List of practice Questions

The only integral root of the equation $ \begin{vmatrix}2-y&2&3\\ 2&5-y&6\\ 3&4&10-y\end{vmatrix} =0 $ is

A length-scale $(\ell)$ depends on the permittivity $(\varepsilon)$ of a dielectric material, Boltzmann constant $\left( k _{ B }\right)$, the absolute temperature $(T)$, the number per unit volume $(n)$ of certain charged particles, and the charge $(q)$ carried by each of the particles. Which of the following expressions (s) for $\ell$ is (are) dimensionally correct?

The structure of $XeF_2$ and $NH_3$ respectively are

$ DDT $ is

Three particles $ P, Q $ and $ R $ are at rest at the vertices of an equilateral triangle of side $ s $ . Each of the particles starts moving with constant speed $ v \,ms^{-1}. P $ is moving along $ PQ, Q $ along $ QR $ and $ R $ along $ RP $ . The particles will meet each other at time $ t $ given by

The rate constant of the reaction $2N_2O_5 \rightarrow 4NO_2 + O_2$ at $300\,K$ is $3 \times 10^{-5}\,s^{-1}$. If the rate of the reaction at the same temperature is $2.4 \times 10^{-5}\, mol\, dm^{-3}\, s^{-1}$, then the molar concentration of $N_2O_5$ is

In the following network potential at $'O'$

Variation of resistance of the conductor with temperature is as shown .The temperature co-efficient $(\alpha)$ of the conductor is

A 220 volt - 1000 watt bulb is connected across a 110 volt mains supply. The power consumed will be

Three resistances $P, Q, R$ each of $2\, \Omega$ and an unknown resistance $S$ form the four arms of a Wheatstone bridge circuit. When a resistance of $6\, \Omega$ is connected in parallel to $S$ the bridge gets balanced. What is the value of $S$ ?

In a potentiometer, auniform potential gradient of $ 0.8 \,V \,m^{-1} $ is maintained across its $ 10 \,m $ wire. The potential difference across two points on the wire located at $ 0 \,m \,65\, cm $ and $ 2 \,m\, 45 \,cm $ is

Mobility of free electrons in a conductor is

The degree of dissociation $(\alpha)$ of a weak electrolyte $A_xB_y$ is related to van?t Hoff factor $(i)$ by the expression

If glucose of $36\, g$ weight is dissolved in $2 \,kg$ of $H_2O$ then, change in boiling point $(\Delta T_b)$ at 1.013 bar will be ($K_b$ for ${H_2O}$ is ${ 0.52\, K\, kg \,mol^{-1}}$)

Concentrated aqueous sulphuric acid is $98 \% \,H _{2} SO _{4}$ by mass and has a density of $1.80 \,g .\, mL ^{-1}$ Volume of acid required to make $1$ litre of $0.1\, M \,H _{2} SO _{4}$ solution is:

With increase in temperature, which one of these changes?

In the plot of $ PV $ vs $ P $ at $ 273\, K $ , positive deviation from ideal behaviour under all pressure conditions is shown by the gas

A particle executing $SHM $ has a maximum speed of $0.5 \, ms^{ -1}$ and maximum acceleration of $1.0 \, ms^{-2}$ The angular frequency of oscillation is

A cylinder of radius $R$, length $L$ and density $\rho$ floats upright in a fluid of density $\rho_0$. If it is given a small downward displacement of amplitude $x$, the time period of resulting undamped oscillation is

Time period of pendulum, on a satellite orbiting the earth, is

In a first order reaction, the time taken for 90% decay is 12 days. The time taken for 99% decay is

Thermal decomposition of $HI$ on gold surface is a

The overall order of a reaction which has the rate expression, rate = $k[A]^{1/2}\, [B]^{1/2}$ is

For a 1st order reaction the unit of rate constant is

Inversion of cane sugar by acid hydrolysis in excess of water is