List of practice Questions

An alternating e.m.f. is given by \( e = e_0 \sin \omega t \). In what time the e.m.f. will have half its maximum value, if \( e_0 \) starts from zero? (T = Time period)
Due to surface tension, the excess pressure inside a smaller drop is 9 units. If 27 smaller drops combine, then the excess pressure inside the bigger drop is
What should be the velocity of earth due to rotation about its own axis so that the weight at equator becomes \( \frac{1}{25} \) of initial value?
(Radius of Earth on equator = 6400 km, \( g = 10 \, \text{m/s}^2 \), \( \cos 0^\circ = 1 \))
When a photosensitive surface is irradiated by lights of wavelengths \( \lambda_1 \) and \( \lambda_2 \), kinetic energies of emitted photoelectrons are \( E_1 \) and \( E_2 \) respectively. The work function of the photosensitive surface is
If a gas is compressed isothermally then the r.m.s. velocity of the molecules
A circular and a square coil is prepared from two identical metal wires and a current is passed through them. Ratio of magnetic dipole moment associated with circular coil to that with square coil is
Light of incident frequency 2 times the threshold frequency is incident on a photosensitive material. If the incident frequency is made \( \frac{1}{3} \)rd and intensity is doubled then the photoelectric current will
Evaluate the integral \( \int_0^1 \frac{x^2}{1 + x^2} dx \)
If \( y = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots \), then \[ \frac{dy}{dx} = \]
Two galvanometers 'G1' and 'G2' require 2 mA and 3 mA respectively to produce the same deflection. Then
The particular solution of the differential equation \( \cos \left( \frac{dy}{dx} \right) = a \), under the conditions \( a \in \mathbb{R} \) and \( y(0) = 2 \) is
If \( \sqrt{x + y} + \sqrt{y - x} = 5 \), then \( \frac{d^2y}{dx^2} = \)
If \( f(x) = x^2 - 3x + 4 \) and \( f(x) = f(2x + 1) \), then \( x = \)
20 meters of wire is available to fence a flower bed in the form of a circular sector. If the flower bed should have the greatest possible surface area, then the radius of the circle is
The equation of the normal to the curve \( 2x^2 + 3y^2 - 5 = 0 \) at \( P(1, 1) \) is
The minimum value for the LPP \( Z = 6x + 2y \), subject to \( 2x + y \geq 16, x \geq 6, y \geq 1 \) is
Write the statement in symbolic form 'Sandeep neither likes tea nor coffee but enjoys a soft drink'. Where \( p \): Sandeep likes tea, \( q \): Sandeep likes coffee, \( r \): Sandeep enjoys a soft drink
The principal value of \( \sin^{-1} \left( -\frac{1}{2} \right) \) is
Evaluate \( 2 \tan^{-1} \left( \frac{1}{3} \right) - \tan^{-1 \left( \frac{3}{4} \right) \)}
If \( f(x) = \frac{|x - 2|}{x - 2} \) for \( x \neq 2 \), and \( f(x) = 1 \) for \( x = 2 \), then which of the following statements is true?
Which of the following oxyacids of chlorine does not contain lone pair of electrons on chlorine atom?
Which among the following is an example of a zero order reaction?
Calculate the amount of work done during isothermal expansion of a gas from a volume of 4 dm\(^3\) to 6 dm\(^3\) against a constant external pressure of 3 atmosphere.
The SI unit of pressure is
Identify 'A' in the following reaction:
\[ \text{C}_6\text{H}_5\text{-CH}_2\text{-Cl} + \text{H}_2\text{Pd-BaSO}_4 \rightarrow \text{C}_6\text{H}_5\text{-CH}_2\text{-CHO} + \text{HCl} \]