List of practice Questions

A $20$ Henry inductor coil is connected to a $10$ ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor is :

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$\mathring A $. The radius of the atom in the excited state, it terms of Bohr radius $a_0$, will be : ($h_c$ = $12500\, eV - \mathring A $)

A metal ball of mass $0.1\, kg$ is heated upto $500^{\circ}C$ and dropped into a vessel of heat capacity $800 \; JK^{-1}$ and containing $0.5\, kg$ water. The initial temperature of water and vessel is $30^{\circ}C$. What is the approximate percentage increment in the temperature of the water ? [Specific Heat Capacities of water and metal are, respectively, $4200 \; Jkg^{-1} K^{-1}$ and $400 \; JKg^{-1} K^{-1}$]

If $x = 3 \,tan \,t $ and $y = 3 \,sec \,t$, then the value of $\frac{d^2 y}{dx^2}$ at $t = \frac{\pi}{4}$, is :

Let $f : (-1,1) \to R$ be a function defined by $f(x) = max \{- | x |,- \sqrt{ 1- x^2} \}$. If $K$ be the set of all points at which $f$ is not differentiable, then $K$ has exactly :

In the figure, given that $V_{BB}$ supply can vary from $0$ to $5.0 \,V, V_{CC} = 5\,V, \beta_{dc} = 200, R_B = 100 \,k\,\Omega, R_C=l\, k\Omega$ and $V_{BE}=1.0\, V$, The minimum base current and the input voltage at which the transistor will go to saturation, will be, respectively :

A $27\, mW$ laser beam has a cross-sectional area of $10 \; mm^2$. The magnitude of the maximum electric field in this electromagnetic wave is given by [Given permittivity of space $\in_0 = 9 \times 10^{-12} $ SI units, Speed of light $c = 3 \times 10^8 \; m/s$] :

A test particle is moving in a circular orbit in the gravitational field produced by a mass density \(\rho(r) = \frac{K}{r^2}\). Identify the correct relation between the radius \(R\) of the particle's orbit and it's period \(T\) :

A force acts on a $2\, kg$ object so that its position is given as a function of time as $x = 3t^2 + 5$. What is the work done by this force in first $5$ seconds ?

A satellite of mass $M$ is in a circular orbit of radius $R$ about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be :

A straight rod of length $L$ extends from $x = a$ to $x = L + a$. The gravitational force is exerts on a point mass $'m'$ at $x = 0$, if the mass per unit length of the rod is $A + Bx^2$, is given by:

If $f\left(x\right) = \frac{2- x\cos x}{2+x \cos x}$ and $ g\left(x\right) =\log_{e}x ., \left(x>0\right) $ then the value of integral $\int\limits^{\frac{\pi}{4}}_{-\frac{\pi}{4}} g\left(f\left(x\right)\right)dx $ is :

If $ \int \frac{\sqrt{1-x^{2}}}{x^{4}} dx = A \left(x\right)\left(\sqrt{1-x^{2}}\right)^{m} + C $ , for a suitable chosen integer $m$ and a function $A(x)$, where $C$ is a constant of integration then $(A(x))^m$ equals :

Let $N$ be the set of natural numbers and two functions $f$ and $g$ be defined as $f,g : N \to N$ such that : $f(n) = \begin{cases} \frac{n+1}{2} & \quad \text{if } n \text{ is odd}\\ \frac{n}{2} & \quad \text{if } n \text{ is even} \end{cases}$ and $g(n) = n-(-1)^n$. The $fog$ is :

The number of integral values of m for which the equation $(1 + m^2)x^2 - 2(1 + 3m)x + (1 + 8m) = 0$ has no real root is :

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $K_1, K_2, K_3, K_4$ arranged as shown in the figure. The effective dielectric constant K will be :

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of $10\, A$. The magnetic field at point $O$ will be close to :

For the given cyclic process $CAB$ as shown for a gas, the work done is :

Freezing point of a $4\%$ aqueous solution of $X$ is equal to freezing point of $12\%$ aqueous solution of $Y$. If molecular weight of $X$ is $A$, then molecular weight of $Y$ is :

The term independent of x in the expansion of $\bigg(\frac{1}{60} - \frac{x^8}{81}\bigg). \bigg(2x^2 - \frac{3}{x^2}\bigg)^6$ is equal to:

Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas ? (Assume non-expansion work is zero)

The IUPAC name of the following compound is:

Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures $T_1$ and $T_2 (T_1 < T_2)$. The correct graphical depiction of the dependence of work done $(w)$ on the final volume $(V)$ is:

Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?

Considering only the principal values of inverse functions, the set $A = \{ x \ge 0 : \tan^{-1} (2x) + \tan^{-1} (3x) = \frac{\pi}{4} \}$