List of practice Questions

The intercept on the line $y = x$ by the circle $x^2 + y^2 - 2x = 0$ is $AB$. Equation of the circle with $AB$ as diameter is

Which one of the following will be most basic?

Choose the correct option.
This book ............... five sections

A dice is rolled twice and the sum of the numbers appearing on them is observed to be $7$. What is the conditional probability that the number $2$ has appeared at least once ?

Evaluate $\int\limits^{3\pi/4}_{\pi/4} \frac{1}{1+cos\,x}dx$

Evaluate $\int \frac{x^{2}+4}{x^{4}+16}dx.$

If $X$ is a poisson variate such that $P(X = 1) = P(X = 2)$, then $P(X=4)$ is equal to

In an equilateral triangle, the inradius, circumradius and one of the exradii are in the ratio

In how many ways 6 letters be posted in 5 different letter boxes?

If $D$ is the set of all real $x$ such that $1-e^{\left(1/ x\right)-1}$ is positive, then $D$ is equal to

The number of ways of painting the faces of a cube of six different colours is

The sum of the coefficients of $(6\,a-5\,b)^n$, where $n$ is a positive integer, is

$1 \,g$ of $U -235$ is converted into $UF _{6}$. The radioactivity of $UF _{6}$ thus obtained is :

$1 \,L$ of a gas is at a pressure of $10^{-6} \, mm$ of Hg at $25^{\circ} C$. How many molecules are present in the vessel?

$\int\limits^2_0 |1 -x| dx$ is equal to

$\int \frac{\sin 2 x}{\sin ^{4} x+\cos ^{4} x}$ is equal to:

A bag contains $3$ white and $5$ black balls. One ball is drawn at random. Then the probability that it is white is:

A ball is dropped from height h and another from $2h.$ The ratio of time taken by the two balls to reach the ground is

A cube has a side of length $1.2 \times 10^{-2} m$. Calculate its volume.

A passenger in an open car travelling at $30\, m / s$ throws a ball out over the bonnet. Relative to the car the initial velocity of the ball is $20 m / s$ at $60^{\circ}$ to the horizontal. The angle of projection of the ball with respect to the horizontal road will be :

A point source of light is placed $4 \,m$ below the surface of water of refractive index $\frac{5}{3}$. The minimum diameter of a disc, which should be placed over the source, on the surface of water to cut-off all right coming out of water is

A steady current flow in a metallic conductor of non-uniform cross-section. The quantity/quantities remaining constant along the whole length of the conductor is/are

A synthetic rubber which is resistant to the action of oils, gasoline and other solvents is

A toroidal solenoid with an air core has an average radius of $15 \,cm$, area if crosssection $12\, cm ^{2}$ and $1200$ turns. Ignoring the field variation across the cross- section of the toroid, the self-inductance of the toroid is:-

An electron is accelerated under a potential difference of 182 V. The maximum velocity of electron will be (Charge of electron is $1.6 \times 10^{-19}C $ and its mass is $9.1 \times 10^{-31}kg) $