List of practice Questions

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. $\begin{vmatrix}\left(1+\alpha\right)^{2}&\left(1+2\alpha \right)^{2}&\left(1+3\alpha \right)^{2}\\ \left(2+\alpha \right)^{2}&\left(2+2\alpha \right)^{2}&\left(2+3\alpha \right)^{2}\\ \left(3+\alpha \right)^{2}&\left(3+2\alpha \right)^{2}&\left(3+3\alpha \right)^{2}\end{vmatrix} = -648\alpha ?$

A spherical shell of radius $10\, cm$ is carrying a charge $q$. If the electric potential at distances $5 \, cm, 10 \, cm$ and $15 \, cm$ from the centre of the spherical shell is $V_1, V_2$ and $V_3$ respectively, then respectively, then

1000 similar electrified rain drops merge together into one drop so that their total charge remains unchanged. The electric energy gets increased by

A proton is released from rest in a uniform electric field of magnitude $8.0\times 10^{4}\, V/m$, directed along positive $x$-axis. The proton undergoes a displacement of $0.30\,m$ in the direction of the field. What is the change in electric potential of the proton as a result of this displacement?

A hexagon of side $8 \,cm$ has a charge $4\,\mu\,C$ at each of its vertices. The potential at the centre of the hexagon is

The enolic form of ethyl acetoacetate as below has

$CN^-$ ion is an ambident nucleophile. Nucleophiles are electron rich species.

$ CH_3 - CH_2 - CH = CH_2 + HBr$ $ \xrightarrow{ROOR\text{(peroside)}} \underset{\text{Major}}{(X)} + \underset{\text{Minor}}{(Y)}$ $X$ and $Y$ respectively are

At Curie point, a ferromagnetic material becomes

Consider the circular loop having current $i$ and with central point $O$. The magnetic field at the central point $O$ is

The variation of magnetic susceptibility with the temperature of a ferromagnetic material can be ploted as

If $pK_a$ of acetic acid and $pK_b$ of ammonium hydroxide are $4.76$ each. The $pH$ of ammonium acetate is

The %yield of ammonia as a function of time in the reaction $N_{2}\left(g\right) + 3H_{2}\left(g\right) {\rightleftharpoons} 2NH_{3}\left(g\right), ?H < 0$ at $\left(P, T_{1}\right)$ is given below. If this reaction is conducted at $\left(P, T_{2}\right)$, with $T_{2} > T_{1}$, the %yield of ammonia as a function of time isrepresented by -

For a reaction, $C_{(s)}+C O_{2}(g) \rightarrow 2 C O_{(g)}$; the partial pressure of $C O_{2}$ and $C O$ are $4$ and $8$ atm, respectively. $K_{p}$ for the reaction is

What is the minimum volume of water required to dissolve $ 1\, g $ of calcium sulphate at $ 298 K? K_{sp} $ for $ CaSO_{4} $ is $ 9.0 \times 10^{-6} $ . (Molar mass of $ CaSO_4 = 136 \,g \,mol ^{-1}) $

What will be the $pH$ of $0.1\, M$ ammonium acetate solution? $\left(p K_{a}=p K_{b}=4.74\right)$

In which of the following case $K_p = K_c$ ?

A vessel of one litre capacity containing $1$ mole of $SO_3$ is heated till a state of equilibrium is attained. $ {2SO3_{(g)} <=> 2SO2_{(g)} + O2_{(g)}}$ At equilibrium, $0.6 \,moles$ of $SO_2$ had formed. The value of equilibrium constant is

When $0.100$ mole of ammonia, $NH_3$ is dissolved in sufficient water to make $1.0 \,L$ of solution, the solution is found to have a hydroxide ion concentration of $1.34 \times 10^{-3}\, M$. Calculate $K_b$ for ammonia.