Explanation : 

A boy plays with a ball

Starting height = 1.5 meters
Bounce ratio = 4/5 (ball reaches 4/5th of previous height)
Stop condition = height < 0.5 meters (50 cm)

Height Calculations:

1. Initial Drop: 1.5 meters

2. First Bounce:
Height = 1.5 × 4/5 = 1.2 meters

3. Second Bounce:
Height = 1.2 × 4/5 = 0.96 meters

4. Third Bounce:
Height = 0.96 × 4/5 = 0.768 meters

5. Fourth Bounce:
Height = 0.768 × 4/5 = 0.6144 meters

6. Fifth Bounce:
Height = 0.6144 × 4/5 = 0.49152 meters
(This is less than 50 cm, so ball stops)

Result:
– Ball hits ground 5 times before stopping
– Final height (0.49152 m) is below stopping condition (0.5 m)
– Answer: 5 bounces

Explanation : 

A student appeared in 6 papers

– Total marks per subject = 100
– Total subjects = 6
– Total possible marks = 600
– Overall score = 60% = 360 marks
– Marks distribution pattern: 5x, 6x, 7x, 8x, 9x, 10x

Step 1: Form equation
5x + 6x + 7x + 8x + 9x + 10x = 360
45x = 360

Step 2: Solve for x
x = 360/45 = 8

Step 3: Calculate marks in each subject
Subject 1: 5x = 5 × 8 = 40 marks
Subject 2: 6x = 6 × 8 = 48 marks
Subject 3: 7x = 7 × 8 = 56 marks
Subject 4: 8x = 8 × 8 = 64 marks
Subject 5: 9x = 9 × 8 = 72 marks
Subject 6: 10x = 10 × 8 = 80 marks

Step 4: Count subjects below 60%
60% of 100 = 60 marks
Subjects below 60 marks:
1. 40 marks
2. 48 marks
3. 56 marks

Therefore: Student scored less than 60% in 3 subjects.

Explanation :

There are two classes a and b

Class A (Initial):
– Total students: 25
– Highest score: 21
– Lowest score: 17
– Four students will be shifted out

Class B (Initial):
– Total students: 30
– Highest score: 30
– Lowest score: 22
– Will receive four students from Class A

Analysis:

1. Effect on Class B’s Average:
– Initial students: 30
– New total: 34 students
– All incoming students have scores ≤ 21
– All original students have scores ≥ 22
– Therefore, adding any four students from Class A will definitely lower Class B’s average

2. Effect on Class A’s Average:
– Initial students: 25
– New total: 21 students
– Cannot determine if average will increase because:

• If highest scoring students (around 21) are shifted out → average will decrease
• If lowest scoring students (around 17) are shifted out → average will increase
• Without knowing which students are shifted, change in average is uncertain

Conclusion:
– Class B’s average will definitely decrease
– Class A’s average could increase or decrease depending on which students are shifted

Explanation:

Sum of 3-Digit Numbers with Digits 3, 6, and 9

Given Digits: 3, 6, 9

Step 1: List all possible 3-digit combinations (without repetition)
1. 369
2. 396
3. 639
4. 693
5. 936
6. 963

Step 2: Calculate sum (S)
369 + 396 + 639 + 693 + 936 + 963 = 3996

Step 3: Verify divisibility by 74
3996 ÷ 74 = 54
Therefore, 3996 is divisible by 74

Step 4: Verify divisibility by 9
3996 ÷ 9 = 444
Therefore, 3996 is divisible by 9

Explanation : 

Number of zeroes at the end of product

1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60

= 1 × 5 × (5 × 2) × (5 × 3) × (5 × 2^2) × (5 × 5) × (5 × 3 × 2) × (5 × 7) × (5 × 2^3) × (5 × 9) × (5 × 5 × 2) × (5 × 11) × (5 × 2^2 × 3)

Here, number of 2s = 10
And number of 5s = 14
The lesser of the two will determine the number of zeros.
Hence, there will be 10 zeros at the end in the given expression.

Model Answer:

If you have two straight sticks of length 7.5 feet and 3.25 feet

To find the minimum length that can be measured using two straight sticks of length 7.5 feet and 3.25 feet using the Highest Common Factor (HCF) method, we can first convert the lengths to inches:

7.5 feet = 90 inches
3.25 feet = 39 inches

Then, we can find the HCF of 90 and 39:

90 = 2 * 3 * 3 * 5
39 = 3 * 13

The common factor is 3, so the HCF is 3 inches.

Therefore, the minimum length that can be measured with these two sticks is 3 inches, which is equivalent to 0.25 feet.

Hence, the correct answer is (b) 0.25 foot.

Explanation : 

As a result of 25 hike -> Finding original price of rice 

Given Information:
– Original price of rice = x rupees per kg
– Price increased by 25%
– New price = 1.25x rupees per kg
– Available money = Rs. 1,200
– Difference in quantity = 6 kg

Step 1: Calculate quantity before price hike
Original quantity = 1200/x kg

Step 2: Calculate quantity after price hike
New quantity = 1200/(1.25x) kg

Step 3: Set up equation using difference
1200/x – 1200/(1.25x) = 6

Step 4: Solve for x
1200/x – 960/x = 6
(1200 – 960)/x = 6
240/x = 6
x = 40

Therefore:
– Original price of rice = Rs. 40 per kg
– After 25% increase, new price = Rs. 50 per kg
– Original quantity = 1200/40 = 30 kg
– New quantity = 1200/50 = 24 kg
– Difference = 30 – 24 = 6 kg

Explanation : 

All cats are dogs. All cats are black.

1. For Conclusion I – “All dogs are black”:
– While we know all cats are black and all cats are dogs
– We cannot conclude all dogs are black
– Because not all dogs may be cats
– Example: There could be dogs that are not cats, and these dogs could be any color

2. For Conclusion II – “Some dogs are not black”:
– We cannot conclude this either
– The statements give no information about dogs that are not cats
– Making any assumption about non-cat dogs would be illogical

Therefore:
Neither conclusion can be logically derived from the given statements. The statements only tell us about cats (that they are dogs and they are black) but give no complete information about dogs.

Correct Answer: Neither Conclusion-I nor Conclusion-II follows from the given statements.

Explanation : 

A is 16th from the left end in a row

Problem: Finding total number of boys in a row

Given:
– A is 16th from left end
– V is 18th from right end
– Q is 11th from A towards right
– Q is 3rd from V towards right

Solution:
1. Find Q’s position from left:
– A is 16th from left
– Q is 11th right of A
– So Q is 16 + 11 = 27th from left

2. Find Q’s position from right:
– V is 18th from right
– Q is 3rd right of V
– So Q is 18 – 3 = 15th from right

3. Calculate total boys:
– Q’s position from left = 27
– Q’s position from right = 15
– Total boys = Left position + Right position – 1
– Total = 27 + 15 – 1 = 41 (Subtract 1 because Q is counted twice)

Therefore, there are 41 boys in the row.

Explanation :

Problem: Find pairs of numbers whose difference of squares is 63

Given:
– Two natural numbers x and y where x > y
– x² – y² = 63

Solution:
1. Factor the equation:
x² – y² = (x+y)(x-y) = 63

2. Find factors of 63:
63 = 1 × 63
63 = 3 × 21
63 = 7 × 9

3. For each factor pair (a,b):
x + y = larger number
x – y = smaller number

Solving:
x = (larger + smaller)/2
y = (larger – smaller)/2

4. Calculate pairs:
For 63,1:
x = (63 + 1)/2 = 32
y = (63 – 1)/2 = 31

For 21,3:
x = (21 + 3)/2 = 12
y = (21 – 3)/2 = 9

For 9,7:
x = (9 + 7)/2 = 8
y = (9 – 7)/2 = 1

Therefore, three pairs of numbers exist: (32,31), (12,9), and (8,1)