List of practice Questions

To get the maximum flight, a ball must be thrown as
An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be ($m$ is the mass of the electron, $R$, Rydberg constant and $h$ Planck's constant)
Cirrhosis of liver is caused by the chronic intake of
$F _{2}$ generation in a Mendelian cross showed that both genotypic and phenotypic ratios are same as $1: 2: 1.$ It represents a case of
The compressibility factor for a real gas at high pressure is :
Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state.
The ratio of the wavelengths \(\lambda_1 : \lambda_2\) emitted in the two cases is:
A magnetic needle suspended parallel to a magnetic field requires $\sqrt 3 \,J$ of work to turn it through $60^\circ.$ The torque needed to maintain the needle in this position will be
For an ideal system at thermal equilibrium, the velocity distribution of the constituent particles will be governed by
An electron and a proton, both having the same kinetic energy, enter a region of uniform magnetic field, in a plane perpendicular to the field. If their masses are denoted by $m_{e}$ and $m_{p}$ respectively, then the ratio of the radii (electron to proton) of their circular orbits is
The probability that atleast one of the events $A$ and $B$ occurs is $ 0.5 $ . If $A$ and $B$ occur simultaneously with probability $ 0.2, $ then $ P({{A}^{c}})+P({{B}^{c}}) $ is equal to
Let $ f(x)=\frac{k}{1+{{x}^{2}}},\,-\infty < x < \infty $ be the probability density of a random variable. Then, $k$ equals to
The sum of $n$ terms of the series $ \frac{3}{{{1}^{2}}{{.2}^{2}}}+\frac{5}{{{2}^{2}}{{.3}^{2}}}+\frac{7}{{{3}^{2}}{{.4}^{2}}}+..... $ is equal to
What is the resonance frequency of a driven $LCR$ oscillator?
A cheetah, weighing $150 \,kg$, chases a deer, weighing $30 \, kg$, in a straight path. The speed of the cheetah is $20 \,m / s$ and that of the deer is $25 m / s$. The approximate speed of the centre of mass of the pair is
If $(-3, 2)$ lies on the circle $x^2 + y^2 + 2gx + 2fy + c = 0$, which is concentric with the circle $x^2 + y^2 + 6x + 8y - 5 = 0,$ then c is equal to
A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It.
Consider the following reaction ${ ->[H_2][pd-BaSO_4] 'A'}$ The product 'A' is -
The line $x=2 y$ intersects the ellipse $\frac{x^{2}}{4}+y^{2}=1$ at the points $P$ and $Q$. The equation of the circle with $P Q$ as diameter is
If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then the value of $x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}}$ is equal to
A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is $ 200\, kg\, m^2 $. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of $ 1 \,ms^{-1} $ relative to the ground. Time taken by the man to complete one revolution is
The potential energy of a particle in a force field is $ U=\frac{A}{r^2}-\frac{B}{r}$ where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is
Biolistics (gene-gun) is suitable for
There are $100$ students in a class. In an examination, $50$ of them failed in Mathematics, $45$ failed in Physics, $40$ failed in Biology and $32$ failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.
The number of integer values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer, is
In a slide callipers, $(m + 1)$ number of vernier divisions is equal to m number of smallest main scale divisions. If d unit is the magnitude of the smallest main scale division, then the magnitude of the vernier constant is