List of practice Questions

A car is moving with speed $20 \, \, \text{m s}^{- 1}$ on a circular path of radius $100 \, \, \text{m}$ . Its speed is increasing at a rate of $3 \, \text{m s}^{- 2}$ . The magnitude of the acceleration of the car at that moment is

For the arrangement in the figure, the particle $M_{1}$ attached to one end of a string which moves on a horizontal table in a circle of radius $=\frac{l}{2}$ (where $l$ is the length of the string) with the constant angular speed $\omega$ . The other end of the string attached to mass $M_{2}$ which rests on a vertical rod. When the rod collapse, the acceleration of mass $M_{2}$ at that instant

The normal reaction on a body placed in a lift moving up with constant acceleration $2 \, m \, s^{- 1}$ is $120 \, N$ . Mass of the body is (Take $g=10 \, m \, s^{- 2}$ )

Three blocks are connected, as shown in the figure. Calculate the minimum force required to move the blocks with constant velocity. The co-efficient of friction at all surfaces is $0.25$ . [Assume that rod does not exerts force in vertical direction]

$200$ joules of heat was supplied to a system at constant volume. It resulted in the increase in temperature of the system from $298$ to $323\, K$. What is the change in internal energy of the system?

$\,^{221}_{87}$Ra undergoes radiorctive decay with a half life of 4 days. The probability that a Ra nucleus will disintegrate in 8 days is

$20$ persons are invited for a party In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host?

Which will give turbidity fastest on reaction with Lucas reagent ?

Carbylamine reaction is given by

German silver is

Atomic no. $81$ is placed in

Fog is an example of

Electronic configuration of $Na$ is

The number of positive integral solutions of the equation $\tan^{-1} x + \cot^{-1} y = \tan^{-1} 3 ,$ is

The value of $\cos \left(\frac{1}{2} \cos^{-1} \frac{1}{8}\right)$ is equal to

What is the value of $\tan^{-1} \left(\frac{m}{n}\right) - \tan^{-1} \left(\frac{m-n}{m+n}\right) ?$

In a $\Delta ABC$, if $A = tan^{-1}\, 2$ and $B = tan^{ -1}\, 3$ , then $C =$

$sin^{-1}\left(\frac{1}{\sqrt{e}}\right)> tan^{-1}\left(\frac{1}{\sqrt{\pi}}\right)$ $sin^{-1}\,x>tan^{-1}\,y$ for $x>y, \forall \,x, y \,\in\left(0, 1\right)$

The value of $cot^{-1}\left\{\frac{\sqrt{1-sin\,x}+\sqrt{1+sin\,x}}{\sqrt{1-sin\,x}-\sqrt{1+sin\,x}}\right\}\left(0 < x < \frac{\pi}{2}\right)$ is

$2^{\frac{1}{4}}, 4^{\frac{1}{8}}, 8^{\frac{1}{16}}, 16^{\frac{1}{32}}............$ is equal to

The earliest man evolved around

Common ancestor of humans and apes was

Flying Phalanger and Flying squirrel are examples of

The earliest man-like primate was

Tuang Baby or African Ape-Man belonged to