List of practice Questions

In a building there are $15$ bulbs of $45\, W, 15$ bulbs of $100\, W$, $15$ small fans of $10\, W$ and $2$ heaters of $1\, kW$. The voltage of electric main is $220\, V$. The minimum fuse capacity (rated value) of the building will be:

A radioactive nucleus decays by two different processes. The half life for the first process is $10 s$ and that for the second is $100 s$. the effective half life of the nucleus is close to:

The activity of a radioactive sample falls from $700\, s^{-1}$ to $500\, s^{-1}$ in 30 minutes. Its half life is close to :

Two gases - argon (atomic radius $0.07\, nm$, atomic weight $40$) and xenon (atomic radius $0.1\, nm$, atomic weight $140$) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to :

A wire of length $L$ and mass per unit length $6.0 \times 10^{-3} \,kgm^{-1}$ is put under tension of $540\, N$. Two consecutive frequencies that it resonates at are: $420\, Hz$ and $490 \,Hz$. Then $L$ in meters is :

A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{i}}{\sqrt{2}},$ with its polarization along the direction $\hat{k}.$ The correct form of the magnetic field of the wave would be (here $B_0$ is an appropriate constant):

A vessel of depth $2\,h$ is half filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$ The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

Planet $A$ has mass $M$ and radius $R$. Planet $B$ has half the mass and half the radius of Planet $A$. If the escape velocities from the Planets $A$ and $B$ are $v_A$ and $v_B$, respectively, then $\frac{v_{A}}{v_{B}}=\frac{n}{4}$. The value of $n$ is :

Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ Ls carved out of it, as shown, the ratio $\frac{\left|\overrightarrow{E_{A}}\right|}{\left|\overrightarrow{E_{B}}\right|}$ of magnitude of electric field $\overrightarrow{E_{A}}$ and $\overrightarrow{E}_{B}$ respectively, at points A and B due to the remaining portion is :

A rod of length $L$ has non-uniform linear mass density given by $\rho\left(x\right)=a+b\left(\frac{x}{L}\right)^{2},$ where a and b are constants and $0 \le x \le L.$ The value of $x$ for the centre of mass of the rod is a t :

A bead of mass \(m\) stays at point \(P(a, b)\) on a wire bent in the shape of a parabola \(y=4 c x^{2}\) and rotating with angular speed \(\omega\) (see figure).

The value of \(\omega\) is (neglect friction) :

Consider two solid spheres of radii $R, = 1m, \,R_2 = 2m$ and masses $M_1$ and $M_2$, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $\frac{m_{1}}{m_{2}}$ is :

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : ($1 \,HP = 746 \,W, \,g = 10\, ms^{-2}$ )

The correct order of the spin-only magnetic moments of the following complexes is : $(I)\, [Cr(H_2O)_6]Br_2$ $(II)\, Na_4[Fe(CN)_6]$ $(III)\, Na_3[Fe(C_2O_4)_3] (\Delta_0 > P)$ $(IV)\, (Et_4N)_2[CoCl_4]$

The de Broglie wavelength of an electron in the $4^{th}$ Bohr orbit is :

For following reactions ${A ->[700\,K][] Product}$ ${A ->[500\,K][{\text{catalyst}}] Product}$ it was found that the $E_a$ is decreased by 30 k J/mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponential factor is same):

A crystal is made up of metal ions 'M $_{1}$ ' and 'M $_{2}$ ' and oxide ions. Oxide ions. form a ccp lattice structure. The cation '$M_1$ occupies $50 \%$ of octahedral voids and the cation 'M $_{2}$ ' occupies $12.5 \%$ of tetrahedral voids of oxide lattice. The oxidation numbers of ' $M _{1}$ ' and ' $M _{2}$ ' are, respectively:

A diatomic molecule $X_{2}$ has a body-centred cubic (bcc) structure with a cell edge of $300\, pm$. The density of the molecule is $6.17 \,g \,cm ^{-3}$. The number of molecules present in $200\, g$ of $X _{2}$ is (Avogadro constant $\left.\left( N _{ A }\right)=6 \times 10^{23} \,mol ^{-1}\right)$

An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the centres of two nearest octahedral voids in the crystal lattice is

Two particles of equal mass m have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right).$ They collide completely inelastically. The energy lost in the process is :

A capacitor $C$ is fully charged with voltage $V _{0}$. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance $\frac{ C }{2} .$ The energy loss in the process after the charge is distributed between the two capacitors is :

A capacitor is made of two square plates each of side $'a'$ making a very small angle a between them, as shown in figure. The capacitance will be close to :

A galvanometer of resistance $G$ is converted into a voltmeter of range $0-1 V$ by connecting a resistance $R _{1}$ in series with it. The additional resistance that should be connected in series with $R _{1}$ to increase the range of the voltmeter to $-2 V$ will be :

A sample of red ink (a colloidal suspension) is prepared by mixing eosin dye, egg white, $HCHO $ and water. The component which ensures stability of the ink sample is :-