Let $A = \{ x: x \in R, |x| < 1 \}$ and $B = \{ x: x \in R, |x - 1| \ge 1 \}$. If $A \cup B = R - D$,then the set $D$ is:

Which of the following does not contain any co-ordinate bond?

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is:

In a co-axial,straight cable,the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero:

If $A=\begin{bmatrix} 1 & -2 \\ 4 & 5 \end{bmatrix}$ and $f(t)=t^2-3t+7$,then $f(A)+\begin{bmatrix} 3 & 6 \\ -12 & -9 \end{bmatrix}$ is equal to

If $\int \sec ^2 x \operatorname{cosec}^4 x \, dx = -\frac{1}{3} \cot ^3 x + k \tan x - 2 \cot x + C$, then $k$ is equal to