Explanation

A cube has 6 equal square faces, and each face has area a².

So, surface area = 6a².

Explanation

2x² - 2 = 0

2x² = 2

x² = 1

x = ±1

Explanation

Let's check each option:

1. 31 = 2 + 29 (both prime)

2. 19 = 2 + 17 (both prime)

3. 23 = No combination works (e.g., 2 + 21, 21 is not prime)

4. 7 = 2 + 5 (both prime)

The answer is 23.

Explanation

If A is a non-singular square matrix, then its inverse A⁻¹ exists.

The product AA⁻¹ = I, where I is the identity matrix.

Explanation

 The function that is to be maximized or minimized is called the objective function

 It represents the goal of the optimization process and is typically a mathematical expression that relates to the quantity being optimized, such as cost, profit, or efficiency. 

Explanation

Multiplying 0.2 × 10 gives 2, and 2 × 0.5 equals 1.

Hence, the correct answer is 1.

Explanation

24 ÷ 8 = 3.

24 divided by 8 equals 3, with no remainder.

Explanation

To evaluate this expression, follow the order of operations (PEMDAS):

1. Evaluate the expression inside the parentheses:

2 + 3 = 5

So, the expression becomes:

8 * 5 - 4^2

2. Multiply 8 and 5:

8 * 5 = 40

3. Calculate 4 squared:

4^2 = 16

4. Finally, subtract 16 from 40:

40 - 16 = 24

Explanation

600 × 3 = 1800

Explanation

Person 1 receives: Rs. 180

Person 2 receives: Rs. 240 (total prize) - Rs. 180 (received by Person 1) = Rs. 60

So, the difference between the amounts received by the two persons is:

Rs. 180 (Person 1) - Rs. 60 (Person 2) = Rs. 120

The correct answer is: Rs. 120.