$A$ concave mirror of focal length $f$ (in air) is immersed in water $(\mu = 4/3)$. The focal length of the mirror in water will be

For $|x| < \frac{1}{5}$,the coefficient of $x^3$ in the expansion of $\frac{1}{(1-5 x)(1-4 x)}$ is

The conjugate acid of $NH_2^-$ is

Suppose $\overrightarrow{a}=\lambda \hat{i}-7 \hat{j}+3 \hat{k}$ and $\overrightarrow{b}=\lambda \hat{i}+\hat{j}+2 \lambda \hat{k}$. If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is greater than $90^{\circ}$,then $\lambda$ satisfies the inequality

The focus of the parabola $y = 2x^2 + x$ is

$A$ body takes $1\frac{1}{3}$ times as much time to slide down a rough inclined plane as it takes to slide down an identical but smooth inclined plane. If the angle of the inclined plane is $45^\circ$,the coefficient of friction is: