List of practice Questions

Two electrons one moving in opposite direction with speeds $0.8\,c$ and $0.4\,c$ where c is the speed of light in vacuum. Then the relative speed is about

The output stage of a television transmitter is most likely to be a

Radio carbon dating is done by estimating in specimen

The antenna current of an $AM$ transmitter is $8\,A$ when only the carrier is sent, but it increases to $8.93\,A$ when the carrier is modulated by a single sine wave. Find the percentage modulation.

Assuming $f$ to be the frequency of first line in Balmer series, the frequency of the immediate next (i.e. second) line is Assuming $f$ to be the frequency of first line in Balmer series, the frequency of the immediate next (i.e. second) line is

The electric field intensity $\vec{E}$, due to an electric dipole of moment $\vec{p}$, at a point on the equatorial line is

Four independent waves are represented by equations : (1) $X_{1}=a_{1} \sin \omega t$ (2) $X_{2}=a_{1} \sin 2 \omega t$ (3) $X_{3}=a_{1} \sin \omega_{1} t$ (4) $X_{4}=a_{1} \sin (\omega t+\delta)$ Interference is possible between waves represented by equations :

Radar waves are sent towards a moving airplane and the reflected waves are received. When the airplane is moving towards the radar, the wavelength of the wave

Indicate which one of the following statements is not correct?
(a) Intensities of reflections from different crystallographic planes are equal
(b) According to Bragg's law higher order of reflections have high $\theta$ values for a given wavelength of radiation
(c) For a given wavelength of radiation, there is a smallest distance between the crystallographic planes which can be determined
(d) Bragg's law may predict a reflection from a crystallographic plane to be present but it may be absent due to the crystal symmetry

If (x +y )sin u = $x^2y^2$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = $

The product of all values of $(\cos \alpha + i \sin \alpha)^{3/5}$ is equal to

If the normal at $(ap^2, 2ap)$ on the parabola $y^2 = 4ax,$ meets the parabola again at $(aq^2, 2aq)$, then

A box contains $9$ tickets numbered $1$ to $9$ inclusive. If $3$ tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even, odd} or {even, odd, even} is

The sum of the series $ \frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+... $ upto $ n $ term is

If the rank of the matrix $\begin{bmatrix}-1 &2&5\\ 2&-4&a-4\\ 1&-2&a+1\end{bmatrix}$ is 1, then the value of $a$ is

The length of the straight line $x - 3y = 1$ intercepted by the hyperbola $x^2 - 4y^2 = 1$ is

The curve described parametrically by $x = t^2 + 2t - 1, y = 3t + 5$ represents

If $\sin^{-1} x + \sin^{-1} y = \frac{\pi}{2}$ , then $\cos^{-1} x + \cos^{-1} y$ is equal to

$\frac{1+\tan ^{2} x}{1-\tan ^{2} x} d x$ is equal to

The function $f(x) = x^2 \; e^{-2} x, x > 0$. Then the maximum value of $f(x)$ is

A particle executes SHM of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points 12.5 cm on either side of the mean position?

In the diagram shown below all three rods are of equal length $L$ and equal mass $M$. The system is rotated such that rod $B$ is the axis. What is the moment of inertia of the system?

Which of the following is correct for the process of formation of a chemical bond?

What number will replace the question mark ?

Where should the letter ‘W’ be placed ?