List of practice Questions

The variance of first $20$ natural numbers is

A radiation of energy 'E ' falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (C = Velocity of light)

If $\omega$ is an imaginary cube root of unity, then the value of the determinant $\begin{vmatrix}1+\omega&\omega^{2}&-\omega\\ 1+\omega^{2}&\omega&-\omega^{2}\\ \omega+\omega^2&\omega&-\omega^{2}\end{vmatrix}$

The value of $2 \cot ^{-1} \frac{1}{2}-\cot ^{-1} \frac{4}{3}$ is

A gas can be liquefied at temperature $T$ and pressure $P$ provided

Cold ferrous sulphate solution on absorption of $NO$ develops brown colour due to the formation of

In a certain town, $60\%$ of the families own a car, $30\%$own a house and $20\%$ own both a car and a house. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both ?

The length of a metal wire is $L_1$ when the tension is $T_1$ and $L_2$ when the tension is $T_2$. The unstretched length of the wire is

For all real values of \(a_0, a_1, a_2, a_3\) satisfying \(a_{0}+\frac{a_{1}}{2}+\frac{a_{2}}{3}+\frac{a_{3}}{4}=0\), the equation \(a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}=0\) has a real root in the interval

If the four points with position vectors $-2\hat{i}+\hat{j}+k, \hat{i} +\hat{j}+\hat{k}, \hat{j}-\hat{k}, $ and $\lambda\hat{j}+\hat{k}$ are coplanar, then $\lambda=$

The minimum value of $\cos\,\theta + \sin\,\theta+\frac{2}{\sin\,2\theta}$ for $\theta\,\in \left(0, \pi/2\right)$ is

A fair coin is tossed a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is

The area of the region bounded by the curve $y = x^3$, its tangent at $(1, 1)$ and $x-axis$ is

Consider the following salts: $NaCl,\, HgCl_2,\, Hg_2Cl_2,\, CuCl_2,\, CuCl$ and $AgCl$. Identify the correct set of insoluble salts in water

In a mixture, two enantiomers are found to be present in $85\%$ and $15\%$ respectively. The enantiomeric excess $(e, e)$ is

A simple pendulum of length $L$ swings in a vertical plane. The tension of the string when it makes an angle $\theta$ with the vertical and the bob of mass m moves with a speed $v$ is ($g$ is the gravitational acceleration

If $\sin^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\frac{x^{4}}{8}+...\right)-\frac{\pi}{6}$ where $\left|x\right| < 2$ then the value of $x$ is

Match each disease with its correct type of vaccine.

Which of the following diseases is caused by a protozoan?

If $f \left(x\right)=\begin{vmatrix}1&x&x+1\\ 2x&x\left(x-1\right)&\left(x-1\right)x\\ 3x\left(x-1\right)&x\left(x-1\right)\left(x-2\right)&\left(x-1\right)\end{vmatrix}$ Then $f (100)$ is equal to

A potentiometer wire has length 4 m and resistance $8\, \Omega.$ The resistance that must be connected in series with the wire and an accumulator of e.m.f. 2 V, so as to get a potential gradient 1 mV per cm on the wire is

If potential (in volts) in a region is expressed as $V(x, y , z)$ = $6xy - y + 2yz$, the electric field $(in\, N/C)$ at point $(1, 1, 0)$ is

A stretched string is vibrating in the second overtone, then the number of nodes and anti nodes between the ends of the string are respectively

The terga, sterna and pleura of cockroach body are joined by

A straight conductor $0.1\, m$ long moves in a uniform magnetic field $0.1\, T$. The velocity of the conductor is $15\, m / s$ and is directed perpendicular to the field. The emf induced between the two ends of the conductor is