If $A$ and $B$ are square matrices of order $3$,$A$ is non-singular,and $AB = O$,then $B$ is a

If $A$ is a square matrix such that $A(\operatorname{adj} A) = \begin{bmatrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{bmatrix}$,then $\operatorname{det}(\operatorname{adj} A)$ is equal to

It takes $10$ minutes to cool a liquid from $61^oC$ to $59^oC$. If room temperature is $30^oC$,then the time taken in cooling from $51^oC$ to $49^oC$ is ....... $\min$.

Considering only the principal values of inverse functions,the set $A = \{x \geq 0, \tan^{-1}(2x) + \tan^{-1}(3x) = \frac{\pi}{4}\}$

The limiting points of the co-axial system containing the two circles $x^2+y^2+2x-2y+2=0$ and $25(x^2+y^2)-10x-80y+65=0$ are

$A$ closed organ pipe and an open organ pipe of the same length produce $2 \text{ beats } \sec^{-1}$ when they are set into vibrations together in their fundamental mode. The length of the open pipe is now halved and that of the closed pipe is doubled. The number of beats produced will be