List of practice Questions

If = $\int x \log\left(1+ \frac{1}{x}\right)dx = f\left(x\right)\log\left(x+1\right)+g\left(x\right)x^{2}+Lx +C$, then

When ${ }^{92} U _{235}$ undergoes fission $0.1 \%$ of its original mass is changed into energy. How much energy is released if $1 \,kg$ of ${ }^{92} U _{235}$ undergoes fission

A resistor of resistance $R$, capacitor of capacitance $C$ and inductor of inductance $L$ are connected in parallel to $A C$ power source of voltage $\epsilon_{0} \sin \omega_{t}$. The maximum current through the resistance is half of the maximum current through the power source. Then value of $R$ is

Two identical charged spheres suspended from a common point by two massless strings of lengths $l$, are initially at a distance $d(d < < l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $v$. Then $v$ varies as a function of the distance $x$ between the spheres, as:

A source of sound $S$ emitting waves of frequency $100\, Hz$ and an observor $O$ are located at some distance from each other. The source is moving with a speed of $19.4\, m s^{-1}$ at an angle of $60^{\circ}$ with the source observer line as shown in the figure. The observor is at rest. The apparent frequency observed by the observer is (velocity of sound in air $330\, ms ^{-1}$ )

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index :

A deuteron of kinetic energy $50 \,keV$ is describing a circular orbit of radius $0.5$ metre in a plane perpendicular to the magnetic field $B$. The kinetic energy of the proton that describes a circular orbit of radius $0.5$ metre in the same plane with the same $B$ is

Find the number of photon emitted per second by a $25$ watt source of monochromatic light of wavelength $ 6600\, ??. What is the photoelectric current assuming $3\%$ efficiency for photoelectric effect ?

Kepler's third law states that square of period of revolution $(T)$ of a planet around the sun, is proportional to third power of average distance $r$ between sun and planet i.e. $T^{2}=K r^{3}$ here $K$ is constant. If the masses of sun and planet are $M$ and $m$ respectively then as per Newton's law of gravitation force of attraction between them is $F=\frac{G M m}{r^{2}}$ here $G$ is gravitational constant. The relation between $G$ and $K$ is described as

The approximate depth of an ocean is $2700\, m$. The compressibility of water is $45.4 \times 10^{-11} Pa ^{-1}$ and density of water is $10^{3} kg / m 3 .$ What fractional compression of water will be obtained at the bottom of the ocean?

Two spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting of ice in the larger sphere is $25$ minute and for smaller one is $16$ minute, the ratio of thermal conductivities of the materials of larger spheres to that of smaller sphere is

Formation of polyethylene from calcium carbide takes place as follows $ CaC _{2}+2 H _{2} O \longrightarrow Ca ( OH )_{2}+ C _{2} H _{2}$ $C _{2} H _{2}+ H _{2} \longrightarrow C _{2} H _{4} $ $ nC _{2} H _{4} \longrightarrow\left(- CH _{2}- CH _{2}-\right) n$ The amount of polyethylene obtained from $64.1\, kg$ of $CaC _{2}$ is

A compound of Xe and F is found to have 53.5% of Xe. What is oxidation number of Xe in this compound ?

The hypothetical complex chloropentaamminecobalt (III) chloride can be represented as

Nucleotides are joined together by between $ 5' $ and $ 3' $ carbon atoms of pentose sugar

$1.25\, g$ of a sample of $Na _{2} CO _{3}$ and $Na _{2} SO _{4}$ is dissolved in $250\, ml$ solution. $25 ml$ of this solution neutralises $20\, ml$ of $0.1\, N\, H _{2} SO _{4}$. The $\%$ of $Na _{2} CO _{3}$ in this sample is

Which of the following has two stereoisomers?

The degree of dissociation of $P C l_{5}(\alpha)$ obeying the equilibrium $PCl _{5} \rightleftharpoons PCl _{3}+ Cl _{2}$ is related to the equilibrium pressure by

The normality of $26\%$ (wt/vol) solution of ammonia (density $= 0.855$ ) is approximately :

$CH _{3} C \equiv CCH _{3} \xrightarrow{H 2 / P t} A \xrightarrow{D_{2} / P t} B$ The compounds $A$ and $B$, respectively are

Which of the following compound has all the four types $\left(1^{\circ}, 2^{\circ}, 3^{\circ}\right.$ and $\left.4^{\circ}\right)$ of carbon atoms?

A light meter measures the intensity \( I \) of the light falling on it. Theory suggests that this varies as the inverse square of the distance \( d \). Which graph of the results supports this theory?

A long string with a charge of a per unit length passes through an imaginary cube of edge L.
The maximum possible flux of electric field through the cube will be

It takes 16 min to boil some water in an electric kettle. Due to some defect, it becomes necessary to remove 10% turns of heating coil of the kettle. After repairs, how much time will it take to boil the same mass of water?

The magnetic moment of atomic neon (in units of Bohr's magnetron) is