List of practice Questions

If the $(2p)^{th}$ term of a H.P. is $q$ and the $(2q)^{th}$ term is $p$, then the $2(p + q)^{th}$ term is-

If $\frac{1}{a} , \frac{1}{b} , \frac{1}{c} $ are in A. P., then $\left(\frac{1}{a} + \frac{1}{b} - \frac{1}{c}\right) \left(\frac{1}{b} + \frac{1}{c} - \frac{1}{a}\right) $ is equal to

If $P_1$ and $P_2$ be the length of perpendiculars from the origin upon the straight lines $x \sec \theta + y cosec \theta = a$ and $x \cos \theta - y \sin \theta = a \cos 2 \theta$ respectively, then the value of $4P_1{^2} + P_2{^2}$.

The angle of intersection of the two circles $x^2 + y^2 - 2x - 2y = 0$ and $x^2 + y^2 = 4$, is

Let $a \in R$ and let $f: R \rightarrow R$ be given by $f(x)=x^{5}-5 x+a$, then

The complex number $z = z + iy$ which satisfies the equation $\left| \frac{z-3i}{z+3i}\right| = 1 $, lies on

The number of all three elements subsets of the set $\{a_1, a_2, a_3 . . . a_n\}$ which contain $a_3$ is

The product of n positive numbers is unity, then their sum is :

An elemental crystal has a density of $8570 \,kg / m ^{3}$. The packing efficiency is $0.68$. The closest distance of approach between neighbouring atom is $2.86 \,?$. What is the mass of one atom approximately?

Consider the following phenols : The decreasing order of acidity of the above phenols is

Consider $\frac{x}{2} + \frac{y}{4} \ge1 $ and $\frac{x}{3} + \frac{y}{2} \le 1 , x ,y \ge0 $. Then number of possible solutions are :

If $A = \begin{bmatrix}1&1\\ 1&1\end{bmatrix}$ then $A^{100}$ :

If $\begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix}$ is square root of identity matrix of order $2$ then

If M. D. is $12$, the value of S.D. will be

In how many ways can a committee of $5$ made out $6$ men and $4$ women containing atleast one woman?

The correct order of magnetic moments (spin only values in B.M.) is:

The number of double bonds in gammexane is :

Two particles $P$ and $Q$ describe S.H.M. of same amplitude a, same frequency $f$ along the same straight line. The maximum distance between the two particles is $a \sqrt{2}$ The initial phase difference between the particle is

Which form coloured salts :

A small block of mass $m$ is kept on a rough inclined surface of inclination $\theta $ fixed in a elevator. The elevator goes up with a uniform velocity $v$ and the block does not slide on the wedge. The work done by the force of friction on the block in time $t$ will be :

An equilateral prism of mass $m$ rests on a rough horizontal surface with coefficient of friction $\mu$.

A horizontal force $F$ is applied on the prism as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is -

A spherically symmetric gravitational system of particles has a mass density $ \rho = \begin{cases} \rho_0 & \text{for} \; r \le R \\ 0 & \text{for} \; r > R \end{cases}$ where $r_0$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $V$ as a function of distance $r (0 < r < \infty) $ from the centre of the system is represented by

The work done in blowing a soap bubble of surface tension $ 0.06 ??Nm^{-1}$ from $2 \,cm$ radius to $5 \,cm$ radius is.

A projectile is fired with a velocity $u$ making an angle $\theta $ with the horizontal. What is the magnitude of change in velocity when it is at the highest point -