List of practice Questions

$5\,\cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) +7\,\sin^{-1}\left(\frac{2x}{1+x^2}\right)-4\,\tan^{-1}\left(\frac{2x}{1+x^2}\right)-\tan^{-1}x=5\pi$ , then x is equal to
$4\,tan^{-1} \frac{1}{5} -tan^{-1} \frac{1}{70} + tan^{-1} \frac{1}{99}$ is equal to
$4 a^2 \, \sin^2 \left( \frac{3\pi}{4} \right) - 3 [a\, \tan \,225^\circ ]^2 + [ 2a \, \cos \, 315^\circ ]^2$
4.48 litres of an ideal gas at STP requires 12.0 calories to raise its temperature by 15$\circ$C at constant volume. The $C_p$ of the gas is
$3\,\tan^{-1}a$ is equal to
Maximum surface area of circulating system is seen in
Layers of an ovum from outside to inside is
Struggle for existence and survival of the fittest theories were given by
Deamination occurs in
Dental formula of rabbit is
Regeneration of liver is
Which of the following statements are correct? (i) venom of cobra is neurotoxic (ii) venom of sea snake is neurotoxic (iii) venom of viper is haemotoxic
In housefly pseudotracheae is found in
3-segmented club shaped maxillary palp is present in
Mosquito receives air through
$\sqrt{-3}\sqrt{-6}$ is equal to
3-hydroxy butanal is formed when X reacts with Y in dilute Z solution. What are X, Y and Z?
$\sqrt{2i}$ is equal to
$|2x - 3| < |x + 5|$, then $x$ belongs to
$ {2CuFeS_2 + O_2 -> Cu_2S + 2FeS + SO_2}$ Which process of metallurgy of copper is represented by above equation?
A horizontal disk is rotating with angular velocity $\omega $ about a vertical axis passing through its centre. A ball is placed at the centre of groove and pushed slightly. The velocity of the ball when it comes out of the groove-
A block of mass $M$ is resting on a smooth horizontal plane. One end of a uniform rope of mass $\frac{M}{4}$ is fixed to the block, which pulled it in the horizontal direction by applying a force $F$ at the other ends. The tension in the middle of the rope is
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 $g=10 \, m \, s^{- 2}$ )