Login/Sign Up
CBSE Class 10 Lakhmir Singh
Lakhmir Singh

When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the photocurrent is $\frac{\mathrm{V}_{0}}{2} .$ When the surface is illuminated by monochromatic light of frequency $\frac{\mathrm{v}}{2}$, the stopping potential is $-\mathrm{V}_{0}$. the threshold frequency for photoelectric emission is:
(A) $\frac{3 \mathrm{v}}{2}$
(B) $2 \mathrm{v}$
(C) $\frac{4}{3} \mathrm{v}$
(D) $\frac{5 \mathrm{v}}{3}$

Correct option is (A) $\frac{3 \mathrm{v}}{2}$ $\begin{array}{l} \mathrm{hv}=\mathrm{W}+\frac{\mathrm{v}_{0}}{2} \mathrm{e} \\ \frac{\mathrm{h} v}{2}=\mathrm{W}+\mathrm{v}_{0} \mathrm{e}...

read more

Identify the invalid equation.

(A) $\vartriangle $H = $\sum $H products - $\sum $Hreactants (B) $\vartriangle $H = $\vartriangle $U + P$\vartriangle $V (C) $\vartriangle $ HOreaction = $\sum $H0(product bonds) - $\sum...

read more

In balanced metre bridge, the resistance of bridge wire is $0.1 \Omega / \mathrm{cm}$. Unknown resistance ‘ $\mathrm{X}$ ‘ is connected in left gap and $6 \Omega$ in right gap, null point divides the wire in the ratio $2: 3$. Find the current drawn from the battery of $5 \mathrm{~V}$ having negligible resistance.
A) $1 \mathrm{~A}$
B) $1.5 \mathrm{~A}$
C) $2 \mathrm{~A}$
D) $5 \mathrm{~A}$

Answer is (A) $\frac{\ell_{1}}{\ell_{2}}=\frac{2}{3}=\frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}$ Now $\quad \mathrm{v}_{1}+\mathrm{v}_{2}=\mathrm{v}=5 \mathrm{~V} \quad \mathrm{QV}=\mathrm{IR}$ For...

read more

Two particles $\mathrm{X}$ and $\mathrm{Y}$ having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii ‘ $\mathrm{r}_{1}$ ‘ and ‘ $r_{2}$ ‘ respectively. The ratio of the mass of $X$ to that of $Y$ is
A) $\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}$
B) $\sqrt{\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}}$
C) $\left[\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}\right]^{2}$
D) $\left[\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}\right]^{2}$

Answer is (A) The force acting on the particle inside magnetic field is $F_{B}=q v B \sin \theta$ This provides the necessary centripetal force $F_{c}=\frac{m v^{2}}{r}$ $\begin{array}{l} \therefore...

read more

When light of wavelength ‘ $\lambda$ ‘ is incident on photosensitive surface, the stopping potential is ‘ $\mathrm{V}$ ‘. When light of wavelength ‘ $3 \lambda$ ‘ is incident on same surface, the stopping potential is $\frac{\mathrm{V}^{\prime}}{6}$. Threshold wavelength for the surface is
A) $2 \lambda$
B) $3 \lambda$
C) $4 \lambda$
D) $5 \lambda$

Answer is (D) Using $\frac{\mathrm{hc}}{\lambda}-\phi=\mathrm{eV}$ When, wavelength $\lambda$ is incident on metallic surface, the stopping potential required to stop most energetic electron is...

read more

Two coherent sources ‘P’ and ‘Q’ produce interference at point ‘A’ on the screen where there is a dark band which is formed between $4^{\text {th }}$ bright band and $5^{\text {th }}$ bright band. Wavelength of light used is $6000 \AA$. The path difference between PA and QA is
A) $1.4 \times 10^{-4} \mathrm{~cm}$
B) $2.7 \times 10^{-4} \mathrm{~cm}$
C) $4.5 \times 10^{-4} \mathrm{~cm}$
D) $6.2 \times 10^{-4} \mathrm{~cm}$

Answer is (B) Here $\Delta \mathrm{x}=\frac{\lambda \delta}{2 \pi}$ For $n=4^{\text {th }}$ dark bone $\delta=(2 n+1) \pi \Rightarrow \delta=(8+1) \pi=9 \pi$ $\begin{array}{l} \Delta x=\frac{\lambda...

read more

A galvanometer of resistance $30 \Omega$ is connected to a battery of emf $2 V$ with $1970 \Omega$ resistance in series. A full scale deflection of 20 divisions is obtained in the galvanometer. To reduce the deflection to 10 divisions, the resistance in series required is
A) $4030 \Omega$
B) $4000 \Omega$
C) $3970 \Omega$
D) $2000 \Omega$

Answer is (C) $\mathrm{i}=\frac{\mathrm{V}}{\mathrm{R}_{\mathrm{eff}}}=\frac{\mathrm{V}}{1790+30}=\frac{2}{2000}=1 \times 10^{-3} \mathrm{~A}=1 \mathrm{~mA}$ This current provides full scale...

read more

Two identical parallel plate air capacitors are connected in series to a battery of e.m.f. ‘V’. If one of the capacitor is completely filled with dielectric material of constant ‘ $K$ ‘, then potential difference of the other capacitor will become
A) $\frac{\mathrm{K}}{\mathrm{V}(\mathrm{K}+1)}$
B) $\frac{\mathrm{KV}}{\mathrm{K}+1}$
C) $\frac{\mathrm{K}-1}{\mathrm{KV}}$
D) $\frac{\mathrm{V}}{\mathrm{K}(\mathrm{K}+1)}$

Answer is (B) When capacitors are connected is series $C_{e q}=\frac{C_{1} C_{2}}{C_{1}+C_{2}}$ and the potential areas plates of capacitors is given by $\mathrm{V}=\frac{\mathrm{Q}}{\mathrm{C}}$ If...

read more

The maximum frequency of transmitted radio waves above which the radio waves are no longer reflected back by ionosphere is – $\mathrm{N}=$ maximum electron density of ionosphere, $\mathrm{g}=$ acceleration due to gravity)
A) $\mathrm{gN}$
B) $\mathrm{gN}^{2}$
C) $g \sqrt{N}$
D) $\mathrm{g}^{2} \mathrm{~N}^{2}$

Answer is (C) For ionosphere, the maximum frequency of radio waves that can be reflected back is given by $g \sqrt{N}$. Where $N$ is maximum electron density of ionosphere and $g$ is acceleration...

read more

Light of wavelength ‘ $\lambda$ ‘ which is less than threshold wavelength is incident on a photosensitive material. If incident wavelength is decreased so that emitted photoelectrons are moving with same velocity then stopping potential will
A) increase
B) decrease
C) be zero
D) become exactly half

Answer is (A) According to photoelectric equation, $\frac{\mathrm{hc}}{\lambda}-\phi=\mathrm{E} \quad$ where $\mathrm{E}=\frac{\mathrm{p}^{2}}{2 \mathrm{~m}}(\mathrm{~K} . \mathrm{E})$ If $E$ is...

read more

Three parallel plate air capacitors are connected in parallel. Each capacitor has plate area $\frac{‘ A^{\prime}}{3}$ and the separation between the plates is ‘ $d$ ‘, ‘ $2 d$ ‘ and ‘ 3 d’ respectively. The equivalent capacity of combination is $\left(\epsilon_{0}=\right.$ absolute permittivity of free space)
A) $\frac{7 \in_{0} A}{18 \mathrm{~d}}$
B) $\frac{11 \in_{0} A}{18 \mathrm{~d}}$
C) $\frac{13 \in_{0} A}{18 \mathrm{~d}}$
D) $\frac{17 \in_{0} A}{18 \mathrm{~d}}$

Answer is (B) $\mathrm{C}=\mathrm{QV} \quad$ and $\mathrm{C}=\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}$ As given $\mathrm{C}_{1}=\frac{\varepsilon_{0} \cdot \mathrm{A}}{3 \mathrm{~d}} ; \quad...

read more

Interference fringes are produced on a screen by using two light sources of intensities ‘I’ and ‘9I’. The phase difference between the beams is $\frac{\pi}{2}$ at point $\mathrm{P}$ and $\pi$ at point $\mathrm{Q}$ on the screen. The difference between the resultant intensities at point $\mathrm{P}$ and $\mathrm{Q}$ is
A) $2 \mathrm{I}$
B) $4 \mathrm{I}$
C) $6 \mathrm{I}$
D) $8 \mathrm{I}$

Answer is (C) At point $\mathrm{P}$, resultant intensity of interfering wave is $\left(\mathrm{I}_{\mathrm{p}}\right)_{\mathrm{res}}=\mathrm{I}_{1}+\mathrm{I}_{2}+2 \sqrt{\mathrm{I}_{1}...

read more

An electron of mass ‘ $\mathrm{m}$ ‘ has de-Broglie wavelength ‘ $\lambda$ ‘ when accelerated through potential difference ‘ $\mathrm{V}^{\prime} .$ When proton of mass ‘ $\mathrm{M}$ ‘, is accelerated through potential difference ‘ $9 \mathrm{~V}$ ‘, the de-Broglie wavelength associated with it will be (Assume that wavelength is determined at low voltage)
A) $\frac{\lambda}{3} \sqrt{\frac{M}{m}}$B) $\frac{\lambda}{3} \cdot \frac{\mathrm{M}}{\mathrm{m}}$
C) $\frac{\lambda}{3} \sqrt{\frac{m}{M}}$
D) $\frac{\lambda}{3} \cdot \frac{m}{M}$

Answer is (C) When electron or any charged particle is accelerated through potential difference $v$, then kinetic energy gained is given by $E=e V$ $\begin{array}{l} E=\frac{1}{2} m...

read more

Alternating current of peak value $\left(\frac{2}{\pi}\right)$ ampere flows through the primary coil of the transformer. The coefficient of mutual inductance between primary and secondary coil is 1 henry. The peak e.m.f. induced in secondary coil is (Frequency of a.c. $=50 \mathrm{~Hz}$ )
A) $100 \mathrm{~V}$
B) $200 \mathrm{~V}$
C) $300 \mathrm{~V}$
D) $400 \mathrm{~V}$

Answer is (B) Peak value of current $I_{0}=1_{\operatorname{nms}} \times\sqrt{2}=\left(\frac{2}{\pi}\right)$ Amp Co-efficient of mutual inductance is $M=1$ horn Induced emf in secondary is given by...

read more

An iron rod is placed parallel to magnetic field of intensity $2000 \mathrm{~A} / \mathrm{m}$. The magnetic flux through the rod is $6 \times 10^{-4} \mathrm{~Wb}$ and its cross-sectional area is $3 \mathrm{~cm}^{2}$. The magnetic permeability of the rod in $\mathrm{Wb} / \mathrm{A}-\mathrm{m}$ is
A) $10^{-1}$
B) $10^{-2}$
C) $10^{-3}$
D) $10^{-4}$

Answer is (C) $\mu=\mathrm{B} \cdot \mathrm{H}=\frac{\phi}{\mathrm{A}} \times \mathrm{H}=\frac{6 \times 10^{-4}}{3 \times 10^{-4}} \times \frac{1}{2 \times 10^{3}}=10^{-3}$

read more

In potentiometer experiment, null point is obtained at a particular point for a cell on potentiometer wire $\mathrm{x} \mathrm{cm}$ long. If the length of the potentiometer wire is increased without changing the cell, the balancing length will (Driving source is not changed)
A) increase
B) decrease
C) not change
D) becomes zero

Answer is (A) For potentiometer, when null point is obtained for a particular cell (EV) at L $\mathrm{cm}$, (say). Whose length is $\mathrm{x} \mathrm{cm} \quad \therefore \mathrm{E}=\mathrm{L}...

read more

A simple pendulum of length ‘ $l$ ‘ has maximum angular displacement ‘ $\theta$ ‘. The maximum kinetic energy of the bob of mass ‘ $\mathrm{m}$ ‘ is (g = acceleration due to gravity)
A) $\operatorname{mg} l(1+\cos \theta)$
B) $\operatorname{mg} l\left(1+\cos ^{2} \theta\right)$
C) $\operatorname{mg} l(1-\cos \theta)$
D) $\mathrm{mg} l(\cos \theta-1)$

Answer is (C) When bob is at rest, the pendulum has only potential energy which is given as $\mathrm{P.E}=\mathrm{mg} \ell$. When bob displaces by small angler displacement $\theta$, the pendulum...

read more

Let ‘ $\mathrm{M}$ ‘ be the mass and ‘ $\mathrm{L}$ ‘ be the length of a thin uniform rod. In first case, axis of rotation is passing through centre and perpendicular to the length of the rod. In second case axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case is
A) 1
B) $\frac{1}{2}$
C) $\frac{1}{4}$
D) $\frac{1}{8}$

Answer is (B) M.I of rod whose axis of rotation is passing through center and perpendicular to the plane of rod is $\mathrm{I}=\frac{\mathrm{ML}^{2}}{12} \quad$ and $\quad...

read more

A black rectangular surface of area ‘A’ emits energy ‘E’ per second at $27^{\circ} \mathrm{C}$. If length and breadth are reduced to $\frac{1}{3}$ rd of initial value and temperature is raised to $327^{\circ} \mathrm{C}$ then energy emitted per second becomes
A) $\frac{4 \mathrm{E}}{9}$
B) $\frac{7 E}{9}$
C) $\frac{10 \mathrm{E}}{9}$
D) $\frac{16 \mathrm{E}}{9}$

Answer is (D) $\mathrm{E}=\mathrm{e} \sigma \cdot \mathrm{A}\left(\mathrm{T}^{4}-\mathrm{T}_{0}^{4}\right) \text { and } \mathrm{A}=\ell \mathrm{b}$ When $\ell$ and $b$ changes to $\frac{\ell}{3}$...

read more

Two particles of masses ‘ $\mathrm{m}$ ‘ and ‘ $9 \mathrm{~m}$ ‘ are separated by a distance ‘ $\mathrm{r}$ ‘. At a point on the line joining them the gravitational field is zero. The gravitational potential at that point is (G = Universal constant of gravitation)
A) $-\frac{4 \mathrm{Gm}}{\mathrm{r}}$
B) $-\frac{8 \mathrm{Gm}}{\mathrm{r}}$
C) $-\frac{16 \mathrm{Gm}}{\mathrm{r}}$
D) $-\frac{32 \mathrm{Gm}}{\mathrm{r}}$

Answer is (C) For the system described above $\mathrm{U}=\mathrm{m} \cdot \mathrm{V} \quad \therefore \mathrm{V}=\frac{\mathrm{U}}{\mathrm{m}}=\frac{-\mathrm{GM}}{\mathrm{X}}$ Here $M=16...

read more

A progressive wave is represented by $\mathrm{y}=12 \sin (5 \mathrm{t}-4 \mathrm{x}) \mathrm{cm}$. On this wave, how far away are the two points having phase difference of $90^{\circ}$?
A) $\frac{\pi}{2} \mathrm{~cm}$
B) $\frac{\pi}{4} \mathrm{~cm}$
C) $\frac{\pi}{8} \mathrm{~cm}$
D) $\frac{\pi}{16} \mathrm{~cm}$

Answer is (C) $y=12 m(5 t-4 y)$ Comparing in $y=A \sin (w t-k x)$ We have $A=12, w=5$ and $k=4$ $(w t-k x)=$ phase difference $=\frac{\pi}{2}$ $\therefore \quad 5 t-4 x=\frac{\pi}{2}$ When $t=0,4...

read more

Let a steel bar of length ‘ $l$ ‘, breadth ‘b’ and depth ‘d’ be loaded at the centre by a load ‘ $W$ ‘. Then the sag of bending of beam is ( $\mathrm{Y}=$ Young’s modulus of material of steel)
A) $\frac{\mathrm{Wl}^{3}}{2 \mathrm{bd}^{3} \mathrm{Y}}$
B) $\frac{\mathrm{W} l^{3}}{4 \mathrm{bd}^{3} \mathrm{Y}}$
C) $\frac{\mathrm{Wl}^{2}}{2 \mathrm{bd}^{3} \mathrm{Y}}$
D) $\frac{\mathrm{W} l^{3}}{4 \mathrm{bd}^{2} \mathrm{Y}}$

Answer is (B) The sag of bending of beam is given by. $\delta=\frac{W L^{3}}{48 \mathrm{YI}} \quad$ Where $W$ is load, $L$ is length, $Y$ is young's modules and $I$ is $\frac{b d^{3}}{12}$ (area...

read more

A disc of radius ‘ $R$ ‘ and thickness $\frac{\mathrm{R}}{6}$ has moment of inertia ‘I’ about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is
A) $\frac{\mathrm{I}}{5}$
B) $\frac{\mathrm{I}}{6}$
C) $\frac{\mathrm{I}}{32}$
D) $\frac{\mathrm{I}}{64}$

Answer is (A) Volume of disc is $\mathrm{A} \cdot \mathrm{d}=\pi \cdot \mathrm{R}^{2} \times \frac{\mathrm{R}}{6}=\frac{\mathrm{R}^{3} \times \pi}{6}$ Moment of inertia of disc is...

read more

In a capillary tube of radius ‘ $R$ ‘, a straight thin metal wire of radius ‘ $r$ ‘ $(R>r)$ is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is $[\mathrm{T}=$ surface tension of water, $\rho=$ density of water, $\mathrm{g}=$ gravitational acceleration $]$
A) $\frac{\mathrm{T}}{(\mathrm{R}+\mathrm{r}) \rho \mathrm{g}}$
B) $\frac{\mathrm{R} \rho \mathrm{g}}{2 \mathrm{~T}}$
C) $\frac{2 T}{(R-r) \rho g}$
D) $\frac{(\mathrm{R}-\mathrm{r}) \rho \mathrm{g}}{\mathrm{T}}$

Answer is (C) $\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta}{\rho g(\mathrm{R}-\mathrm{r})}$ For $\cos \theta=0, \mathrm{~h}=\frac{2 \mathrm{~T}}{\rho g(\mathrm{R}-\mathrm{r})}$

read more

The bob of a simple pendulum performs S.H.M. with period ‘ $\mathrm{T}$ ‘ in air and with period ‘ $\mathrm{T}_{1}$, in water. Relation between ‘ $\mathrm{T}$ ‘ and ‘ $\mathrm{T}_{1}$ ‘ is (neglect friction due to water, density of the material of the bob is $=\frac{9}{8} \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, density of water $=1 \mathrm{~g} / \mathrm{cc}$ )
A) $\mathrm{T}_{1}=3 \mathrm{~T}$
B) $\mathrm{T}_{1}=2 \mathrm{~T}$
C) $\mathrm{T}_{1}=\mathrm{T}$
D) $\mathrm{T}_{1}=\frac{\mathrm{T}}{2}$

Answer is (A) $\mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}_{\mathrm{eff}}}}$ In air $\mathrm{g}_{\text {eff }}=\mathrm{g}$ where as in water $\begin{array}{l} g_{\text {eff...

read more

Two strings $\mathrm{A}$ and $\mathrm{B}$ of same material are stretched by same tension. The radius of the string A is double the radius of string B. Transverse wave travels on string A with speed ‘ $\mathrm{V}_{\mathrm{A}}$ ‘ and on string $B$ with speed ‘ $V_{B}$ ‘. The ratio $\frac{V_{A}}{V_{B}}$ is
A) $\frac{1}{4}$
B) $\frac{1}{2}$
C) 2
D) 4

Answer is (C) The velocity of wave travelling on string is $\begin{array}{l} v=n \lambda=\frac{\lambda}{2 L} \sqrt{\frac{T}{\mu}}=\sqrt{\frac{T}{\mu}} \\ \because \quad n=\frac{1}{2 L}...

read more

A particle moves along a circle of radius ‘r’ with constant tangential acceleration. If the velocity of the particle is ‘ $v$ ‘ at the end of second revolution, after the revolution has started then the tangential acceleration is
A) $\frac{v^{2}}{8 \pi r}$
B) $\frac{v^{2}}{6 \pi r}$
C) $\frac{v^{2}}{4 \pi r}$
D) $\frac{v^{2}}{2 \pi r}$

Answer is (A) Using $v^{2}-u^{2}=2 a s$ and $u=u_{1}$ and $s=4 \pi r$ $\therefore \quad 2 \mathrm{as}=\mathrm{v}^{2} \Rightarrow \frac{\mathrm{v}^{2}}{2...

read more

A mass ‘ $\mathrm{m}_{1}$ ‘ connected to a horizontal spring performs S.H.M. with amplitude ‘$A$’. While mass ‘ $\mathrm{m}_{1}$ ‘ is passing through mean position another mass ‘ $\mathrm{m}_{2}$ ‘ is placed on it so that both the masses move together with amplitude $\mathrm{A}_{1}$, The ratio of $\frac{\mathrm{A}_{1}}{\mathrm{~A}}$ is $\left(\mathrm{m}_{2}<\mathrm{m}_{1}\right)$
A) $\left[\frac{m_{1}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}$
B) $\left[\frac{\mathrm{m}_{1}+\mathrm{m}_{2}}{\mathrm{~m}_{1}}\right]^{\frac{1}{2}}$
C) $\left[\frac{m_{2}}{m_{1}+m_{2}}\right]^{\frac{1}{2}}$
D) $\left[\frac{\mathrm{m}_{1}+\mathrm{m}_{2}}{\mathrm{~m}_{2}}\right]^{\frac{1}{2}}$

Answer is (A) P.E of the oscillating mass is given by $E=\frac{1}{2} m \omega x^{2}=\frac{1}{2} k x^{2} \quad \text { Where } k=m \omega^{2}$ When only black is oscillating, at $x=A$ $E=E_{\max...

read more

Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that pressure is
A) $[\frac{1}{3}]^{rd}$ kinetic energy per unit volume of a gas
B) $[\frac{2}{3}]^{rd}$ kinetic energy per unit volume of a gas
C) $[\frac{3}{4}]^{th}$ kinetic energy per unit volume of a gas
D) $\frac{3}{2}\times$ kinetic energy per unit volume of a gas

Answeris (B) The pressure exerted by the gas on the walls of container is $\mathrm{P}=\mathrm{P}_{0}+\mathrm{P}_{1}+\mathrm{P}_{2}$ i.e. $\quad \mathrm{P}=\mathrm{P}_{0}+\frac{1}{3} 8...

read more

When the observer moves towards the stationary source with velocity, ‘$V_1$’, the apparent frequency of emitted note is ‘$F_1$’. When the observer moves away from the source with velocity ‘$V_1$’, the apparent frequency is ‘$F_2$’. If ‘$V$’ is the velocity of sound in air and $\frac{F_1}{F_2}=2$ then $\frac{V}{V_1}=?$
A) 2
B) 3
C) 4
D) 5

Answer is (B) $\frac{\mathrm{f}_{1}}{\mathrm{f}_{2}}=2, \quad$ Speed of approach $=$ Speed of leaving The apparent frequency of sound level by observer when it is approaching source is given by...

read more

Identify the incorrect statement.

(1) Gangue is an ore contaminated with undesired materials (2) The scientific and technological process used for isolation of the metal from its ore is known as metallurgy (3) Minerals are naturally...

read more

Match the catalyst with the process

Catalyst                                                        Process (i) V2O5                                    (a) the oxidation of ethyne to ethanal (ii) TiCl4+ Al(CH3)3                 (b)...

read more