List of practice Questions

The probability that atleast one of the events $A$ and $B$ occurs is $ 0.5 $ . If $A$ and $B$ occur simultaneously with probability $ 0.2, $ then $ P({{A}^{c}})+P({{B}^{c}}) $ is equal to

Let $ f(x)=\frac{k}{1+{{x}^{2}}},\,-\infty < x < \infty $ be the probability density of a random variable. Then, $k$ equals to

The sum of $n$ terms of the series $ \frac{3}{{{1}^{2}}{{.2}^{2}}}+\frac{5}{{{2}^{2}}{{.3}^{2}}}+\frac{7}{{{3}^{2}}{{.4}^{2}}}+..... $ is equal to

What is the resonance frequency of a driven $LCR$ oscillator?

A cheetah, weighing $150 \,kg$, chases a deer, weighing $30 \, kg$, in a straight path. The speed of the cheetah is $20 \,m / s$ and that of the deer is $25 m / s$. The approximate speed of the centre of mass of the pair is

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It.

Consider the following reaction ${ ->[H_2][pd-BaSO_4] 'A'}$ The product 'A' is -

The line $x=2 y$ intersects the ellipse $\frac{x^{2}}{4}+y^{2}=1$ at the points $P$ and $Q$. The equation of the circle with $P Q$ as diameter is

If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then the value of $x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}}$ is equal to

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is $ 200\, kg\, m^2 $. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of $ 1 \,ms^{-1} $ relative to the ground. Time taken by the man to complete one revolution is

The potential energy of a particle in a force field is $ U=\frac{A}{r^2}-\frac{B}{r}$ where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is

Biolistics (gene-gun) is suitable for

The number of integer values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer, is

In a slide callipers, $(m + 1)$ number of vernier divisions is equal to m number of smallest main scale divisions. If d unit is the magnitude of the smallest main scale division, then the magnitude of the vernier constant is

Let $A$ and $B$ be two events with $P\left(A^{c}\right)=0.3, P\left(B\right)=0.4$ and $P\left(A\cap B^{c}\right)=0.5$ Then $P\left(B|A \cup B^{c} \right) $ is equal to

Rolle's theorem is applicable in the interval $[-2, 2]$ for the function

If $\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)$, then

The incentre of an equilateral triangle is $(1,1)$ and the equation of one side is $3 x+4 y+3=0$ Then, the equation of the circumcircle of the triangle is

The coefficient of $x^{10}$ in the expansion of $1+\left(1+x\right)+\ldots+\left(1+x\right)^{20}$ is

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then the probability that balls of both colours are drawn is

If the first ionization energy of $H$ atom is $13.6\, eV$, then the $2^{nd}$ ionization energy of He atom is

Zoospores are absent in

The value of $\displaystyle \lim_{n \to \infty}\frac{\left(n!\right)^{\frac{1}{n}}}{n}$ is

The eccentric angle in the first quadrant of a point on the ellipse $\frac{x^{2}}{10}+\frac{y^{2}}{8}=1$ at a distance $3$ units from the centre of the ellipse is

Multiplication of DNA is called