List of practice Questions

A simple harmonic motion is represented by $x(t) = \sin^2 \omega t - 2 \, \cos^2 \, \omega t$ . The angular frequency of oscillation is given by

A vessel of depth $x$ is half filled with oil of refractive index $ {{\mu }_{1}} $ and the other half is filled with water of refractive index $ {{\mu }_{2}} $ The apparent depth of the vessel when viewed from above is

A wave of frequency $500\, Hz$ travels with a speed of $360 \,ms^{-1}$. The distance between two nearest points which are $60^{\circ}$ out of phase is

In neutral or faintly alkaline medium, thiosulphate is quantitatively oxidized by $KMnO_4$ to

Which one of the following has a different crystal lattice from those of the rest?

The crystal field splitting energy for octahedral $(\Delta_0)$ and tetrahedral $(\Delta_t) $complexes is related as

An aircraft is flying at a height of $3400\, m$ above the ground. If the angle subtended at a ground observation point by the aircraft positions $10\,s$ apart is $30^\circ$ then the speed of the aircraft is

Nitrogen shows different oxidation states in the range

The expression for van der Waals equation for the gas law is

Benzoic acid when heated with soda ltme yields

An electric dipole of moment $\overrightarrow {p}$ is placed in a uniform electric field $\overrightarrow {E}$. Then (i) the torque on the dipole is $p \times E$ (ii) the potential energy of the system is $\overrightarrow{p}$.$\overrightarrow{E}$ (iii) the resultant force on the dipole is zero.

Dry air is passed through a solution containing $ 10\,g $ of a solute in $ 90\,g $ of water and then through pure water. The loss in weight of solution is $ 2.5\,g $ and that of pure solvent is $ 0.05 \,g $ . Calculate the molecular weight of the solute.

Glucose on oxidation with bromine water gives

If $ {{E}_{c}}=20\,\,\sin \,{{10}^{5}}\,\pi t $ and $ {{E}_{m}}=10\sin 400\pi t $ it are carrier and modulating signals, the modulation index is

If $T$ is the surface tension of a liquid, the energy needed to break a liquid drop of radius $R$ into $64$ drops is

If the susceptibility of dia, para and ferro magnetic materials are $\chi_{d} , \chi_{p} , \chi_{f} $ respectively, then

In the estimation of sulphur by Carius method, $0.480\, g$ of an organic compound gives $0.699 \,g$ of barium sulphate. The percentage of sulphur in this compound is (Atomic masses: $Ba\, = 137, S = 32, 0 = 16)$

lf the length of a seconds pendulum is increased by 2%, then in a day the pendulum

The increasing order of the density of alkali metals is

The period of oscillation of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{L}{g}}$ , where L is the length of the pendulum and g is the acceleration due to gravity. The length is measured using a meter scale which has $2000$ divisions. If the measured value L is $50\, cm,$ the accuracy in the determination of g is $1.1\%$ and the time taken for 100 oscillations is 100 seconds, what should be the resolution of the clock (in milliseconds) .

The reaction of $ CHC{{l}_{3}} $ and alcoholic $ KOH $ with $ p $ -toluidine gives

When methane is heated with dioxygen in the presence of $Mo_2O_3$ catalyst, the organic product obtained is

Which of the following pairs contain metalloid elements in the periodic table?

Let $A$ and $B$ be two events such that $P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right).$ If $0 < P\left(A\right)< 1$ and $0 < P\left(B\right)< 1$ , then $P\left(A\cup B\right)^{'}=$

If one root of the equation $ l{{x}^{2}}+mx+n=0 $ is $ \frac{9}{2} $ $ (l,m $ and n are positive integers) and $ \frac{m}{4n}=\frac{l}{m}, $ then $ \frac{1}{x}+\frac{1}{y} $ is equal to