If $f(x) = \sqrt{\frac{x - \sin x}{x + \cos^2 x}}$,then $\lim_{x \to \infty} f(x)$ is

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ $(\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is

If $\tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c=\pi$,then which of the following statements is true?

The resolving power of an astronomical telescope is $0.2\, sec$. If the central half portion of the objective lens is covered,the resolving power will be....$sec$

The natural frequency of an $L-C$ circuit is $1,25,000 \text{ cycles/s}$. Then the capacitor $C$ is replaced by another capacitor with a dielectric medium of dielectric constant $K$. In this case,the frequency decreases by $25 \text{ kHz}$. The value of $K$ is

$A$ body is projected vertically upwards with a velocity $u$ from the top of a tower. The time taken by it to reach the ground is $n$ times the time taken by it to reach the highest point in its path. The height of the tower is: