In the adjoining diagram the length of PR is :

1. $3\sqrt{3}$ cm

2. $6\sqrt{3}$ cm

3. $9\sqrt{3}$ cm

4. 18 cm

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

A bag contains 3 red and 2 blue marbles. A marble is drawn at random. The probability of drawing a black marble is :

1. 0

2. $\dfrac{1}{5}$

3. $\dfrac{2}{5}$

4. $\dfrac{3}{5}$

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.