List of practice Questions

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $Cp/Cv$ of the mixture is

The direction ratios of a normal to the plane through $ (1, 0, 0), (0, 1, 0)$ which makes angles of $\frac{\pi}{4}$ with the plane $x + y = 3$ are

If the sum of the coefficients in the expansion of $(a + b)^n$ is 4096, then the greatest coefficient in the expansion is

The positive integer just greater than $(1 + 0.0001)^{10000}$ is

r and n are positive integers $r > 1, n > 2$ and coefficient of $(r+2)^{th}$ term and $3r^{th}$ term in the expansion of $(1 + x)^{2n }$ are equal, then n equals

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

$\displaystyle\lim_{x \to 0} \frac{ \sqrt{1 -\cos \, 2x}}{\sqrt{2} x}$ is

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 :

$1$ 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

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 :

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?