List of practice Questions

The ratio of molar heat capacity at constant volume of one mole monoatomic gas to the one mole diatomic gas is given as a/b, where a and b are co-prime number, then find (a + b)

In a diffraction pattern of a monochromatic light of wavelength 6000 pm, the slit width is 3 mm. If the angular position of 2nd minima is N x 10^-6 rad, find N.

Three particles having different masses have the same momentum. Find the ratio of their kinetic energy. (m₁ = 400 gm,m₂ = 1.2 kg,m³ = 1.6 kg)

An electromagnetic radiation of intensity 360 W /cm² is incident normally on a non-reflecting surface having area A. Average force on the surface is found to be 2.4 x 10^-4 N. Find the value of A.

In a series LCR Circuit, the value of resistance as well as (X_L - X_C) is halved, then the new current amplitude (I₂) will satisfy: (I₁ is old current amplitude)

The acceleration of a moving body is found from the

If the amount of heat given to a system is $35\, J$ and the amount of work done on the system is $15\, J$, then the change in internal energy of the system is

Which of the following is not tetrahedral in shape ?

\(\lim\limits_{n\rightarrow \infin}\frac{\sum(n^4-2n^3+n^2)}{\sum ((3n)^4+n^3-n^2)}\) is equal to

If the orthocentre of triangle formed by (8, 3), (5, 1) and (h, k) is (6, 1), then (h, k) lie on

The locus of P such that the ratio of distance P from A(3, 1) and B(1, 2) is 5 : 4 is

Sides of a triangle are AB = 9, BC = 7, AC = 8. Then cos 3C equals to

If α, ß are the roots of the equation x² - √2 x - 8 = 0 and A_n = αⁿ + ßⁿ, n ∈ N, then the value of (A₁₀ - √2A₉) / 2A₈

If \(\int\frac{dx}{a^2\sin x+b^2\cos^2x}=\frac{1}{12}\tan^{-1}(3\tan x)+c,\)then the maximum value of a sinx + bcosx is____

Find the ratio of energy stored in the two given capacitor systems.

A car of mass 800 kg is moving in a circular path of radius 300 m on a banked road with an angle 30°. Coefficient of friction between the car and road is 0.2. Find the maximum safe speed (to the nearest integer in m/s) with which the car can travel. (Take √3 = 1.7)

For a device, power consumed = 110 W and voltage supplied is 220 V. The number of electrons that flow in 1 is \(\frac{x}{4}\) × 10¹⁷ . Find x.

Find net kinetic energy (maximum possible) associated with 20 diatomic molecules (Here k_B is Boltzmann constant and T is absolute temperature of diatomic gas).

An ammeter consisting of 240 Ω galvanometer and 10 Ω shunt resistance is connected in circuit as shown. Reading of ammeter is

Find the longest wavelength of the Paschen series for hydrogen atom. (Rydberg constant = 10⁷ /m)

The weight of an object measured on the surface of earth is 300 N. What will be the weight of the same object at depth R/4 inside the earth? (Given R = Radius of earth)

A tree branch holds a weight of 200 N by a uniform chain of mass 10 kg. The force applied by branch to hold this weight is ______ (Take g = 10 m/s² )

There are two fixed charged spheres P and Q repelling each other with a force of 16 N. A third neutral sphere is placed between the charged spheres. The new force between the spheres is _________ (assuming all the spheres are insulating)

Let $ {{(1+x)}^{n}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}} $ .If $ {{a}_{1}},{{a}_{2}} $ and $ {{a}_{3}} $ are in $AP$, then the value of $n$ is

$\int \limits^{2017}_{2016} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{4033 - x}} dx $ is equal to