List of practice Questions

An object flying in air with velocity $\left(20\hat{i} + 25\hat{j} - 12\hat{k}\right)$ suddenly breaks in two pieces whose masses are in the ratio $1 : 5$. The smaller mass flies off with a velocity $\left(100\hat{i} + 35\hat{j} + 8\hat{k}\right)$. The velocity of the larger piece will be :

A particle starting from rest, moves in a circle of radius 'r'. It attains a velocity of V0 m/s in the $n^{th}$ round. Its angular acceleration will be :-

Pinus seed cannot germinate and establish without fungal association This is because

Select the correct sequence of organs in the alimentary canal of cockroach starting from mouth:

Select the correctly written scientific name of Mango which was first described by Carolus Linnaeus:

Which of the following statements about ozone is correct?

An electron, moving along the x-axis with an initial energy of $100\, eV$, enters a region of magnetic field $\vec{B} \, = (1.5 \times 10^{-3} T) \hat{k}$ at $S$ (See figure). The field extends between $x = 0$ and $x = 2\, cm$. The electron is detected at the point $Q$ on a screen placed $8\, cm$ away from the point $S$. The distance $d$ between $P$ and $Q$ (on the screen) is : (electron's charge = $1.6 \times 10^{-19}C.$ mass of electron = $9.1 \times 10^{-31}kg)$

A series $AC$ circuit containing an inductor $(20\, mH)$, a capacitor $(120 \; \mu F) $and a resistor $(60 \Omega)$ is driven by an AC source of $24\, V/50 \,Hz$. The energy dissipated in the circuit in $60\, s$ is :

Due to increasing air-borne allergens and pollutants, many people in urban areas are suffering from respiratory disorder causing wheezing due t o :

Placentation in which ovules develop on the inner wall of the ovary or in peripheral part, is

Which of the following is against the rules of ICBN?

A clock gains 2 minutes every hour. Then the angle traversed by the second hand in one minute is:

A train 600 meters long is running at a speed of 90 kms/hr. If it crosses a tunnel in one minute, then the length of the tunnel is:

A tree grows at the rate of \(\frac 15^{th}\) of its height annually. By how much height will it grow after 2 years, if its present height is 75 cms?

The perimeter of a rectangle is 60 cms. If its length is twice its breadth, then its area is:

If a, b, c are odd positive integers, then number of integral solutions of a + b + c = 13, is

The sum of the values of x satisfying \(\tan(\frac{\pi}{4}+x)+\tan(\frac{\pi}{4}-x)=2\) in the interval \([0,2\pi]\) is:

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