainly an important issue, the passage identifies balancing demand and supply of food as the biggest challenge, not the eradication of hunger alone.
• Hunger is presented as a consequence of imbalances in food distribution and purchasing power, but it is not identified as the primary challenge in world agriculture according to the passage.
• This option is incorrect.

Option (c): “to achieve a balance between the production of food and non-food items”

• The passage does not discuss a balance between food and non-food items. Instead, it focuses specifically on balancing the demand and supply of food in order to avoid hunger and starvation.
• This option is incorrect.

Option (d): “to achieve a balance between demand for and supply of food”

• This option aligns directly with the main message of the passage. The passage emphasizes that the biggest challenge in world agriculture is to maintain a balance between food demand and supply to prevent hunger and ensure food security, both at the country level and globally.
• This option is correct.

Conclusion

The correct answer is: (d) to achieve a balance between demand for and supply of food

Explanation:

Passage Analysis

The passage discusses the global challenge of food security and the difficulties in achieving a balance between the demand and supply of food. Key points include:

1. Demand-Supply Balance: For a closed economy, especially if populous and lacking sufficient agricultural growth, balancing demand and supply for food can be challenging. In contrast, an open economy with enough exchange surpluses can buy food from abroad, reducing this constraint.
2. Global Distribution Issues: The passage emphasizes that even if there is a global surplus, food does not automatically reach deficit areas if these areas lack purchasing power. The issue of hunger and malnourishment is thus largely due to “empty-pocket hungry mouths” in underdeveloped economies.
3. Global Nature of Food Security: Food production, marketing, and pricing, especially price-affordability for the poor, are identified as global issues that need global solutions.

The passage suggests that improving affordability for the poor and addressing global issues in food marketing and pricing are essential for achieving food security.

Evaluation of Each Option

Let’s examine each option to see which ones align with the passage’s message.

Statement 1: “Setting up more agro-based industries”

• The passage does not mention the need to set up more agro-based industries as a solution to food security. While agro-based industries could theoretically increase food processing and storage capacity, the passage is more focused on issues of affordability and distribution.
• This statement is not directly supported by the passage.

Statement 2: “Improving the price affordability by the poor”

• This statement aligns directly with the passage. The passage highlights price-affordability for the poor as a critical issue, particularly in underdeveloped economies where many people cannot afford food even if it is available.
• This statement is correct.

Statement 3: “Regulating the conditions of marketing”

• This statement aligns with the passage’s emphasis on global solutions for food marketing and pricing. Ensuring fair and accessible marketing conditions can help address some of the distribution challenges mentioned in the passage, such as ensuring food reaches deficit areas.
• This statement is correct.

Statement 4: “Providing food subsidy to one and all”

• The passage does not suggest providing a universal food subsidy to everyone as a solution. The focus is on affordability for the poor, but it does not advocate a blanket subsidy for everyone, which would be economically impractical and is not mentioned as a solution.
• This statement is not supported by the passage.

Conclusion

Based on the analysis, only Statements 2 and 3 are directly supported by the passage.

The correct answer is: (b) 2 and 3 only

Explanation:

Passage Analysis

The passage explains a chain reaction that could be triggered by an increase in human-made carbon dioxide in the atmosphere. Key points include:

1. Soil as a Carbon Reservoir: Soil contains twice as much carbon as plants and the Earth’s atmosphere combined, making it one of the largest carbon reservoirs on the planet.
2. Impact of Increased Carbon Dioxide: An increase in carbon dioxide can enhance plant growth because carbon dioxide supports photosynthesis in plants.
3. Chain Reaction in Soil: As plants grow more in a carbon dioxide-rich environment, their roots could stimulate microbial activity in the soil. This increase in microbial activity may accelerate the decomposition of soil carbon, leading to its release back into the atmosphere as carbon dioxide.

The overall implication of the passage is that increased plant growth due to higher levels of carbon dioxide could lead to the release of stored carbon in soil back into the atmosphere, thus potentially increasing atmospheric carbon dioxide levels further.

Evaluation of Each Option

Let’s examine each option to see which one best aligns with the passage.

Option (a): “Carbon dioxide is essential for the survival of microorganisms and plants.”

• While the passage states that carbon dioxide supports plant growth, it does not claim that carbon dioxide is essential for the survival of plants or microorganisms. The passage focuses on how increased carbon dioxide affects plant growth and microbial activity, not on its necessity for their survival.
• This option is incorrect.

Option (b): “Humans are solely responsible for the release of carbon dioxide into the atmosphere.”

• The passage does mention that human-made carbon dioxide is contributing to the chain reaction, but it does not claim that humans are the sole source of carbon dioxide emissions. Carbon dioxide also comes from natural processes, and the passage does not imply that humans are the only cause.
• This option is incorrect.

Option (c): “Microorganisms and soil carbon are mainly responsible for the increased plant growth.”

• This option misinterprets the passage. The passage states that increased carbon dioxide leads to increased plant growth, not that microorganisms and soil carbon are responsible for it. In fact, the passage implies the opposite: that increased plant growth could stimulate microbial activity, leading to soil carbon decomposition.
• This option is incorrect.

Option (d): “Increasing green cover could trigger the release of carbon trapped in soil.”

• This option aligns well with the passage. The passage describes how increased plant growth (i.e., “green cover”) in a carbon dioxide-rich environment can stimulate microbial activity, which could in turn lead to the release of carbon stored in soil. This is exactly the chain reaction that the passage describes.
• This option is the most logical corollary based on the passage.

Conclusion

The correct answer is: (d) Increasing green cover could trigger the release of carbon trapped in soil

Explanation:

Passage Analysis

The passage explains the evolution of lactose tolerance in humans. Key points include:

1. Early Lactose Intolerance: Initially, humans stopped producing lactase (the enzyme that digests lactose) after infancy because, once weaned, they did not need to digest milk.
2. Domestication of Cattle: Around 10,000 years ago, cattle domestication began, and this introduced milk into the diets of certain human groups.
3. Evolution of Lactose Tolerance: For groups that depended on cattle (e.g., in Europe, the Middle East, and Africa), it became advantageous to digest milk. This led to the evolution of lactose tolerance in these populations.
4. Continued Lactose Intolerance in Non-Cattle Herding Groups: Groups that did not domesticate cattle, such as the Chinese and Thai, did not develop lactose tolerance and remain lactose intolerant.

The passage implies that a permanent dietary change (in this case, consuming milk) can lead to genetic adaptations over generations.

Evaluation of Each Option

Let’s examine each option to see which one best aligns with the passage.

Option (a): “About 10,000 years ago, the domestication of animals took place in some parts of the world.”

• This statement is supported by the passage, which mentions that cattle domestication began approximately 10,000 years ago in certain parts of the world.
• However, while this is a factual statement derived from the passage, it is not the most logical assumption that can be made. The passage’s main focus is on the genetic adaptation of lactose tolerance due to a change in diet, not merely the fact that domestication occurred.
• This option is correct but not the most insightful assumption based on the passage’s main idea.

Option (b): “A permanent change in the food habits of a community can bring about a genetic change in its members.”

• This option is directly supported by the passage. The passage describes how the introduction of milk into the diet of cattle-herding communities led to the evolution of lactose tolerance in those populations. This suggests that a permanent dietary change (such as the regular consumption of milk) can bring about a genetic change (lactose tolerance) in a community over generations.
• This option is the most logical and insightful assumption based on the passage.

Option (c): “Lactose tolerant people only are capable of getting simple sugars in their bodies.”

• This statement is not correct. The passage does mention that lactose is broken down into simple sugars by lactase, but it does not imply that lactose-tolerant people are the only ones capable of obtaining simple sugars from other sources. People can obtain simple sugars from other foods, not just milk.
• This option is incorrect.

Option (d): “People who are not lactose tolerant cannot digest any dairy product.”

• This statement is also incorrect. Lactose intolerance means difficulty digesting lactose, a specific sugar found in milk, but it does not imply an inability to digest all dairy products. For example, many lactose-intolerant people can consume products like hard cheese or yogurt, which contain lower levels of lactose.
• This option is incorrect.

Conclusion

The most logical assumption that can be made from the passage is: (b) A permanent change in the food habits of a community can bring about a genetic change in its members

Explanation:

Passage Analysis

The passage discusses the need to feed a growing population by 2050 and the impact of dietary choices on the planet’s resources. Key points include:

1. Impact of Diet on Resources: The passage argues that a diet focused on meat and dairy (which is becoming more common in the developing world) will place a greater strain on the world’s resources than a diet based on unrefined grains, nuts, fruits, and vegetables.
2. Urgency of Dietary Choice: Given the expected population increase by 2050, the passage emphasizes the importance of choosing a diet that minimizes resource use to sustainably feed everyone.

The overall message of the passage is that the choice between a diet high in animal products and a diet based on plant-based foods will have significant consequences for the planet’s resources.

Evaluation of Each Option

Let’s examine each option to see which one best captures the main message of the passage.

Option (a): “Our increasing demand for foods sourced from animals puts a greater burden on our natural resources.”

• This option aligns well with the passage’s message. The passage specifically mentions that a diet focused on meat and dairy will have a greater toll on resources than a diet focused on plant-based foods.
• This option accurately reflects the critical message of the passage.

Option (b): “Diets based on grains, nuts, fruits and vegetables are best suited for health in developing countries.”

• The passage does mention grains, nuts, fruits, and vegetables as part of a resource-efficient diet, but it does not discuss the health benefits of this diet for developing countries. The focus of the passage is on the environmental impact of dietary choices, not on their health benefits.
• This option is not supported by the passage.

Option (c): “Human beings change their food habits from time to time irrespective of the health concerns.”

• The passage does not discuss the frequency of dietary changes or suggest that people change their diets regardless of health concerns. The focus is on the environmental impact of a diet high in animal products.
• This option is not relevant to the passage.

Option (d): “From a global perspective, we still do not know which type of diet is best for us.”

• The passage does not suggest uncertainty about which diet is best. In fact, it implies that a diet based on plant-based foods (grains, nuts, fruits, and vegetables) is more sustainable and will place less strain on resources.
• This option is incorrect and does not align with the passage.

Conclusion

The correct answer is: (a) Our increasing demand for foods sourced from animals puts a greater burden on our natural resources

Explanation:

Passage Analysis

The passage suggests that the legal imperatives (or laws) in any state are shaped by the demands that the state encounters. These demands, in turn, are influenced by the distribution of economic power within the society that the state governs.

This implies an interrelationship between Politics (laws and state imperatives) and Economics (economic power distribution). Specifically, the passage indicates that the legal requirements or political actions of a state are, to some extent, dependent on or influenced by the economic structure of society.

Evaluation of Each Option

Let’s examine each option to see which one best captures the idea expressed in the passage.

Option (a): “The antithesis of Politics and Economics”

• Antithesis means a strong contrast or opposition between two things. This option would imply that Politics and Economics are in direct opposition or contradiction to each other.
• The passage, however, suggests an interdependence between Politics and Economics rather than an opposition. It does not present them as opposing forces but rather as influencing each other.
• This option is not supported by the passage.

Option (b): “The interrelationship of Politics and Economics”

• This option aligns well with the passage. The passage suggests that legal imperatives (Politics) are influenced by economic demands, which in turn depend on the economic power distribution (Economics) in society.
• This reflects a clear interrelationship between Politics and Economics, as each affects the other.
• This option is the best match for the passage.

Option (c): “The predominance of Economics over Politics”

• This option suggests that Economics has a dominant or overriding influence over Politics. While the passage mentions that legal imperatives are influenced by economic power distribution, it does not suggest that Economics is predominant over Politics. Instead, it implies that Politics and Economics are interconnected and influence each other.
• This option is too strong and is not fully supported by the passage.

Option (d): “The predominance of Politics over Economics”

• This option suggests that Politics has a dominant or overriding influence over Economics. However, the passage does not imply that Politics is predominant over Economics. Instead, it describes how legal imperatives (Politics) are influenced by economic demands and power distribution (Economics).
• This option is also incorrect.

Conclusion

The correct answer is: (b) the interrelationship of Politics and Economics

Explanation:

Passage Analysis

The passage highlights the importance of safe and sustainable sanitation in slums, especially for women and girls in terms of health, safety, privacy, and dignity. However, it mentions two key issues:

1. Lack of Focus on Women: The passage notes that women are often excluded from schemes and policies on urban sanitation.
2. Existence of Manual Scavenging: The passage states that manual scavenging still exists, indicating that there is insufficient promotion of pour-flush toilets and other modern sanitation solutions, and that dry latrines continue to be used. The passage emphasizes the need for a large-scale campaign to ensure the right to sanitation and to abolish manual scavenging.

The passage suggests that while abolishing manual scavenging is essential, it is not the only solution. The broader goal of promoting safe and sustainable sanitation practices is also crucial.

Evaluation of Each Statement

Let’s examine each statement to see if it aligns with the passage.

Statement 1: “Urban sanitation problems can be fully solved by the abolition of manual scavenging only.”

• This statement is not supported by the passage. While the passage emphasizes the need to abolish manual scavenging, it does not suggest that this is the only solution to urban sanitation problems. The passage implies that additional measures, such as promoting pour-flush toilets and increasing awareness of sanitation practices, are also necessary.
• Therefore, Statement 1 is incorrect.

Statement 2: “There is a need to promote greater awareness on safe sanitation practices in urban areas.”

• This statement aligns with the passage. The passage calls for a sustained and rigorous campaign focused on sanitation and mentions the need to discontinue the use of dry latrines in favor of pour-flush toilets. This implies a need to increase awareness about safe sanitation practices.
• Therefore, Statement 2 is correct.

Conclusion

Based on the analysis, only Statement 2 is correct.

The correct answer is: (b) 2 only

Explanation:

Passage Analysis

The passage describes the recent restructuring of the banking sector, which has focused on automation and the development of products primarily serving the middle-class and upper middle-class. It then highlights the need for a new agenda that does not exclude the “common man.” This suggests that the current banking services are not adequately accessible or inclusive for the broader population, especially the lower-income groups.

The main implication of the passage is a need to make banking services more inclusive and accessible to everyone, not just the middle and upper classes.

Evaluation of Each Option

Let’s analyze each option to see which one aligns best with the message of the passage.

Option (a): “Need for more automation and more products of bank”

• The passage mentions that the banking sector has already undergone a high degree of automation and developed products, primarily for middle- and upper-class customers.
• The message of the passage, however, is not about the need for more automation or products, but rather about addressing the exclusion of the common man from banking services.
• This option does not align with the main message of the passage.

Option (b): “Need for a radical restructuring of our entire public finance system”

• Although the passage mentions a need for a “new agenda,” it does not imply a radical restructuring of the entire public finance system. Instead, it focuses on making banking services more inclusive.
• This option is too broad and does not capture the specific need for financial inclusion expressed in the passage.
• This option is not the best inference.

Option (c): “Need to integrate banking and non-banking institutions”

• The passage does mention both banking and non-banking financial services, but it does not suggest that integration of these institutions is necessary. Instead, it emphasizes the need for a new agenda that includes the common man.
• This option is not implied in the passage.

Option (d): “Need to promote financial inclusion”

• This option aligns well with the passage’s message. The passage points out that the banking sector has primarily served the middle and upper classes, and it calls for a new agenda that does not exclude the common man.
• Financial inclusion—making financial services accessible to all, including the common man—is exactly what the passage implies is needed.
• This option is the most logical and accurate inference based on the passage.

Conclusion

The correct answer is: (d) Need to promote financial inclusion

Explanation:

Passage Analysis

The passage discusses the interdependence of biodiversity and the hydrological cycle. Key points in the passage include:

1. Definition of Biodiversity: Biodiversity refers to the variety of plants, animals, microorganisms, and ecosystems.
2. Interdependence of Water and Biodiversity: The passage states that water and biodiversity are interconnected, with the hydrological cycle influencing how biodiversity functions, while vegetation and soil affect the movement of water.
3. Purification of Water by Ecosystems: The passage explains that water we drink has passed through various organisms and ecosystems, which cleanse it, making it fit for consumption.
4. Environmental Service of Water Supply: The passage concludes that the supply of clean water is a critical service provided by the environment through the functioning of biodiversity and ecosystems.

The overall emphasis of the passage is on how biodiversity sustains the natural water cycle and the purification of water.

Evaluation of Each Option

Let’s examine each option to see if it follows logically from the passage.

Option (a): “Biodiversity sustains the ability of nature to recycle water.”

• This option is directly supported by the passage. The passage describes how biodiversity (vegetation, soil, and organisms) contributes to the movement and purification of water, making it a vital part of the hydrological cycle.
• The passage implies that biodiversity plays an essential role in sustaining nature’s ability to recycle and purify water.
• This option is a logical and critical inference based on the passage.

Option (b): “We cannot get potable water without the existence of living organisms.”

• While the passage discusses the role of organisms in cleansing and making water fit for consumption, it does not explicitly state that potable water cannot exist without living organisms. This statement is stronger than the passage implies.
• This option is an overstatement and does not align exactly with the passage’s message.
• This option is not the best inference.

Option (c): “Plants, animals and microorganisms continuously interact among themselves.”

• Although biodiversity involves interactions between plants, animals, and microorganisms, this is not the main point of the passage. The passage primarily discusses the interaction between biodiversity and the hydrological cycle, not the interactions within biodiversity itself.
• This option is not a critical inference from the passage.

Option (d): “Living organisms could not have come into existence without the hydrological cycle.”

• The passage does not suggest that the hydrological cycle is necessary for the existence of living organisms. It only discusses the relationship between biodiversity and water in terms of water purification and supply.
• This option is incorrect and unsupported by the passage.

Conclusion

The most critical inference that can be made from the passage is: (a) biodiversity sustains the ability of nature to recycle water

Explanation:

Passage Analysis

The passage suggests that climate adaptation needs to be considered in the broader context of other development concerns to be effective. It provides an example of a comprehensive strategy to improve food security in the context of climate change, which would include measures related to agriculture, water management, and pest control. The passage emphasizes that some of these measures are related to climate adaptation, while others are related to economic development.

In essence, the passage argues that climate adaptation cannot be treated in isolation but should be integrated with other developmental strategies to be effective.

Evaluation of Each Option

Let’s analyze each option to see if it follows logically from the passage.

Option (a): “It is difficult to pursue climate adaptation in the developing countries.”

• This option is not directly supported by the passage. While the passage highlights the complexity of climate adaptation and its interconnections with other development issues, it does not specifically mention the difficulty of pursuing climate adaptation in developing countries.
• The passage is more focused on the need to consider development concerns alongside climate adaptation, rather than discussing specific challenges faced by developing countries.
• This option is not a logical inference.

Option (b): “Improving food security is a far more complex issue than climate adaptation.”

• The passage does not suggest that improving food security is more complex than climate adaptation. Rather, it indicates that climate adaptation and food security are interconnected issues that need to be addressed together.
• The passage does not imply that one issue is more complex than the other, only that they are linked.
• This option is not a logical inference.

Option (c): “Every developmental activity is directly or indirectly linked to climate adaptation.”

• While the passage suggests that climate adaptation should be considered alongside development issues, it does not imply that every developmental activity is directly or indirectly linked to climate adaptation.
• The passage gives an example of food security, but it does not generalize this relationship to all developmental activities.
• This option is an overstatement and is not a logical inference.

Option (d): “Climate adaptation should be examined in tandem with other economic development options.”

• This option is directly supported by the passage. The passage clearly states that climate adaptation may be ineffective if not considered within the context of other development concerns. It provides an example of a comprehensive strategy for food security that integrates both climate and economic development measures.
• This option captures the main idea of the passage: climate adaptation should be coordinated with other development strategies for it to be effective.
• This option is the most logical and rational inference.

Conclusion

The correct answer is: (d) Climate adaptation should be examined in tandem with other economic development options

Explanation:

Passage Analysis

The passage discusses the negative impact of crony capitalism on transparency, competition, free enterprise, opportunity, and economic growth. Crony capitalism is described as a system in which the wealthy and influential receive special favors (like land, natural resources, and licenses) through payoffs to corrupt politicians. This creates oligarchies that can inhibit the growth of developing economies, such as India.

The passage suggests that crony capitalism kills competition and transparency, which are essential for economic growth, and that it could trap developing countries in a “middle-income trap”.

Evaluation of Each Option

Let’s examine each option to see which one best addresses the issues presented in the passage.

Option (a): “Launching more welfare schemes and allocating more finances for the current schemes are urgently needed.”

• This option does not logically follow from the passage. While welfare schemes can improve living standards, they do not address the core issue highlighted in the passage, which is crony capitalism and the need for transparency and competition in the economy.
• This option is not a logical corollary.

Option (b): “Efforts should be made to push up economic growth by other means and provide licenses to the poor.”

• Although pushing for economic growth is a positive goal, this option does not address the core issue of crony capitalism. The passage does not suggest giving licenses to the poor as a solution to economic stagnation caused by crony capitalism. The focus of the passage is on transparency and competition, not on issuing more licenses.
• This option is not a logical corollary.

Option (c): “Greater transparency in the functioning of the government and promoting financial inclusion are needed at present.”

• This option addresses the core issue highlighted in the passage. Since the passage discusses the negative effects of crony capitalism, such as the lack of transparency and competition, promoting transparency in government operations would help counteract crony capitalism. Additionally, financial inclusion can provide fair opportunities for economic participation and growth, which would help reduce the oligarchic effects of crony capitalism.
• This option is a logical corollary to the passage.

Option (d): “We should concentrate more on developing the manufacturing sector than the service sector.”

• This option does not logically follow from the passage. The passage does not suggest any sector-specific solutions, nor does it imply that focusing on manufacturing over services would solve the issues related to crony capitalism. The problem is more about transparency and fair competition, not about choosing one sector over another.
• This option is not a logical corollary.

Conclusion

The most logical corollary to the passage is: (c) Greater transparency in the functioning of the government and promoting the financial inclusion are needed at present

Explanation:

To determine the exact duration of each period, we need to calculate the total class time, subtract the break times, and then divide the remaining time by the number of periods.

Step-by-Step Solution

1. Total Class Duration (11:00 am to 2:27 pm):

• From 11:00 am to 2:27 pm, the total time is:
  $$
  3 \, \text{hours and} \, 27 \, \text{minutes} = 3 \times 60 + 27 = 180 + 27 = 207 \, \text{minutes}
  $$

2. Total Rest Time:

• There are 4 periods and a 5-minute break after each period, except for the last period.
• Therefore, there are only 3 breaks in total.
• Total rest time is:
  $$
  3 \times 5 = 15 \, \text{minutes}
  $$

3. Net Time for All Periods:

• Subtract the total rest time from the total class duration to get the net instructional time:
  $$
  207 – 15 = 192 \, \text{minutes}
  $$

4. Duration of Each Period:

• There are 4 periods of equal duration, so the duration of each period is:
  $$
  \frac{192}{4} = 48 \, \text{minutes}
  $$

Conclusion

The exact duration of each period is: $ \text{(a) 48 minutes} $

Explanation:

Passage Analysis

The passage discusses the impact of the Green Revolution on agriculture, with an emphasis on biodiversity and food security. Key points include:

1. Heavy Reliance on High-Yield Crops: The Green Revolution has led farmers to rely heavily on high-yield, broadly adapted crops. These crops have been chosen to maximize yield and meet immediate food needs.
2. Monocropping: Farmers practice monocropping with genetically uniform seeds to boost yield. However, this practice reduces biodiversity in the food supply.
3. Risks of High-Yield Crops: High-yield varieties are genetically weaker and require expensive chemical fertilizers and toxic pesticides. This creates environmental and economic challenges.
4. Long-Term Risks: The focus on high-yield crops and monocropping may lead to a reduction in biodiversity, which can result in food shortages and threaten food security in the future.

The passage suggests that, while the Green Revolution has helped to increase food production, it has also inadvertently put food security at risk in the long term by reducing biodiversity.

Evaluation of Each Option

Let’s analyze each option to see if it logically follows from the passage.

Option (a): “In our agricultural practices, we have become heavily dependent on expensive chemical fertilizers and toxic pesticides only due to the Green Revolution.”

• This statement is partially correct; the passage does suggest that high-yield varieties promoted by the Green Revolution require fertilizers and pesticides. However, it does not claim that the Green Revolution is the only reason for dependency on chemical fertilizers and pesticides.
• This option overstates the role of the Green Revolution by implying it is the sole cause.
• This option is not the most logical and critical inference.

Option (b): “Monocropping vast fields with high-yield varieties is possible due to the Green Revolution.”

• This statement is factually correct based on the passage, as the Green Revolution promoted high-yield crops and monocropping to increase food production.
• However, this option is merely a factual observation rather than a critical inference. It does not capture the main concern of the passage, which is the threat to biodiversity and long-term food security.
• This option is not the most critical inference.

Option (c): “Monocropping with high-yield varieties is the only way to ensure food security to millions.”

• The passage does not claim that monocropping with high-yield varieties is the only way to ensure food security. Instead, it emphasizes the potential risks of this approach, especially in terms of reduced biodiversity and future food security.
• This option is an incorrect inference, as it contradicts the concerns expressed in the passage.
• This option is incorrect.

Option (d): “Green Revolution can pose a threat to biodiversity in food supply and food security in the long run.”

• This statement captures the essence of the passage. The passage highlights that the Green Revolution, while successful in increasing yields, has led to a loss of biodiversity and a reliance on genetically weaker high-yield crops that require chemical inputs. These factors may threaten food security in the long term.
• This option is the most logical and critical inference.

Conclusion

The correct answer is: (d) Green revolution can pose a threat to biodiversity in food supply and food security in the long run

Explanation:

Passage Analysis

The passage discusses biomass as a fuel source for power, heat, and transport, emphasizing its potential for greenhouse gas (GHG) mitigation. Key points in the passage include:

1. Greenhouse Gas Mitigation Potential: The passage explicitly states that biomass has the highest mitigation potential of all renewable sources. This implies that using biomass can help reduce GHG emissions, as some climate-energy models project the potential for biomass use to contribute to lower emissions.
2. Sustainable Biomass Supply and Food and Forest Resources: The passage mentions that the maximum sustainable technical potential of biomass is limited (80–170 exajoules per year by 2050) and that it is possible to use biomass without disrupting food and forest resources if managed properly. However, it also notes that energy crops can compete with food production and may impact food prices if not managed well. Therefore, the passage suggests that it is possible to use biomass sustainably without necessarily disrupting food and forest resources.

Evaluation of Each Assumption

Let’s examine each assumption based on the passage.

Assumption 1: “Some climate-energy models suggest that the use of biomass as a fuel for power generation helps in mitigating greenhouse gas emissions”

• The passage states that biomass has the highest mitigation potential among renewable sources, implying that its use can help in reducing greenhouse gas emissions.
• The passage also mentions that some climate models rely on biomass for achieving negative emissions, further supporting this assumption.
• Therefore, Assumption 1 is valid.

Assumption 2: “It is not possible to use biomass as a fuel for power generation without disrupting food and forest resources”

• The passage suggests that biomass use can be sustainable and does not necessarily disrupt food and forest resources, especially if it is managed properly.
• It does acknowledge potential competition with food production, but it does not claim that disruption of food and forest resources is inevitable.
• Therefore, Assumption 2 is not valid.

Conclusion

Based on the analysis, only Assumption 1 is valid.

The correct answer is: (a) 1 only

Explanation:

Passage Analysis

The passage mentions the following points relevant to food security:

1. Agricultural and Forest Residues: These residues can be used as biomass feedstock for power generation. The passage does not indicate that using residues directly affects food production or food security, as residues are by-products rather than primary crops.
2. Carbon Capture and Storage (CCS): The passage mentions that some climate models rely on biomass-based carbon capture and storage (CCS) to achieve negative emissions. However, it does not suggest that CCS would directly impact food production or food security.
3. Energy Crops: The passage states that promoting energy crops for biomass, if not managed properly, competes with food production and may have undesirable impacts on food prices. This implies that energy crops can indeed lead to food security issues.

Evaluation of Each Statement

Let’s examine each statement in the question to see if it aligns with these points.

Statement 1: “Using agricultural and forest residues as feedstock for power generation”

• The passage mentions that agricultural and forest residues can be used as feedstock for biomass without indicating any adverse impact on food security. Since residues are typically by-products and not primary food sources, their use does not directly compete with food production.
• Therefore, Statement 1 is not likely to lead to a food security problem.

Statement 2: “Using biomass for carbon capture and storage”

• The passage discusses biomass-based CCS but does not suggest that it has any impact on food production or food security. CCS is primarily aimed at reducing carbon emissions, and there is no indication in the passage that this would affect food availability.
• Therefore, Statement 2 is not likely to lead to a food security problem.

Statement 3: “Promoting the cultivation of energy crops”

• The passage clearly states that promoting energy crops can compete with food production and may impact food prices. This implies a potential food security issue because the cultivation of energy crops can reduce land availability for food crops.
• Therefore, Statement 3 is correct and can lead to a food security problem.

Conclusion

Based on the analysis, only Statement 3 is correct as it aligns with the passage’s indication that energy crops can compete with food production, potentially affecting food security.

The correct answer is: (b) 3 only

Explanation:

Passage Analysis

The passage highlights several constraints and challenges in using biomass as a fuel for power generation. Key points in the passage include:

1. Sustainable Supply of Biomass: The passage states that the biggest challenge in using biomass residues is a reliable, long-term supply delivered to the power plant at reasonable costs. It mentions logistical constraints and the costs of fuel collection as specific issues.
2. Competition with Food Production: The passage points out that energy crops, if not managed properly, can compete with food production and may have undesirable impacts on food prices. This competition is a significant constraint.
3. Carbon Emissions of Biofuels on a Life-Cycle Basis: The passage mentions that some liquid biofuels, like corn-based ethanol, can aggravate rather than reduce carbon emissions on a life-cycle basis. This means that certain types of biofuels may not be low carbon when considering the full life cycle.

Evaluation of Each Statement

Let’s examine each statement to see if it is supported by the passage.

Statement 1: “Lack of sustainable supply of biomass”

• The passage clearly mentions that one of the biggest challenges in using biomass is a reliable, long-term supply of biomass at reasonable costs. This indicates that there is a lack of sustainable supply.
• Statement 1 is correct.

Statement 2: “Biomass production competes with food production”

• The passage states that energy crops, if not managed properly, can compete with food production and may have undesirable impacts on food prices. This is a direct constraint mentioned in the passage.
• Statement 2 is correct.

Statement 3: “Bio-energy may not always be low carbon on a life-cycle basis”

• The passage mentions that certain biofuels, such as corn-based ethanol, may actually aggravate carbon emissions on a life-cycle basis rather than reducing them. This implies that bio-energy is not always low carbon when considering the full life cycle.
• Statement 3 is correct.

Conclusion

All three statements are supported by the passage as present constraints in using biomass as fuel for power generation.

The correct answer is: (d) 1, 2 and 3

Explanation:

Information Given

1. There are five persons in the group: P, Q, R, S, and T.
2. The group has one doctor, one lawyer, and one artist.
3. P and S are unmarried students.
4. T is a man married to one of the group members.
5. Q is the brother of P and is neither a doctor nor an artist.
6. R is not a doctor.

Step-by-Step Deduction

Let’s go through each piece of information to deduce who is married to R.

Analyzing the Information

1. P and S are unmarried students:
   • This means P and S are not married to anyone in the group.
   • Therefore, neither P nor S can be R‘s spouse.
2. T is a man married to one of the group members:
   • Since T is married and P and S are unmarried, T must be married to either R or Q.
3. Q is the brother of P and is neither a doctor nor an artist:
   • Since Q is the brother of P (and therefore male), T cannot be married to Q.
   • Therefore, T must be married to R.

Summary of Deductions

Based on the information and the elimination process, we conclude that:

• T is the spouse of R.

Conclusion

The correct answer is: (b) T

Explanation:

Information Given

1. There are five persons in the group: P, Q, R, S, and T.
2. The group has one doctor, one lawyer, and one artist.
3. P and S are unmarried students.
4. T is a man married to one of the group members.
5. Q is the brother of P and is neither a doctor nor an artist.
6. R is not a doctor.

Step-by-Step Deduction

Let’s use each piece of information to determine which individuals are definitely men.

Analyzing the Information

1. T is a man married to one of the group members:
   • This information clearly states that T is a man.
2. Q is the brother of P:
   • Since Q is described as the “brother” of P, this implies that Q is also definitely a man.
3. P and S are unmarried students:
   • The passage does not specify the gender of P or S. All we know is that they are unmarried students, but their genders are not explicitly mentioned.
4. No other information indicates the gender of R.

Conclusion

Based on the information provided, Q is definitely a man (since he is described as the brother of P). T is also explicitly mentioned as a man.

The correct answer is: (c) Q

Explanation:

Information Given

1. There are five persons in the group: P, Q, R, S, and T.
2. The group has one doctor, one lawyer, and one artist.
3. P and S are unmarried students.
   • This means that P and S cannot be professionals, so neither of them can be the doctor, lawyer, or artist.
4. T is a man married to one of the group members.
5. Q is the brother of P and is neither a doctor nor an artist.
6. R is not a doctor.

Step-by-Step Deduction

Let’s use this information to deduce each person’s role and specifically determine who the lawyer is.

Analyzing the Information

1. P and S are unmarried students:
   • Since P and S are students, they are not professionals.
   • Therefore, P and S cannot be the doctor, lawyer, or artist.
2. Q is neither a doctor nor an artist:
   • Since Q is not a doctor or an artist, the only possible profession left for Q is lawyer.
3. R is not a doctor:
   • Since R is not a doctor and Q is the lawyer, the only person left who could be the doctor is T.
   • This also implies that R must be the artist.

Summary of Roles

Based on the deductions:

• Q is the lawyer.
• T is the doctor.
• R is the artist.
• P and S are students.

Conclusion

The correct answer is: (b) Q

Explanation:

Passage Analysis

The passage discusses the relationship between religious traditions, duties, rights, and justice. Here are the key points made in the passage:

1. Derivation of Duties and Rights: Religious traditions emphasize our duty to God (or a universal ethical principle). Duties to one another are derived from these higher duties, and the concept of rights is linked to our relationship with this divinity or principle.

2. Connection to Justice: The passage argues that the balance between rights and duties is essential to understanding justice. Rights and duties should not remain abstract concepts; they need to be grounded in a community to be meaningful.

3. Importance of Community and Solidarity: For justice to be practiced, rights and duties must be connected to a community with a sense of solidarity and common union.

The primary focus of the passage is on the importance of balancing rights and duties within a community to effectively deliver justice.

Evaluation of Each Option

Now, let’s examine each option to see which one best represents the main idea (crux) of the passage.

(a) “Our duties to one another derive from our religious traditions”

• This statement is accurate because the passage does mention that our duties to one another are derived from religious traditions or universal ethical principles. However, this is only one part of the passage and does not encompass the main focus, which is about the connection between rights, duties, and justice.
• This option is not the main crux of the passage.

(b) “Having a relationship to the divine principle is a great virtue”

• While the passage does discuss the relationship to a divine principle, it does not emphasize it as the main point or virtue. Instead, it focuses on how this relationship translates into a balance between rights and duties within a community for justice.
• This option is not the main crux of the passage.

(c) “Balance between rights and duties is crucial to the delivery of justice in a society”

• This option captures the main point of the passage. The passage emphasizes the importance of balancing rights and duties and grounding them in a community to effectively deliver justice.
• This option is the best representation of the crux of the passage.

(d) “Religious concept of rights is primarily derived from our relationship to god”

• While this is a correct statement from the passage, it does not capture the main idea. The passage goes beyond just discussing the religious concept of rights; it focuses on how rights and duties should be balanced and practiced within a community to achieve justice.
• This option is not the main crux of the passage.

Conclusion

The correct answer is: (c) Balance between and duties is crucial to the delivery of justice in a society

Explanation:

Passage Analysis

The passage explains that internal accountability refers to the accountability of civil services to the political executive and within the governance structure itself. Internal accountability is achieved through:

• Internal performance monitoring
• Supervision by official bodies such as the Central Vigilance Commission and Comptroller and Auditor General
• Judicial review of executive decisions

The passage also mentions job security and safeguards under Articles 311 and 312 as factors that support the civil service’s independence, allowing it to function effectively within the governance system.

On the other hand, external accountability refers to the accountability of civil services to society. The passage suggests that decentralization and enhanced public participation in decision-making are ways to improve external accountability by bringing governance closer to the people.

Evaluation of Each Option

Now, let’s examine each option to see if it pertains to internal accountability:

(a) Better job security and safeguards

• This is a means of enhancing internal accountability. The passage explains that job security and safeguards (Articles 311 and 312) protect civil servants, allowing them to function independently while still being accountable within the governance structure.
• Therefore, this option is related to internal accountability.

(b) Supervision by Central Vigilance Commission

• The passage states that internal accountability is achieved through official supervision by bodies like the Central Vigilance Commission.
• Thus, this option is a means of internal accountability.

(c) Judicial review of executive decisions

• Judicial review is another method of maintaining internal accountability within the governance framework, as mentioned in the passage.
• So, this option is also related to internal accountability.

(d) Seeking accountability through enhanced participation by people in decision making process

• The passage mentions decentralization and enhanced public participation as ways to improve external accountability, not internal accountability.
• Therefore, this option is not a means of internal accountability.

Conclusion

The correct answer is: (d) Seeking accountability through enhanced participation by people in decision making process

Passage Analysis

The passage primarily discusses the issue of accountability within civil services and its impact on governance. The main points mentioned in the passage are:

1. Accountability Deficiencies: A lack of accountability in civil services is identified as a major factor contributing to poor governance and public administration.

2. Internal vs. External Accountability: The passage highlights the need to balance internal accountability (to political leaders) with external accountability (to society). It mentions that the current system has not achieved this balance, leading to adverse consequences.

3. Constitutional Safeguards: Articles 311 and 312 provide job security and safeguards to civil servants, allowing them to function in the public interest without being entirely subservient to political leaders.

4. Reforms Needed: The passage suggests specific reforms to improve accountability, such as reviewing Articles 311 and 312, defining roles of civil services and political executives, and creating civil service boards.

5. Proposed Measures: The passage also emphasizes decentralization and devolution of authority to bring decision-making closer to the people as a way to improve accountability.

Evaluation of Answer Choices

Now, let’s examine each option to see which one best captures the essential message of the passage.

(a) “Civil services are not accountable to the society they are serving”

• This statement is partially correct but does not capture the full scope of the passage. The passage does not claim that civil services are entirely unaccountable to society; rather, it discusses the imbalance in accountability, with an emphasis on internal accountability over external accountability.
• Therefore, this option is not the best answer.

(b) “Educated and enlightened persons are not taking up political leadership”

• The passage does not mention anything about the qualifications or enlightenment of political leaders. It focuses on the accountability framework in civil services rather than the qualities of political leaders.
• This option is incorrect.

(c) “The framers of the Constitution did not envisage the problems being encountered by the civil services”

• This statement is also incorrect. The passage specifically mentions that the framers of the Constitution did envisage that safeguards would enable civil services to function in the larger public interest and avoid total subservience to the political executive. Thus, the framers were aware of the potential challenges.
• This option is incorrect.

(d) “There is a need and scope for reforms to improve the accountability of civil services”

• This statement accurately reflects the essential message of the passage. The passage highlights the need for reforms to improve accountability in civil services and suggests specific measures, such as reviewing Articles 311 and 312, creating civil service boards, and decentralizing authority.
• Therefore, this option is correct.

Conclusion

The correct answer is: (d) There is a need and scope for reforms to improve the accountability of civil services

Explanation:

Information Given

1. There are five persons in the group: P, Q, R, S, and T.
2. The group has one doctor, one lawyer, and one artist.
3. P and S are unmarried students.
4. T is a man married to one of the group members.
5. Q is the brother of P and is neither a doctor nor an artist.
6. R is not a doctor.

Step-by-Step Deduction

Let’s go through each piece of information and deduce the professions of each person.

Analyzing the Information

1. P and S are unmarried students:
   • This means P and S are not professionals, so neither of them can be the doctor, lawyer, or artist.
2. Q is neither a doctor nor an artist:
   • Since Q cannot be a doctor or an artist, Q must be the lawyer (the only remaining profession for him).
3. R is not a doctor:
   • Since R is not a doctor and Q is the lawyer, the only two candidates left for the doctor are T and R.
   • Therefore, T must be the doctor (since R cannot be the doctor).
4. With T as the doctor and Q as the lawyer, the only remaining profession (artist) must go to R.

Summary of Professions

Based on the deductions:

• Q is the lawyer.
• T is the doctor.
• R is the artist.

Conclusion

The correct answer is: (c) R

Explanation:

Information Given

1. There are five persons in the group: P, Q, R, S, and T.
2. The group has one doctor, one lawyer, and one artist.
3. P and S are unmarried students.
4. T is a man married to one of the group members.
5. Q is the brother of P and is neither a doctor nor an artist.
6. R is not a doctor.

Step-by-Step Deduction

Let’s analyze each piece of information and use a process of elimination to determine the profession of each person.

Analyzing Information

1. P and S are unmarried students:
   • This means P and S are not professionals (they are students), so neither of them can be the doctor, lawyer, or artist.
2. Q is neither a doctor nor an artist:
   • Since Q cannot be a doctor or an artist, the only possible profession left for Q is lawyer.
3. R is not a doctor:
   • Since R is not a doctor, the only two possible candidates left for the doctor’s position are T and Q.
   • However, from point 2 above, we already know that Q is the lawyer.
   • Therefore, T must be the doctor.
4. T is a man married to one of the group members:
   • This information is consistent with T being a professional (in this case, a doctor), and it does not contradict any of our deductions so far.

Conclusion

Based on the above deductions, the only person who can be the doctor is: (a) T

Explanation:

Passage Analysis

The passage discusses the challenges of accountability in civil services, focusing on internal accountability (to the political executive) versus external accountability (to society). It mentions that:

• There is a need to balance internal and external accountability in civil services.
• Over time, the emphasis has shifted towards internal accountability of civil services to the political leaders.
• Political leaders are expected to be accountable to society through elections, but this system has not worked effectively, resulting in adverse consequences for governance.
• The passage suggests reforms, such as reviewing Articles 311 and 312 and defining roles to enhance accountability, but it does not state that the political executive is inherently an obstacle or is entirely unaccountable.

Evaluation of Each Assumption

Assumption 1: “Political executive is an obstacle to the accountability of the civil services to the society”

• This assumption suggests that the political executive actively hinders civil services from being accountable to society.
• While the passage discusses an imbalance in accountability (favoring internal accountability to political leaders over external accountability to society), it does not state that the political executive is an obstacle. Instead, the passage implies a structural imbalance rather than an intentional obstruction by the political executive.
• Therefore, Assumption 1 is not valid.

Assumption 2: “In the present framework of Indian polity, the political executive is no longer accountable to the society”

• This assumption implies that the political executive has ceased to be accountable to society in any form.
• The passage states that the political executive is expected to be accountable to society through the election process, but this system has not worked well. However, it does not claim that the political executive is completely unaccountable to society; rather, it points out flaws in how this accountability is achieved.
• Therefore, Assumption 2 is also not valid.

Conclusion

Based on the passage, neither of the assumptions can be considered valid.

Thus, the correct answer is: (d) Neither 1 nor 2

Explanation:

Passage Analysis

The passage discusses issues of accountability within civil services and mentions several key factors that contribute to adverse consequences in governance and public administration:

1. Balance between internal and external accountability: The passage emphasizes the importance of balancing internal accountability (toward political leaders) with external accountability (toward society). It states that the current system has not successfully achieved this balance, which has led to adverse consequences for governance.

2. Constitutional provisions: Articles 311 and 312 provide job security and safeguards to the civil services. However, the passage suggests that the roles of the professional civil services and the political executive are not clearly defined, leading to adverse impacts on governance.

3. Proposals for improvement: The passage suggests a need to review Articles 311 and 312 to improve external accountability and to depoliticize the management of civil services.

Evaluating Each Statement

Now let’s evaluate each of the statements based on the information in the passage.

Statement 1: “Inability of civil services to strike a balance between internal and external accountabilities”

This statement is correct. The passage explicitly mentions that the failure to balance internal accountability (to political leaders) and external accountability (to society) has led to adverse consequences for governance.

Statement 2: “Lack of sufficient professional training to the officers of All India Services”

This statement is not supported by the passage. There is no mention of a lack of professional training being a factor in the adverse consequences for governance.

Statement 3: “Lack of proper service benefits in civil services”

This statement is also not supported by the passage. The passage does not mention anything about service benefits as a factor affecting governance.

Statement 4: “Lack of Constitutional provisions to define the respective roles of professional civil services vis-a-vis political executive in this context”

This statement is correct. The passage points out that the roles of civil services and the political executive are not clearly defined in the Constitution, leading to issues in governance.

Conclusion

Based on the passage, the correct statements are 1 and 4.

The correct answer is: (c) 1 and 4 only

Explanation:

Observing the Code Pattern

1. SYSTEM is written as SYSMET:
   • The code takes the first three letters (“SYS”) and the last three letters (“TEM”) and swaps them to get “SYSMET”.
2. NEARER is written as AENRER:
   • Similarly, the code takes the first three letters (“NEA”) and the last three letters (“RER”) and swaps them to get “AENRER”.

Applying the Pattern to FRACTION

Following the same pattern, we need to:

1. Split FRACTION into two parts:
   • The first three letters: FRA
   • The remaining letters: CTION
2. Swap these two parts:
   • Putting “CTION” at the beginning and “FRA” at the end gives CTIONFRA.

Conclusion

Thus, FRACTION can be written as: (d) CARFNOIT

Explanation:

Let’s analyze each statement and condition provided:

1. C is seated next to A.
   This means that C and A are adjacent.
2. A is seated two seats from D.
   This means that there is exactly one person seated between A and D.
3. B is not seated next to A.
   This means that B cannot be adjacent to A.

Now, let’s examine each option based on these conditions:

Statement 1: D is seated next to B

• Since A is seated two seats away from D, and B cannot be seated next to A, B must be positioned such that it ends up next to D. Therefore, statement 1 must be true.

Statement 2: E is seated next to A

• Since A is adjacent to C and B cannot be next to A, the only remaining person who can sit next to A is E. Thus, statement 2 must be true.

Statement 3: D and C are separated by two seats

• Based on the arrangement where A is seated two seats away from D and C is next to A, this condition does not necessarily follow in all possible arrangements. Statement 3 is not necessarily true.

Therefore, the correct answer is: (b) 1 and 2 only

Explanation:

To analyze the statements and draw conclusions, let’s go through each given statement carefully.

Given Statements

1. Statement 1: Either A and B are of the same age or A is older than B.

This implies that:

• If A and B are not the same age, then A is older than B.

2. Statement 2: Either C and D are of the same age or D is older than C.

This implies that:

• If C and D are not the same age, then D is older than C.

3. Statement 3: B is older than C.

Analysis of Possible Conclusions

Let’s evaluate each option based on the given statements:

Option (a): A is older than B

This cannot be concluded directly. From Statement 1, we know that either A and B are of the same age, or A is older than B. Since there is no additional information to confirm which case is true, we cannot definitively conclude that A is older than B. Thus, option (a) is not necessarily true.

Option (b): B and D are of the same age

There is no information in the given statements that directly compares the ages of B and D. Therefore, we cannot conclude that B and D are of the same age. So, option (b) is not necessarily true.

Option (c): D is older than C

From Statement 2, we know that either C and D are of the same age or D is older than C. However, Statement 3 says that B is older than C, but there is no direct comparison between B and D. Therefore, we cannot confirm that D is older than C. So, option (c) is not necessarily true.

Option (d): A is older than C

From Statement 1, we know that either A and B are of the same age or A is older than B. From Statement 3, we know that B is older than C. Therefore, combining these two pieces of information, we can conclude that:

• If A and B are of the same age, then A would still be older than C because B is older than C.
• If A is older than B, then A is also older than C (since B is older than C).

In both cases, A is older than C.

Thus, option (d) is definitely true.

Conclusion

The correct answer is: $ \text{(d) A is older than C} $

Explanation

To determine the sweetness of each solution, we need to compare the concentration of sugar in each vessel. The concentration can be calculated by dividing the mass of sugar by the volume of water in each vessel.

Let the concentration of sugar in each vessel be denoted as follows:

1. For vessel A:
$$
\text{Concentration in A} = \frac{\text{mass of sugar}}{\text{volume of water}} = \frac{30 \, \text{g}}{180 \, \text{ml}} = \frac{1}{6} \, \text{g/ml}
$$

2. For vessel B:
$$
\text{Concentration in B} = \frac{\text{mass of sugar}}{\text{volume of water}} = \frac{40 \, \text{g}}{280 \, \text{ml}} = \frac{1}{7} \, \text{g/ml}
$$

3. For vessel C:
$$
\text{Concentration in C} = \frac{\text{mass of sugar}}{\text{volume of water}} = \frac{20 \, \text{g}}{100 \, \text{ml}} = \frac{1}{5} \, \text{g/ml}
$$

Now, let’s compare these concentrations:

– $\frac{1}{5}$ (vessel C) is greater than $\frac{1}{6}$ (vessel A), which means the solution in vessel C is sweeter than that in vessel A.
– $\frac{1}{5}$ (vessel C) is also greater than $\frac{1}{7}$ (vessel B), which means the solution in vessel C is sweeter than that in vessel B.

Therefore, the correct answer is:

$$
\text{(d) less sweet than that in C}
$$

Explanation:

Given information:

• There are 50 faculty members in total, with 30 males and 20 females.
• No male faculty member knows music.
• Some female faculty members know music.

Since no one at the tea party knew music, the selected faculty members must all be people who do not know music. Given that:

• All male faculty members do not know music, they are eligible for selection.
• Only some female faculty members do not know music, meaning that only a subset of females could be selected if any were chosen.

However, since the entire group of six selected faculty members at the tea party did not know music, the simplest and most direct explanation is that all six faculty members at the party were male, as this guarantees that none of them would know music.

The correct answer is: (a) the party comprised male faculty members only

Explanation:

The statement “We shall go either for a picnic or for trekking” is an exclusive “or” statement, which implies that at least one of the two activities (picnic or trekking) will happen.

To falsify this claim, we would need a situation where neither activity occurs. Let’s analyze each option:

1. (a) We go for a picnic but not for trekking.
   This does not falsify the claim, as going for a picnic satisfies the “either for a picnic or for trekking” condition.
2. (b) Activities such as picnic and trekking are encouraged by the health authorities.
   This statement is irrelevant to the truth of the original claim. It provides context but does not affect the truth of the claim.
3. (c) We go for trekking and not for picnic.
   This also does not falsify the claim, as going for trekking satisfies the “either for a picnic or for trekking” condition.
4. (d) We do not go either for picnic or for trekking.
   This statement directly falsifies the claim because it implies that neither activity takes place, contradicting the original statement that one of the two activities will happen.

Thus, the correct answer is: (d) We do not go either for picnic or for trekking

Explanation:

Let’s analyze each statement:

1. The rate of population growth is increasing in the country.
   This suggests that the population is growing at an accelerating rate.
2. The death rate is declining faster in the country compared to the birth rate.
   This means that even though the birth rate may also be declining, the death rate is decreasing at a faster pace. As a result, more people are added to the population than removed, leading to a net increase in population growth.
3. The birth rate is declining faster in the country compared to the death rate.
   This contradicts statement 2, so this statement cannot be true if statement 2 is true.
4. Rural-urban migration is taking place regularly in the country.
   This statement concerns the movement of people rather than the rate of natural population growth.

The correct answer is: (d) The rate of population growth is increasing due to faster decline in death rate than in birth rate

Explanation:

To determine the cause of sickness, let’s analyze which fruits were consumed by B and C, as they both fell sick.

Given:

• A ate grapes and pineapple.
• B ate grapes and oranges.
• C ate oranges, pineapple, and apple.
• D ate grapes, apple, and pineapple.

Since only B and C fell sick, the cause of sickness must be a fruit that only they consumed and not A or D.

Let’s look at the fruits each person consumed:

• Grapes: Consumed by A, B, and D (not exclusive to B and C).
• Pineapple: Consumed by A, C, and D (not exclusive to B and C).
• Apple: Consumed by C and D (not exclusive to B and C).
• Oranges: Consumed only by B and C.

Thus, the only fruit common exclusively to B and C is oranges. Therefore, oranges are likely the cause of sickness.

Therefore, the correct answer is: (d) Oranges

Explanation:

Passage Analysis:

The passage discusses the challenges of achieving a balance between food demand and supply at the global and national levels. It highlights the following points:

1. In closed economies (especially populous ones), inadequate domestic food production can lead to hunger and starvation if agricultural growth is insufficient.
2. In open economies, food imports can mitigate hunger, but only if these countries have the purchasing power to buy food from abroad.
3. At the global level, food availability does not automatically eliminate hunger because countries with surplus food may not transfer it to deficit countries due to a lack of purchasing power in the latter.
4. Hunger, starvation, and malnutrition are concentrated in underdeveloped economies due to “empty-pocket hungry mouths.”
5. Solutions must involve global thinking and global solutions, including addressing food prices and affordability for the poor.

Evaluating the Statements:

1. Balancing demand and supply of food:

• The passage emphasizes that balancing demand and supply of food is critical for reducing hunger, especially for a closed economy or at the global level.
• This statement is correct.

2. Increasing imports of food:

• The passage mentions that importing food can help open economies mitigate hunger, but only if they have adequate purchasing power.
• Increasing imports alone is insufficient without addressing affordability. This statement is partially correct as a supporting factor.

3. Increasing purchasing power of the poor:

• The passage strongly emphasizes that hunger persists in underdeveloped economies due to a lack of purchasing power. Increasing purchasing power is a key solution to reduce hunger and starvation.
• This statement is correct.

4. Changing the food consumption patterns and practices:

• The passage mentions that the “quantum and composition of demand has been undergoing big changes.” While it suggests that changing consumption patterns may be relevant to food distribution, the emphasis is not placed on this as a primary solution to hunger.
• This statement is partially correct but not as critical as balancing demand and supply or increasing purchasing power.

Correct Option:

From the analysis above:

• Statements 1 and 3 are the most directly relevant for reducing hunger and starvation.
• While 2 and 4 are somewhat related, they are not emphasized as primary solutions.

The correct answer is: (c) 1 and 3 only

Explanation:

Passage Analysis:

The passage explains that:

1. Human beings are naturally inclined toward social life because their individual powers are insufficient to meet all their needs.
2. Nature has designed humans with needs that exceed what one person can fulfill alone, which drives them to form societies to collectively meet these needs.

Answer Choices Analysis:

Let’s examine each answer choice in light of the passage:

(a) Nature has created a great diversity in human society.

• The passage does not discuss diversity in human society. It focuses on the idea that humans have natural wants that lead them to form societies. So, this choice is not correct.

(b) Any given human society is always short of its wants.

• This statement suggests a perpetual shortage of resources or needs in society. The passage does not mention shortages; it only discusses why humans are driven into society to fulfill needs. Thus, this choice is not correct.

(c) Social life is a specific characteristic of man.

• The passage implies that humans are naturally suited for social life because their individual powers are not enough to satisfy all needs. This is close to the main idea conveyed, but it doesn’t fully capture the reason why social life is essential according to the passage.

(d) Diverse natural wants forced man towards social system.

• This option captures the core of the passage. It conveys that humans have various needs that cannot be met individually, and this drives them into forming societies. This choice directly aligns with the reasoning given in the passage.

Conclusion:

The most logical and rational inference that can be made from the passage is: (d) Diverse natural wants forced man towards social system

Explanation:

Problem Analysis

1. Number of Questions:

•  There are 5 questions.

2. Answer Choices for Each Question:

• Each question has 2 choices: True (T) or False (F).

3. Objective:

• We need to determine the maximum number of unique sequences of answers possible, so that no two candidates have given the same sequence of answers.

Solution

Since each question has 2 choices (True or False), we can treat each answer sequence as a binary sequence of length 5 (where each answer is either $T$ or $F$).

1. Total Number of Unique Sequences:

• For each of the 5 questions, there are 2 possible answers.
• Therefore, the total number of unique answer sequences is:
  $$
  2^5 = 32
  $$

2. Interpretation:

• This means that there are 32 unique sequences of answers possible.
• Thus, the maximum number of candidates that can each have a unique answer sequence is 32.

The correct answer is: (d) 32

Explanation:

Problem Analysis:

We are tasked to determine the percentage of male employees in the company.

Given:

1. The overall average salary of all employees = Rs. 5000.

2. The average salary of male employees = Rs. 5200.

3. The average salary of female employees = Rs. 4200.

Let the number of male employees = $x$ and the number of female employees = $y$.

Step-by-Step Solution:

Step 1: Write the equation for the total salary:

The total salary of all employees is the sum of salaries of male and female employees. Using the formula for the average:

$$
\text{Total salary of all employees =} \text{Total salary of males +} \text{Total salary of females}.
$$

In terms of $x$ and $y$:

$$
5000(x + y) = 5200x + 4200y.
$$

Step 2: Simplify the equation:

Expand both sides:

$$
5000x + 5000y = 5200x + 4200y.
$$

Bring all terms involving $x$ and $y$ to one side:

$$
5000y – 4200y = 5200x – 5000x.
$$

Simplify:

$$
800y = 200x.
$$

Step 3: Solve for the ratio of $x$ to $y$:

Divide both sides of the equation by 200:

$$
4y = x.
$$

Thus:

$$
\frac{x}{y} = 4.
$$

This means the ratio of male to female employees is:

$$
x : y = 4 : 1.
$$

Step 4: Find the percentage of male employees:

The total number of employees is:

$$
x + y = 4 + 1 = 5.
$$

The percentage of male employees is:

$$
\text{Percentage of males =} \frac{x}{x + y} \times 100 = \frac{4}{5} \times 100 = 80\%.
$$

The correct answer is: (b) 80%

Explanation:

Let’s solve the problem based on the given clues step-by-step to determine which box contains the golf ball.

Given Information and Clues:

1. Six boxes A,B,C,D,E,F, each painted with a different color: violet, indigo, blue, green, yellow, orange.
2. Each box contains a ball of a different game: cricket, hockey, tennis, golf, football, volleyball.
3. Arrangement of Boxes: They are arranged from left to right, but not necessarily in the same order as given.

Clues:

Clue 1 – “The golf ball is in the violet box and is not in the box $D$.”

• The golf ball is in a violet box.
• Box $D$ does not contain the golf ball.

Clue 2 –“The box $A$, which contains the tennis ball, is orange in color and is at the extreme right.”

• Box $A$ is orange, contains the tennis ball, and is located at the 6th position (extreme right).

Clue 3 – “The hockey ball is neither in box $D$ nor in box E.”

• Hockey ball is not in box $D$ or $E$.

Clue 4 –  “The box C having the cricket ball is painted green.”

• Box $C$ is green and contains the cricket ball.

Clue 5 – “The hockey ball is neither in the box painted blue nor in the box painted yellow.”

• Hockey ball is not in the blue or yellow boxes.

Clue 6 – “The box $C$ is fifth from the right and next to box $B$.”

• Since there are six boxes, box $C$ is in the 2nd position from the left.
• Box $B$ is adjacent to $C$, so $B$ must be in the 1st position from the left.

Clue 7 – “The box $B$ contains the volleyball.”

• Box $B$ contains the volleyball.

Clue 8 – “The box containing the hockey ball is between the boxes containing the golf ball and volleyball.”

• Golf ball → Hockey ball → Volleyball (in that order).

Arranging the Boxes Based on Clues:

Positioning Based on Clues:

1. From Clue 2, we know:
   • $A$ is in the 6th position, is orange, and contains the tennis ball.
2. From Clue 6 and Clue 7, we know:
   • $C$ is in the 2nd position, is green, and contains the cricket ball.
   • $B$ is in the 1st position, contains the volleyball.
3. From Clue 8:
   • The box with the hockey ball must be between the boxes containing the golf ball and the volleyball.
   • Since $B$ (volleyball) is in the 1st position, the only possible position for the hockey ball is in the 4th position.
4. From Clue 3 and Clue 5:
   • The hockey ball cannot be in $D$ or $E$, and it cannot be in a blue or yellow box.
   • Therefore, $F$ is the only box left for the hockey ball.
5. From Clue 1:
   • The golf ball is in the violet box, and it cannot be in box $D$.
   • Since the hockey ball is in $F$ (4th position), the golf ball must be in box $E$.
6. By process of elimination, box $D$ must be blue and contain the football.

The box containing the golf ball is: (b) E

Explanation:

We are tasked to calculate the minimum time required for four friends, $A$, $B$, $C$, and $D$, to cross a bridge under the following conditions:

Given:

1. The time taken by each friend to cross the bridge is:

• A = 1, minute,
• B = 2 minutes,
• C = 7 minutes,
• D = 10 minutes.

2. A maximum of two persons can cross at a time.

3. Both persons crossing must carry the lamp, and the time taken is determined by the slower person in the pair.

4. After each crossing, someone must return with the lamp.

Step-by-Step Solution

Step 1: Fastest pair crosses first

• $A$ and $B$ (the two fastest individuals) cross the bridge first.
• Time taken: 2 minutes, (speed of B)

Now, $A$ and $B$ are on the other side, while $C$ and $D$ remain on the starting side.

Step 2: Fastest person returns

• $A$ (the fastest individual) returns with the lamp.
• Time taken: 1 minute (speed of A).

Now, $A, C, D$ are on the starting side, and $B$ is on the other side.

Step 3: Slowest pair crosses

• $C$ and $D$ (the two slowest individuals) cross the bridge together.
• Time taken: 10 minutes(speed of D)

Now, $C$ and $D$ are on the other side, while $A$ remains on the starting side.

Step 4: Second fastest person returns

• $B$ (the second fastest individual) returns with the lamp.
• Time taken: 2 minutes(speed of B)

Now, $A$ and $B$ are on the starting side, while $C$ and $D$ are on the other side.

Step 5: Fastest pair crosses again

• $A$ and $B$ cross the bridge together.
• Time taken: 2 minutes(speed of B)

Now, all four friends ($A, B, C, D$) are on the other side.

Total Time Calculation:

Adding up the time taken in all steps: 2 + 1 + 10 + 2 + 2 = 17 minutes.

The minimum total time required for all four friends to cross the bridge is: $\boxed{23 minutes}$

Thus, correct answer is: (a) 23 minutes

Explanation:

We are given two conditions:

1. If one bee lands on each flower, one bee will be left out.

This means:

$b = f + 1$.

2. If two bees land on each flower, one flower will be left out.

This means:
$2f = b + 1$.

Here, $f$ represents the number of flowers, and $b$ represents the number of bees. We need to solve these equations to determine the values of $f$ and $b$.

Step-by-Step Solution

Step 1: Express $b$ in terms of $f$ using the first equation:

From $b = f + 1$:

$$
b = f + 1
$$

Step 2: Substitute $b = f + 1$ into the second equation:

Substitute $b = f + 1$ into $2f = b + 1$:

$$
2f = (f + 1) + 1
$$

Simplify:

$$
2f = f + 2
$$

Solve for $f$:

$$
f = 3
$$

Step 3: Find $b$ using $b = f + 1$:

Substitute $f = 3$ into $b = f + 1$:

$$
b = 3 + 1 = 4
$$

Step 4: Verification

1. If $f = 3$ and $b = 4$:

• For Condition 1: One bee per flower means $3$ flowers take $3$ bees, leaving $1$ bee.
• For Condition 2: Two bees per flower mean $3$ flowers need $6$ bees, leaving $1$ flower empty.

Thus, the solution satisfies both conditions.

The number of flowers and bees are: 3 and 4

Thus, correct answer is: (c) 3 and 4