A solid sphere is cut into identical hemispheres.

Statement 1 : The total volume of two hemispheres is equal to the volume of the original sphere.

Statement 2 : The total surface area of two hemispheres together is equal to the surface area of the original sphere.

Which of the following is valid ?

1. Both the statements are true

2. Both the statements are false

3. Statement 1 is true, and statement 2 is false

4. Statement 1 is false, and statement 2 is true

Given that the sum of the squares of the first seven natural numbers is 140, then their mean is :

1. 20

2. 70

3. 280

4. 980

If $A = \begin{bmatrix$}[r] 3 & -2 \end{bmatrix} \text{ and } B = \begin{bmatrix}[r] -1 & 4 \ 2 & 0 \end{bmatrix}

Assertion (A) : Product AB of the two matrices A and B is possible

Reason (R) : Number of columns of matrix A is equal to number of rows in matrix B.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true, and R is the correct reason for A

4. Both A and R are true, and R is incorrect reason for A.

A mixture of paint is prepared by mixing 2 parts of red pigments with 5 parts of the base. Using the given information in the following table, find the values of a, b and c to get the required mixture of paint.

1. a = 10, b = 10, c = 10

2. a = 5, b = 2, c = 5

3. a = 10, b = 5, c = 10

4. a = 10, b = 5, c = 15