List of practice Questions

A circle of maximum possible size is cut from a square sheet. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be area of the final square?

A class has n students, we have to form a team of the students including at least two students and also excluding at least two students. The number of ways of forming the team is

Evaluate the integral. \(\displaystyle\int^{3}_{2}x^4dx\)

The differential equation of all non vertical lines in a plane is:

The function given by: x^myⁿ = (x + y)^m+n is:

The sum of odd integers from 1 to 2001 is:

Area bounded by\( y=x^3 , y=8\) and \(x=0\) is

Let the following system of equations kx + y + z =1x + ky + z = kx + y + kz=k2Has no solution. Find

The average age of 20 students in a class is 15 years. If the teacher’s age is including, the average increases by 1. What is the teacher’s age?

You have a 9 x 9 x 9 cm box. How many cubes of side 5 cm will you be able to fit inside it?

A determinant is chosen at random from the set of order 2 with elements 0 or 1 only. The probability that the determinant chosen non zero is

A magnet of total magnetic moment $10^{-2} \hat{i} \; A-m^2$ is placed in a time varying magnetic field, $B \hat{i} (\cos t\omega t)$ where $B = 1 $Tesla and $\omega = 0.125 \; rad/s$. The work done for reversing the direction of the magnetic moment at $t = 1$ second, is :

Poly-$\beta$-hydroxybutyrate-co-$\beta$ hydroxyvalerate (PHBV) is a copolymer of___.

The correct statement regarding the given Ellingham diagram is:

When neutral or faintly alkaline KMnO4 is treated with potassium iodide, iodide ion is converted into 'X'. 'X' is -

Both, autogamy and geitonogamy are prevented in

Conjugate base for Bronsted acids $H_2O$ and $HF$ are:

Select the correct option.

The distance covered by a particle undergoing SHM in one time period is (amplitude = A) :

The reaction in which $2$ molecules of chlorobenzene reacts with metallic sodium in presence of dry ether forming diphenyl is an example of,

Two small drops of mercury, each of radius $R$, coalesce to form a single large drop. The ratio of the total surface energies before and after the change is

What is the atomicity of aluminium phosphate?

In moving coil galvanometer, strong horse shoe magnet of concave shaped pole pieces is used to

Orbital having 3 angular nodes and 3 total nodes is :-

The given figure represents the Malpighian body. Identify the labelled parts $A$ to $D$ and select the correct option