Explanation

Let's calculate Akram's current age:

Akram's age = 2 × Aslam's age

= 2 × 11

= 22 years

The difference in their ages is:

22 - 11 = 11 years

When Akram is 50 years old, Aslam will be:

50 - 11 = 39 years old

Explanation

To find the number of handshakes, we can use the combination formula:

nC2 = n(n-1)/2

where n is the number of members (13).

For before the meeting: 13C2 = 13(12)/2 = 78

For after the meeting: 13C2 = 13(12)/2 = 78

Total handshakes = 78 + 78 = 156

Explanation

The question asks how many cookies Ali can eat in his completely empty stomach.

The answer is 1 because after eating the first cookie, his stomach won't be empty anymore.

Explanation

Given the series is:

1, 2, 2, 4, 4, 6, 8, 8, 16

Let's break it down:

Powers of 2 are interspersed with repetitions: 1 (2^0), 2 (2^1), 2, 4 (2^2), 4, 8 (2^3), 8, 16 (2^4)

If the pattern continues with repetitions after powers of 2:

The next number would logically be 16 (a repetition of the last number, 16).

Explanation

The perfect squares between 4 and 32 are:

4 = 2²

9 = 3²

16 = 4²

25 = 5²

The largest perfect square between 4 and 32 is 25.

Explanation

Explanation

The expression x³ + 27 can be factored using the sum of cubes formula:

x³ + 27 = x³ + 3³

= (x + 3)(x² - 3x + 9)

Explanation

Let’s analyze each option under the assumption that a and b are integers:

a⁷ → Square of an integer → Always an integer

b* → Ambiguous; if it means b raised to some power (like a^b or b^a), then:

If b = 2 and a = -1, then b^a = 2⁻¹ = 0.5, not an integer

So, this is not necessarily an integer

a * b → Product of two integers → Always an integer

2a – 5b → Linear combination of integers → Always an integer

Explanation

To find the largest number that divides 237, 132, and 62 leaving the same remainder, we need to find the differences between the numbers:

237 - 132 = 105

237 - 62 = 175

132 - 62 = 70

Now, let's find the greatest common divisor (GCD) of 105, 175, and 70:

GCD(105, 175) = 35

GCD(35, 70) = 35

The largest number that divides the given numbers leaving the same remainder is 35.

Explanation

Let's denote the original side of the cube as s. The original volume is s³.

If the side is doubled, the new side is 2s. The new volume is (2s)³ = 8s³.

The new volume is 8 times the original volume.