List of practice Questions

$\displaystyle\lim_{x \to 0} \frac{ \sqrt{1 -\cos \, 2x}}{\sqrt{2} x}$ is
If $a, b, c$ are distinct +ve real numbers and $a^2 + b^2 + c^2 = 1$ then $ab + bc + ca$ is
The coefficients of $x^p$ and $x^q$ (p and q are positive integers) in the expansion of $(1+ x )^{p+q}$ are
A biased coin with probability p, $0
From a building two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ downwards (both vertically). If $v_{A}$ and $v_{B}$ are their respective velocities on reaching the ground, then :
If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero, then the satellite will :
A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (vertically). If the acceleration of the system is $g / 8$, then the ratio of the masses is :
A ball whose kinetic energy is $E$, is projected at an angle of $45^{\circ}$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be :
$1$ mole of a gas with $\gamma = \frac{7}{5}$ is mixed with $1$ mole of gas with $\gamma = \frac{5}{3}$, the value of $\gamma$ of the resulting mixture of
If two mirrors are kept at $60^{\circ}$ to each other, then the number of images formed by them is:
If a current is passed through a spring then the spring will:
In a transformer, number of turns in the primary are 140 and that in the secondary are 280 . If current in primary is $4 A$, then that in the secondary is :
A tuning fork arrangement (pair) produces $4$ beats/s with one fork of frequency $288\, cps$. A little wax is placed on the unknown fork and it then produces $2$ beats/s. The frequency of the unknown fork is :
Aluminium is extracted by the electrolysis of:
Initial angular velocity of a circular disc of mass $M$ is $\omega_{1}$. Then two small spheres of mass $m$ are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?
If the escape velocity at the earth is 11.2 km/s, then what will be the escape velocity of planet having mass 4 times of earth and gravitational acceleration equal to earth?
The ratio of radii to the gravitational acceleration of planets X and Y are R and a respectively. The ratio of escape velocities at them, is
If the range and time period of projectile are related to $ R=5{{T}^{2}}, $ then the angle of projection will be
The acceleration a of moving body from rest is 2 (t - 1). Then, the velocity at 5 s will be
The positive charged ball is suspended by thread of silk. If we place a positive charge $ {{q}_{0}} $ at one point and measure the $ F/{{q}_{0}}, $ then this can say that electric field E
If $ Z=\frac{a{{b}^{2}}}{{{c}^{3}}} $ , then what is the error in Z? The errors in a, b, c are $ \alpha $ , $ \beta $ and $ \gamma $ respectively
The momenta of two particles of masses m and 2m are 2p and p respectively. The ratio of their kinetic energies will be
The potential difference applied to an X-ray tube is 5 kV and the current through it is 3.2 mA. Then the number of electrons striking the target per second is
Let f(x) =$\int_1^x \sqrt{2-t^2}dt $ Then, the real roots of the equation $x^2-f'(x)=0$ are
If $a_1,a_2,...,a_n$ are positive real numbers whose product is a fixed number c, then the minimum value of $ a_1 + a_2 +...+ a_{n-1}+2a_n$ is