List of practice Questions

Boiling point of chloroform was raised by $0.323 \,K$, when $0.5143\, g$ of anthracene was dissolved in its $35 \,g$. Molecular mass of anthracene is $(K_b$ for $CHCl_3 = 3.9 \,K \,kg\,, mol^{-1})$

Setting of plaster of Paris is

When two displacements represented by $ y_1 = a \sin \, (\omega \, t)$ and $ y_2 = b \, cos \, ( \omega \, t )$ are superimposed the motion is

The displacement of a particle varies according to the relation $x = 4(\cos \, \pi t + \sin \, \pi t)$. The amplitude of the particle is

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies $?_1$ and $?_2$ and have total energies $E_1$ and $E_2$, respectively. The variations of their momenta p with positions x are shown in the figures. If $\frac{a}{b} = n^{2}$ and $\frac{a}{R} = n, $ then the correct equation(s) is(are)

A disc of radius a and mass m is pivoted at the rim and is set in small oscillation. If a simple pendulum have the same period as that of the disc, then the length of the simple pendulum should be

A catalyst only

For which of the following order of reaction, half-life is independent of initial concentration?

Match items in Column I with those in Column II and select the correct option.

Which of the following groups of algae produces algin?

Which of the following is a member of Order Sphagnales?

The number of $ Cl^{-} $ ions in $ 100\, mL $ of $ 0.001\, M \,HCl $ solution is

A charge $Q$ is to be divided on two objects. The values of the charges on the objects so that the force between the objects can be maximum are

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $\lambda$ are kept parallel to each other. In their resulting electric field, point charges $q$ and $-q$ are kept in equilibrium between them. The point charges are confined to move in the $x$ direction only. If they are given a small displacement about their equilibrium positions, then the correct statements(s) is(are)

An oil drop of $ n $ excess electrons is held stationary under a constant electric field $E$ in Millikan?s oil drop experiment. The density of oil is $ \rho $ . The radius of the drop is

A hemisphere is uniformly charged positively. The electric field at a point on a diameter away from the centre is directed

The number of equivalence relations on the set {1, 2, 3} containing (1, 2) and (2,1) is

Let $ A = \left\{x\in R; x\ge\frac{1}{2}\right\} $ and $ B = \left\{x\in R; x\ge\frac{3}{4}\right\} $ If $ f : A \rightarrow B $ is defined as $ f(x) = x^2 - x + 1 $ , then the solution set of the equation $ f(x) = f^{-1}(x) $ is

Let $f\left(x\right) = sin\left(\frac{\pi}{6}sin\left(\frac{\pi}{2}sin\,x\right)\right)$ for all $x \in R$ and $g\left(x\right) = \frac{\pi}{2}$ $sin\, x$ for all $x \in R$. Let $(fog) (x)$ denote $f(g(x))$ and $(gof) (x)$ denote $g(f(x))$. Then which of the following is (are) true ?

An elliptically shaped ring of dimensions shown in figure just touches, the horizontal surface of a liquid of surface tension S. The force required to pull the ring away from the liquid surface is

$ Let \,A = [a_{ij}]_{mxn} $ be a matrix such that $ a_{ij} = 1,\forall $ $ i,j. $ Then,

Which of the following values of $\alpha$ satisfy the equation. $\begin{vmatrix}\left(1+\alpha\right)^{2}&\left(1+2\alpha \right)^{2}&\left(1+3\alpha \right)^{2}\\ \left(2+\alpha \right)^{2}&\left(2+2\alpha \right)^{2}&\left(2+3\alpha \right)^{2}\\ \left(3+\alpha \right)^{2}&\left(3+2\alpha \right)^{2}&\left(3+3\alpha \right)^{2}\end{vmatrix} = -648\alpha ?$