List of practice Questions

The incorrect statement about 'B' is:

If \[ \frac{x^2+3}{x^4+2x^2+9} = \frac{Ax+B}{x^2+ax+b} + \frac{Cx+D}{x^2+cx+d} \] then $ aA + bB + cC + dD = $

The half-life period of a radioactive element A is 62 years. It decays into another stable element B. An archaeologist found a sample in which A and B are in 1 : 15 ratio. The age of the sample is:

The conversion of X to Y is:

The current gain of a transistor in a common emitter configuration is 80. The resistances in collector and base sides of the circuit are 5 k$\omega$ and 1 k$\omega$ respectively. If the input voltage is 2 mV, the output voltage is:

The normal drawn at a point $ (2, -4) $ on the parabola $ y^2 = 8x $ cuts again the same parabola at $ (\alpha, \beta) $. Then $ \alpha + \beta $ is:

Which of the following is correct statement?

A light body of momentum $ P_L $ and a heavy body of momentum $ P_H $, both have the same kinetic energy, then:

If the ratio of the distances of a variable point $P$ from the point $(1,1)$ and the line $x - y + 2 = 0$ is $1/\sqrt{2}$, then the equation of the locus of $P$ is:

A block of mass 18.5 kg kept on a smooth horizontal surface is pulled by a rope of 3 m length by a horizontal force of 40 N applied to the other end of the rope. If the linear density of the rope is 0.5 kgm$^-1$ and initially the block is at rest, the time in which the block moves a distance of 9 m is

A man of mass 70 kg jumps to a height of 0.8 m from the ground, then the momentum transferred by the ground to the man is
(g = 10 m/s$^{-2}$):

The length of the tangent drawn from the point $ \left(\frac{k}{4}, \frac{k}{3}\right) $ to the circle $ x^2 + y^2 + 8x - 6y - 24 = 0 $ is:

According to Oppenauer Oxidation reaction, oxidation of secondary alcohol to ketone by reagent (X) in acetone takes place, what is "X" :

The amount of air that moves in or out of the lungs with each respiratory cycle is:

Leprosy is a:

Evaluate the expression \[ 2 \cot h^{-1}(4) + \sec h^{-1}\left( \frac{3}{5} \right). \]

If water is poured into a cylindrical tank of radius 3.5 ft at the rate of 1 cubic ft/min, then the rate at which the level of the water in the tank increases (in ft/min) is:

The internal and external diameters of a hollow cylinder measured with vernier calipers are (5.73 $\pm$ 0.01) cm and (6.01 $\pm$ 0.01) cm respectively. Then the thickness of the cylinder wall is

In the given circuit, the potential difference across the 5 $\mu$F capacitor is

If the period of the function $ f(x) = \frac{\tan 5x \cos 3x}{\sin 6x} $ is $ \alpha $, then find $ f \left( \frac{\alpha}{8} \right) $:

The number of Guanines and Adenines present in the DNA molecule of pitch at 170° with 130 Hydrogen bonds between base pairs:

A certain volume of a gas at 300 K expands adiabatically until its volume is doubled. The resultant fall in temperature of the gas is nearly (The ratio of the specific heats of the gas is 1.5)

If $ (a, \beta) $ is the orthocenter of the triangle with the vertices $ A(2, 5), B(1, 5), C(1, 4) $, then $ a + \beta = $:

At STP $x$ g of a metal hydrogen carbonate (MHCO$_3$) (molar mass $84 \, {g/mol}$) on heating gives CO$_2$, which can completely react with $0.02 \, {moles}$ of MOH (molar mass $40 \, {g/mol}$) to give MHCO$_3$. The value of $x$ is:

A tightly wound coil of 200 turns and of radius 20 cm carrying current 5 A. Magnetic field at the centre of the coil is.