Explanation

Let's follow the order of operations (PEMDAS):

15 × (10 × 6)

= 15 × 60

= 900

Now, let's rewrite 900 in the form ____ × 10:

900 = 90 × 10

Explanation

The power set P(A) of a set A with n elements has 2^n elements.

Here, A = {a, b, c, d, e} has 5 elements, so n = 5.

The number of elements in P(A) is 2^5 = 32.

Explanation

Using the change of base formula:

log_b^a / log_b^d = log_d^a

Explanation

Let's simplify the expression:

√25^(3x) = √(5²)^(3x) = √(5^(6x)) = 5^(3x)

Now, divide by 5^(6x-2):

5^(3x) / 5^(6x-2) = 5^(3x - 6x + 2) = 5^(-3x + 2)

For this to equal one of the given options (5, 10, 15), let's see if -3x + 2 = 1 (for 5¹ = 5):

-3x + 2 = 1

-3x = -1

x = 1/3

Then, 5^(-3(1/3) + 2) = 5¹ = 5

Explanation

5% of 16,000 = 800, so increase = 800.

New population = 16,000 + 800 = 16,800.

A percentage increase means adding the calculated percent value to the original number.

Explanation

The graph of x = a is a vertical line.

It is perpendicular to the y-axis, which is vertical.

Explanation

Supplementary angles add up to 180 degrees but aren't necessarily equal.

Supplementary angles can have various measures (e.g., 90° + 90°, 120° + 60°, 150° + 30°), showing they don't have to be equal.

Explanation

10% of 5400 = 540

5400 - 540 = 4860

Explanation

50 to 60:

Increase = 60 - 50 = 10

Percent increase = (10 / 50) × 100 = 20%

Explanation

Cost of 120 copies = Rs. 6000

Cost of 1 copy = Rs. 6000 / 120

= Rs. 50

Cost of 400 copies = Rs. 50 × 400

= Rs. 20000