List of practice Questions

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is:
An electron of mass $m_e$ and a proton of mass $m_p = 1836 m_e$ are moving with the same speed. The ratio of their de Broglie wavelength $\frac{\lambda_{electron}}{\lambda_{proton}}$ will be:
The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n=2 to n=1 state is:
If a message signal of frequency '$f_m$' is amplitude modulated with a carrier signal of frequency '$f_c$' and radiated through an antenna, the wavelength of the corresponding signal in air is:
Given below are two statements:
Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.
Statement II: In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.
An electron with kinetic energy $K_1$ enters between parallel plates of a capacitor at an angle '$\alpha$' with the plates. It leaves the plates at angle '$\beta$' with kinetic energy $K_2$. Then the ratio of kinetic energies $K_1 : K_2$ will be:
In a ferromagnetic material, below the curie temperature, a domain is defined as:
If the line \( y = mx \) bisects the area enclosed by the lines \( x = 0, y = 0, x = \frac{3}{2} \) and the curve \( y = 1 + 4x - x^2 \), then 12 m is equal to _________.
Let B be the centre of the circle \( x^2 + y^2 - 2x + 4y + 1 = 0 \). Let the tangents at two points P and Q on the circle intersect at the point \( A(3, 1) \). Then \( 8 \cdot \frac{\text{area } \Delta APQ}{\text{area } \Delta BPQ} \) is equal to _________.
Suppose the line $\frac{x - 2}{\alpha} = \frac{y - 2}{-5} = \frac{z + 2}{2}$ lies on the plane $x + 3y - 2z + \beta = 0$. Then $(\alpha + \beta)$ is equal to _________.
If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity $\frac{1}{4\pi\epsilon_0}\frac{e^2}{hc}$ has dimensions of:
A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom simultaneously. The height of the building is:
Negation of the statement \((p \lor r) \implies (q \lor r)\) is :
If \( S = \frac{7}{5} + \frac{9}{5^2} + \frac{13}{5^3} + \frac{19}{5^4} + ... \), then 160 S is equal to _________.
Let \( f(x) \) be a cubic polynomial with \( f(1) = -10 \), \( f(-1) = 6 \), and has a local minima at \( x = 1 \), and \( f'(x) \) has a local minima at \( x = -1 \). Then \( f(3) \) is equal to _________.
If \( \int \frac{\sin x}{\sin^3 x + \cos^3 x} dx = \alpha \log_e |1 + \tan x| + \beta \log_e |1 - \tan x + \tan^2 x| + \gamma \tan^{-1} \left( \frac{2 \tan x - 1}{\sqrt{3}} \right) + C \), when C is a constant of integration, then the value of \( 18(\alpha + \beta + \gamma^2) \) is _________.
The distance of the point \((-1, 2, -2)\) from the line of intersection of the planes \(2x + 3y + 2z = 0\) and \(x - 2y + z = 0\) is :
The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is :
The number of solutions of the equation \(32^{\tan^2 x} + 32^{\sec^2 x} = 81\), \(0 \le x \le \frac{\pi}{4}\) is :
The domain of the function \(f(x) = \sin^{-1} \left( \frac{3x^2 + x - 1}{(x - 1)^2} \right) + \cos^{-1} \left( \frac{x - 1}{x + 1} \right)\) is :
If \( \alpha = \lim_{x \to \pi/4} \frac{\tan^3 x - \tan x}{\cos(x + \frac{\pi}{4})} \) and \( \beta = \lim_{x \to 0} (\cos x)^{\cot x} \) are the roots of the equation, \( ax^2 + bx - 4 = 0 \), then the ordered pair \( (a, b) \) is :
Let \( f \) be any continuous function on \( [0, 2] \) and twice differentiable on \( (0, 2) \). If \( f(0) = 0, f(1) = 1 \) and \( f(2) = 2 \), then :
If \( [x] \) is the greatest integer \( \le x \), then \( \pi^2 \int_{0}^{2} \left( \sin \frac{\pi x}{2} \right) (x - [x])^{[x]} dx \) is equal to :
If \( \frac{dy}{dx} = \frac{2^x y + 2^y \cdot 2^x}{2^x + 2^{x+y} \log_e 2}, y(0) = 0 \), then for \( y = 1 \), the value of \( x \) lies in the interval :
If \( y \frac{dy}{dx} = x \left[ \frac{\phi(y^2/x^2)}{\phi'(y^2/x^2)} + \frac{y^2}{x^2} \right], x>0, \phi>0, \) and \( y(1) = -1 \), then \( \phi\left(\frac{y^2}{4}\right) \) is equal to :