Ans: Given refractive index of glass, $\mu=1.5$ Speed of light, $\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ Now, we have the speed of light in glass given by the relation, $$...

### Consider interference between two sources of intensities I and 4I. What will be the intensity at points where phase differences are:

Ans: We know that, $I=a^{2}+b^{2}+2 a b \cos \phi$ Where, $a$ and $b$ are amplitudes of two coherent waves that are having phase difference of $\phi$. Here $a^{2}=I, b^{2}=41$ $$ \begin{array}{l}...

### Write two points of difference between interference and diffraction.

Ans: Some differences between interference and diffraction are the following: \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Interference } & \multicolumn{1}{c|}{ Diffraction } \\ \hline...

### The frequency at which the impedance of the circuit boorens mavimum is

a

b

c

D

Correct option is c $\frac{1}{2 \pi} \sqrt{\frac{1}{L C}-\frac{R^{2}}{L^{2}}}$ Megritude of admittanos $Y=\frac{1}{Z}$ is given by: $$ |\mathrm{Y}|=\frac{\mid \mathrm{H}^{2}...

### State whether the following is true or false: The magnetic field inside a long circular coil carrying current will be parallel straight lines.

The given statement is True.

### Derive an expression for electric potential at a point due to an electric dipole. Discuss the special cases.

Let an electric dipole consist of two equal and opposite point charges $-\mathrm{q}$ at $A$ and $+\mathrm{q}$ at $\mathrm{B}$,separated by a small distance $\mathrm{AB}=2 \mathrm{a}$, with centre at...

### Derive an expression for the potential at a point due to a short dipole. Hence show what will be the potential at an axial and an equatorial point :

Consider an electric dipole $A B$ in which point charges $+q$ and $-q$ are separated by a distance 2l. Let $\mathrm{P}$ be a point on it's axis seperated by a distance r from the dipole's center...

### Find out the wavelength at which a black body at temperature emits maximum energy

Wien's constant $=2 \cdot 9 \times 10^{-3} \mathrm{~m}-\mathrm{K}$ Temperature at which maximum energy is radiated $\mathrm{T}=427^{\circ} \mathrm{C}$ $\therefore \mathrm{T}=427+273=700 \mathrm{~K}$...

### How does concave lens correct myopia?

A Increases the curvature of the eye lens

B Forms the image of the object at the retina

C Decreases the elongation of the eyeball

D All of the above Correct option is (B) Forms the image of the object at the retina

A person with myopia cannot see distant objects clearly since the far point for that person is nearer than infinity. Such a person may see clearly up to a distance of a few meters. In this...

### Above the curie temperature the susceptibility of ferromagnetic substance varies

1. inversely as the square root of absolute temperature

2. directly as the square root of absolute temperature

3. directly as the absolute temperature

4. inversely as the absolute temperature

SOLUTION: Correct option is 4. Above the curie temperature the susceptibility of ferromagnetic substance varies inversely as the absolute temperature. Explanation: $\chi \propto...

### For a transistor, αdc and βdc are the current ratios, then the value of is

1 1.5 2 2.5 Solution: the correct answer is A. 1 $ \frac{{{\beta }_{dc}}-{{\alpha }_{dc}}}{{{\alpha }_{dc}}.{{\beta }_{dc}}}=\frac{\frac{\alpha }{1-\alpha }-\alpha }{\frac{\alpha }{1-\alpha }\times...

### Two identical light waves having phase difference ′ϕ′ propagate in same direction. When they superpose, the intensity of resultant wave is proportional to

A. cos2ϕ/2 B. cos2ϕ/4 C. cos2ϕ/3 D. cos2ϕ Solution: The correct answer is A. cos2ϕ/2 The intensity of two similar light waves propagating in the same direction with a phase difference is as follows:...

### The polarising angle for transparent medium is ′ θ ′ , ′ v ′ is the speed of light in that medium. Then the relation between ′ θ ′ and ′ v ′ is ( c = velocity of light in air)

Solution: The correct answer is B. $ We\,know\,that: $ $ \tan \theta =\frac{{{n}_{2}}}{{{n}_{1}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1) $ $ {{n}_{1}}=1,\,\sin...

### Two parallel plate air capacitors of same capacity ′ C ′ are connected in series to a battery of emf ′ E ′ . Then one of the capacitors is completely filled with dielectric material of constant ′ K ′ . The change in the effective capacity of the series combination is

Solution: the correct answer is D. $ \frac{1}{{{C}_{initial}}}=\frac{1}{C}+\frac{1}{C} $ $ {{C}_{initial}}=\frac{C}{2} $ $ \frac{1}{{{C}_{final}}}=\frac{1}{KC}+\frac{1}{C} $ $...

### In series LCR circuit R=18Ω and impedance is 33Ω. An r.m.s. voltage 220 V is applied across the circuit. The true power consumed in a.c. circuit is

400 W 800 W 600 W 200 W Solution: The correct answer is A 400 W Given : Vrms = 220 V, R = 18Ω and Z = 33Ω We get P = 400W

### The resistivity of potentiometer wire is and its area of cross-section is . If 0.2 ampere current is flowing through the wire, the potential gradient of the wire is:

10−1V/m 10−2V/m 10−3V/m 10−4V/m Solution: The correct answer is 2. 10−2V/m $ We\,have:\, $ $ \rho =40\times {{10}^{-8}}\,\Omega m\, $ $ I=0.2A $ $ A=8\times {{10}^{-6}}{{m}^{2}} $ $...

### A parallel plate air capacitor has capacity ′C′ farad, potential ′V′ volt and energy ′E′ joule. When the gap between the plates is completely filled with dielectric.

Both V and E increase Both V and E decrease V increases, E decreases V decreases, E increases Solution: The correct answer is B Both V and E decrease A dielectric capacitor with parallel plates....

### According to de-Broglie hypothesis, the wavelength associated with moving electron of mass ′m′ is ′λ′e. Using mass energy relation and Planck’s quantum theory, the wavelength associated with photon is ′λ′p. If the energy (E) of electron and photon is same then relation between ′λ′e and ′λ′p is

λp ∝ λe λp ∝ λ2e λp ∝ √λe λp ∝ 1/λe Solution: The correct answer is A λp∝λe λe denotes the wavelength of the electron and λp denotes the wavelength of the proton. $ {{E}_{p}}=hv=\frac{hc}{{{\lambda...

### Out of the following graphs, which graphs shows the correct relation (graphical representation) of LC parallel resonant circuit?

(2) (1) (3) (4) Solution: The correct answer is At resonance ω =1/√LC f = 1/2π√LC The impedance is highest at resonance, and the frequency and current are lowest.

### On a photosensitive material, when frequency of incident radiation is increased by 30% kinetic energy of emitted photo electrons increases from 0.4 eV to 0.9 eV. The work function of the surface is :

1.8 eV 1.4 eV 1 eV 1.267 eV Solution: The solution is D 1.267 eV According to the Einstein's Photoelectric equation:

### The magnetic flux near the axis and inside the air core solenoid of length 60 cm carrying current ′I′ is . Its magnetic moment will be (cross – sectional area of a solenoid is very small as compared to its length, SI unit)

A. 0.25 A B. 0.50 A C. 0.75 A D. 1 A Solution: the correct answer is C. 0.75 A Magnetic induction inside the solenoid is given by: $ B=\frac{{{\mu }_{0}}NI}{L} $ $ Magnetic\,Flux\,: $ $ \phi...

### A bar magnet has length 3 cm, cross-sectional area 2 cm2 and magnetic moment 3Am2. The intensity of magnetisation of bar magnet is

A. 2×105A/m B. 4×105A/m C. 3×105A/m D. 5×105A/m Solution: The correct answer is D. 5×105A/m $ Length\text{...

### In communications system, the process of superimposing a low frequency signal on a high frequency wave is known as

Repeater Modulation Attenuation Demodulation Solution: The correct answer is B. Modulation Modulation is the process of superimposing a signal on a high-frequency wave that functions as a carrier...

### In Young’s double slit experiment, in an interference pattern second minimum is observed exactly in front of one slit. The distance between the two coherent sources is ′d′ and the distance between source and screen is ′D′. The wavelength of light source used is :

A. d2/D B. d2/2D C. d2/3D D. d2/4D Solution: The correct answer is C. d2/3D Because the second minima occur right in front of one of the slits, y = d/2 $ For\text{ }second\text{...

### Two coils P and Q are kept near each other. When no current flows through coil P and current increases in coil Q at the rate 10A/s, the e.m.f. in coil P is 15 mV. When coil Q carries no current and current of 1.8 A flows through coil P, the magnetic flux linked with the coil Q is

1.4 m Wb 2.2 m Wb 2.7 m Wb 2.9 m Wb Solution: The correct solution is C. 2.7 m Wb We have, di/dt = 10 M = E/(di/dt) =15/10 Flux = Mi = 1.5 × 1.8 Flux =2.7mWb

### Photodiode is a device

(A) which is always operated in reverse bias (B) which is always operated in forward bias (C) in which photo current is independent of intensity of incident radiation (D) which may be operated in...

### The magnetic moment of electron due to orbital motion is proportional to (n= principal quantum number)

A.1/n2 B. n2 C.1/n D. n Solution: The correct answer is D. n The magnetic moment of an electron can be expressed as: μ = −(neh)/(4πme) The magnetic moment is directly proportional to the primary...

### If the electron in hydrogen atom jumps from second Bohr orbit to ground state and difference between energies of the two states is radiated in the form of photons. If the work function of the material is 4.2 eV then stopping potential is

2 eV 4 eV 8 eV 6 eV Solution: The correct answer is D 6 eV E = (−13.6/4) + (13.6/1) = 10.2 So stopping potential equals to hv = ϕ(0) + Vs 10.2 − 4.2 = Vs Vs = 6 eV

### When the same monochromatic ray of light travels through glass slab and through water, the number of waves in glass slab of thickness 6 cm is same as in water column of height 7 cm. If refractive index of glass is 1.5 then refractive index of water is :

1.258 1.269 1.310 1.286 Solution: The correct answer is D 1.286 The number of waves on the glass slab equals the number of waves in the water column. μghg = μwhw μw = μghg/hw = 1.5 × 67 μw = 1.286...

### A radioactive element has rate of disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it becomes 2500 disintegrations per minute. The decay constant per minute is

A. 0.2 $ \log _{e}^{2} $ B. 0.5 $ \log _{e}^{2} $ C. 0.6 $ \log _{e}^{2} $ D. 0.8 $ \log _{e}^{2} $ Solution: The correct answer is 0.5 $ \log _{e}^{2} $ $ {{N}_{0}}\lambda =10000 $ $ N\lambda =2500...

### In Fraunhofer diffraction pattern, slit width is 0.2 mm and screen is at 2 m away from the lens. If wavelength of light used in 5000∘A then the distance between the first minimum on either side of the central maximum is (θ is small and measure in radian):

A. 10−2 m B. 10−1 m C. 2×10−2 m D. 2×10−1 m Solution: The correct answer is A. 10−2 m expression for the distance between the first two minimum on the other side is given by: = 2λD/d...

### Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at 40 cm from left end. A 30Ω resistance is connected in series with the smaller of the two resistances, the null point shifts by 20 cm to the right end. The value of smaller resistance in Ω is

12 24 48 36 Solution: The correct answer is B. 24 let the resistance at right be R and at left be r $ \frac{r}{R}=\frac{{{l}_{x}}}{{{l}_{R}}}=\frac{40}{60} $ $ \frac{r+30}{R}=\frac{60}{40} $ $...

### Sensitivity of moving coil galvanometer is ‘s’. If a shunt of (1/8)th of the resistance of galvanometer is connected to moving coil galvanometer, its sensitivity becomes:

s/3 s/6 s/12 s/9 Solution: The correct answer is D. s/9 S = G/8 S = G/(n−1) Now, we get: G/8 = G/(n−1) ⇒ n = 9 When a galvanometer's range is increased nine times, its sensitivity drops to 1/9. S'=...

### When three capacitors of equal capacities are connected in parallel and one of the same capacity is connected in series with its combination. The resultant capacity is 3.75μF. The capacity of each capacitor is

5μF 7μF 6μF 8μF Solution; The correct answer is A. 5μF Let the capacitance be C when connected in parallel combination, C1 = C + C + C = 3C when other was connected in series, we get: 1/Cf = 1/3.75...

### The frequencies for series limit of Balmer and Paschen series respectively are ′v′1 and ′v′3. If frequency of first line of Balmer series is ′v′2 then the relation between ′v′1,′v′2 and ′v′3 is

v1−v2=v3 v1+v3=v2 v1+v2=v3 v1−v3=2v1 Solution: The correct answer is A. v1−v2=v3 $ The\,Balmer\,\lim it\,wavelength\,is: $ $ \frac{1}{{{\lambda }_{1}}}=R\left( \frac{1}{{{2}^{2}}}-\frac{1}{\infty }...

### A simple pendulum of lenght ′L′ has mass ′M′ and it oscillates freely with amplitude ′A′. At extreme position, its potential energy is (g= acceleration due to gravity)

A. MgA2/2L B. MgA/2L C. MgA2/L D. 2MgA2/L Solution: The correct answer is A. MgA2/2L $ PE=\frac{m{{\omega }^{2}}{{x}^{2}}}{2} $ $ \omega =\sqrt{\frac{g}{L}}\,at\,extreme\,po\operatorname{int}\,x=A $...

### For a particle moving in vertical circle, the total energy at different positions along the path

is conserved increases decreases may increase or decrease Solution: The correct answer is A. is conserved The kinetic energy of a particle travelling in a vertical circle is converted into potential...

### The fundamental frequency of an air column in a pipe closed at one end is 100 Hz. If the same pipe is open at both the ends, the frequencies produced in Hz are

100,200,300,400,..... 100,300,500,700,.... 200,300,400,500,..... 200,400,600,800,..... Solution: The correct answer is D. 200,400,600,800,..... $ Fundamental\text{ }frequency\text{ }of\text{...

### A particle is performing S.H.M. starting from extreme position. Graphical representation shows that, between displacement and acceleration, there is a phase difference of

0 rad π/4 rad π/2 rad π rad Solution: The correct answer is D. pi rad The following is the displacement of the particle executing SHM. x = A coswt Differentiating w.r.t. time we get v = dx/dt v =−...

### The depth ′ d ′ at which the value of acceleration due to gravity becomes 1/n times the value at the earth’s surface is ( R = radius of earth)

Solution: The correct answer is B. The following is the expression for acceleration due to gravity at a depth of d below the earth's surface. $ g'={{g}_{s}}\left( 1-\frac{d}{R} \right) $ $...

### For a rigid diatomic molecule, universal gas constant R=nCp where ′Cp′ is the molar specific heat at constant pressure and ′n′ is a number. Hence n is equal to

0.4 0.2857 0.2257 0.3557 Solution: The correct answer is B. 0.2857 $ Universal\text{ }gas\text{ }constant\text{ }is\text{ }given\text{ by:} $ $ R=nCp $ $ For\text{ }diatomic\text{ }molecule,\text{...

### When one end of the capillary is dipped in water, the height of water column is ′h′. The upward force of 105 dyne due to surface tension balanced by the force due to the weight of water column. The inner circumference of the capillary is (Surface tension of water = 0.07 N/m)

1.5 cm 2 cm 2.5 cm 3 cm Solution: The correct answer is A. 1.5 cm $ Upward\text{ }force\,is:\,\,\,F=105~dyne~=105\times {{10}^{-5}}~N $ $ Surface\text{ }tension\text{ }of\text{ }water~T=7\times...

### Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire then the ratio of the lengths of the first wire to second wire is

1/3 1/5 1/4 1/6 Solution: The correct answer is A. 1/3 $ Fundamental\text{ }frequency\text{ }of\text{ }the\text{ }first\text{ }wire~\,is: $ $...

### A flywheel at rest is to reach an angular velocity of 24 rad/s in 8 second with constant angular acceleration. The total angle turned through during this interval is

96 rad 48 rad 24 rad 72 rad Solution: The correct answer is 96 rad Angular acceleration is given by: α = 24/8 = 3 rad/s2 Now angular displacement becomes: θ = 0 + αt2/2 θ...

### A solid sphere of mass 2 kg is rolling on a frictionless horizontal surface with velocity 6m/s. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring =36N/m)

√14 m √2.8 m √1.4 m √0.7 m Solution: The correct answer is B. √2.8 m $ We\,have:\,\,m=2kg~~and\,~v=6m/s $ $ Total\text{ }kinetic\text{ }energy\text{ }of\text{ }the\text{ }sphere\text{...

### A metal rod of length ′ L ′ and cross-sectional area ′ A ′ is heated through ′ T ′ degree C . What is the force required to prevent the expansion of the rod lengthwise? [ Y = Young’s modulus of the material of rod, α − coefficient of linear expansion]

Solution: The correct answer is B. $ change\text{ }in\text{ }length:\,~\delta L=L\alpha T $ $ final\text{ }length~\,{{L}_{f}}=L+\delta L $ Now, in order to limit the expansion, there must be a force...

### The observer is moving with velocity ′v0’ towards the stationary source of sound and then after crossing moves away from the source with velocity ′v0’. Assume that the medium through which the sound waves travel is at rest. If ′v′ is the velocity of sound and ′n′ is thee frequency emitted by the source then the difference between apparent frequencies heard by the observer is

A. 2nv0/v B. v/2nv0 C. v/nv0 D. nv0/v Solution: The correct answer is A. 2nv0/v $ \text{Making use of the }doppler\text{ }effect $ $ Case\text{ }I:~Observer\,is\text{ }approaching\text{ }the\text{...

### A particle performs linear S.H.M. At a particular instant, velocity of the particle is ′ u ′ and acceleration is ′ α ′ while at another instant velocity is ′ v ′ and acceleration is ′ β ′ ( 0 < α < β ) . The distance between the two positions is

The correct option is B. $ u=\omega \sqrt{({{A}^{2}}-{{x}^{2}})} $ $ \alpha =-{{\omega }^{2}}x $ $ v=\omega \sqrt{({{A}^{2}}-{{y}^{2}})} $ $ \beta =-{{\omega }^{2}}y $ $...

### A disc of moment of inertia ‘I1’ is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed ′ ω ′ 1 . Another disc of moment of inertia I2 having zero angular speed is placed coaxially on a rotating disc. Now both the discs are rotating with constant angular speed ω2 . The energy lost by the initial rotating disc is

Solution: The correct answer is D. $ Initial\text{ }angular\text{ }momentum\text{ }of\text{ }the\text{ }system~is\,given\,by: $ $ {{L}_{i}}={{I}_{1}}{{\omega }_{1}}+{{I}_{2}}\omega \prime ~ $ $...

### A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes (1/4)th of the original in time ′t′ and ′n′ revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are (Angular retardation is uniform).

8n/15 4n/15 16n/15 32n/15 Solution: The correct answer is C. 16n/15 $ {{(\omega /4)}^{2}}={{\omega }^{2}}-2\alpha ~n(2\pi ) $ $ \therefore 2\alpha n(2\pi )={{\omega }^{2}}-\frac{{{\omega }^{2}}}{16}...

### A lift of mass ′ m ′ is connected to a rope which is moving upward with the maximum acceleration ′ a ′ . For maximum safe stress, the elastic limit of the rope is ′ T ′ . The minimum diameter of the rope is ( g = gravitational acceleration):

Solution: The correct answer is B. $ Let\text{ }the\text{ }tension\text{ }be\text{ }F.\,So, $ $ F-mg=ma\to F=m(g+a) $ $ Now,\,~T=\frac{F}{\pi {{r}^{2}}} $ $ r={{\left( \frac{m\left( g+a \right)}{\pi...

### The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made 1/3rd and close pipe is made three times the original, the number of beats produced will be

8 14 20 17 Solution: The correct answer is D. 17 $ The\,fundamental\text{ }frequencyfor\,closed\,pipe\,is: $ $ {{f}_{c}}=\frac{v}{4l} $ $ for\,open\,pipe:\,\,{{f}_{o}}=\frac{v}{2l} $ $ \therefore...

### Two spherical black bodies have radii ′r′1 and ′r′2. Their surface temperatures are ′T′1 and ′T′2. If they radiate same power then r2/r1 is

T1/T2 (T1/T2)2 (T2/T1)2 T2/T1 Solution: The correct answer is 2. (T1/T2)2

### The equation of the progressive wave is Y=3sin[π(t/3−x/5)+π/4] where x and Y are in metre and time in second. Which of the following is correct?

Velocity V=1.5m/s Frequency F=0.2 Hz Wavelength λ=10 m Amplitude A=3 cm Solution: The correct answer is C. Wavelength λ=10 m $ Y=3\sin \left[ \pi \left( \frac{t}{3}-\frac{x}{5} \right)+\frac{\pi...

### A wheel of moment of inertia 2 Kg m is rotating about an axis passing through centre and perpendicular to its plane at a speed 60 rad/s. Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is

24 Kg m2/s 48 Kg m2/s 72 Kg m2/s 96 Kg m2/s Solution: The correct answer is C. 72 Kg m2/s $ {{w}_{f}}=w+\alpha t\to 0=60+\alpha \times 300 $ $ \alpha =\frac{-1}{5} $ $ now\text{ }to\text{...

### In a sonometer experiment, the string of length ′L′ under tension vibrates in second overtone between two bridges. The amplitudes of vibration is maximum at

L/6,L/2,5L/6 L/8,L/4,L/2 L/2,L/4,L/6 L/6,L/2,L/6 Solution: The correct answer is A. L/6,L/2,5L/6 $ For\text{ }second\text{ }overtone~:\frac{3\lambda }{2}=L $ $ first\text{ }maxima\text{ }will\text{...

### A particle performing S.H.M. starts from equilibrium position and its time period is 16 second. After 2 seconds its velocity is π m/s. Amplitude of oscillation is (cos45∘=1/√2)

2√2m 4√2m 6√2m 8√2m Solution: The correct answer is D. 8√2m $ We\,have~: $ $ x=A\,sin\omega t $ $ Upon\text{ }differentiating\text{ }both\text{ }side,\,we\,get: $ $ ~v=A\omega \,cos\omega t $ $...

### The ratio of binding energy of a satellite at rest on earth’s surface to the binding energy of a satellite of same mass revolving around the earth at a height ′h′ above the earth’s surface is (R= radius of the earth)

2(R+h)/R (R+h)/2R (R+h)/R R/(R+h) Solution: The correct answer is 1. 2(R+h)/R

### A big water drop is formed by the combination of ′n′ small water drops of equal radii. The ratio of the surface energy of ′n′ drops to the surface energy of big drop is

n2:1 n:1 3√n:1 √n:1 Solution: The correct answer is C. $ By\text{ }mass\text{ }conservation\text{ }new\text{ }radius\text{ }R\text{ }is~ $ $ R={{n}^{1/3}}r $ $ ratio\text{ }of\text{ }energy\text{...

### An ideal gas has pressure ′P′, volume ′V′ and absolute temperature ′T′. If ′m′ is the mass of each molecule and ′K′ is the Boltzmann constant then density of the gas is

Pm/KT KT/Pm Km/PT PK/Tm Solution: The correct answer is A. Pm/KT The ideal gas equation is PV = nRT, we can also write: PV = NKT here K is a Boltzmann constant Now we have: ρ = m/V = Nm/V putting...

### A pipe closed at one end has length 83 cm. The number of possible natural oscillations of air column whose frequencies lie below 100Hz are (velocity of sound in air = 332 m/s)

0 4 5 6 Solution: The correct answer is A. 0 The frequency for a pipe closed at one end is given by: f = (n×v )/4L v = speed of sound = 332m/s L = length of pipe = 83cm = 0.83m n = 0,1,2... f =...

### A satellite is revolving in a circular orbit at a height ‘h’ above the surface of the earth of radius ‘R’. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between ‘h’ and ‘R’ is

h=2R h=3R h=5R h=7R Solution: The correct answer is D. h=7R $ Escape\,velocity,\,{{v}_{e}}=\sqrt{\frac{2GM}{R}} $ $ v=\frac{{{v}_{e}}}{4}=\frac{1}{4}\sqrt{\frac{2GM}{R}} $ $ Centripetal\text{...

### The ratio of magnetic fields due to a bar magnet at the two axial points P1 and P2 which are separated from each other by 10cm is 25:2. Point P1 is situated at 10cm from the centre of the magnet.Points P1and P2 are on the same side of magnet and distance of P2 from the centre is greater than distance of P1 from the centre of magnet,then magnetic length is

5 cm 20 cm 15 cm 10 cm Solution: The correct answer is D. 10cm We know that the magnetic field at a distance d from the magnet's centre on the axis is given as follows for a magnet of length 2l and...

### The increase in energy of a metal bar of length ‘L’ and cross-sectional area ‘A’ when compressed with a load ‘M’ along its length is (Y = Young’s modulus of the material of metal bar)

F2L/2AY FL/2AY FL/AY F2L2/2AY Solution: The correct answer is 1. $ Energy,\,\,U=\frac{1}{2}\times stress\times strain\times volume $ $ Stress=\frac{F}{A} $ $ Strain=\frac{Stress}{Y}=\frac{F}{AY} $ $...

### ‘n’ number of waves are produced on a string in 0.5 second. Now the tension in the string is doubled (Assume length and radius constant), the number of waves produced in 0.5 second for the same harmonic will be

n √n n√2 n√5 Solution: The correct answer is A. n The number of waves is determined by the same harmonic. As a result, the needed number of waves is the same, n.

### The energy of an electron having de-Broglie wavelength ′λ′ is: [h = Planck’s constant, m = mass of electron]

h2/mλ h2/2m2λ h2/2m2λ2 h2/2mλ2 Solution: $ \lambda =\frac{h}{mv} $ $ v=\frac{h}{m\lambda } $ $ K=\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m{{\left( \frac{h}{m\lambda } \right)}^{2}} $ $...

### In compound microscope, the focal length and aperture of the objective used is respectively

(A) large and large (B) large and small (C) short and large (D) short and small Solution: The correct answer is (C) short and small Two convex lenses make up a compound microscope. The objective...

### Following graphs show the variation of stopping potential corresponding to the frequency of incident radiation (F) for a given metal. The correct variation is shown in graph ( v 0 = Threshold frequency) :

(1) (2) (3) (4) Solution: The correct answer is A. (1) The stopping potential is the amount of energy required to prevent an electron from reaching the outside world. Electrons are emitted from the...

### Let be the physical quantity. If the percentage error in the measurement of physical quantities a, b and c is 2,3 and 4 percent respectively then percentage error in the measurement of x is

28% 7% 21% 14% Solution: The correct option is D. 14%

### Two metal wire ‘P’ and ‘Q’ of same length and material are stretched by same load. Their masses are in the ratio m1:m2. The ratio of elongations of wire ‘P’ to that of ‘Q’ is

Solution: The correct answer is C. $ Y=\frac{F/A}{\Delta l/l} $ $ \Delta l=\frac{Fl}{AY} $ $ \Delta l\,\alpha \,\frac{1}{A} $ $ m=Al\rho \Rightarrow m\,\alpha \,A $ $ Hence,\,\frac{\Delta...

### Heat energy is incident on the surface at the rate of 1000J/min. If coefficient of absorption is 0.8 and coefficient of reflection is 0.1 then heat energy transmitted by the surface in 5 minutes is

100J 500J 700J 900J Solution: The correct answer is 2. 500 J Let, the heat transmitted per minute be given by H. Now, The total incident energy = energy absorbed + energy reflected + energy...

### A series combination of N1capacitors (each of capacity C 1 ) is charged to potential difference ′ 3 V ′ . Another parallel combination of N 2 capacitors (each of capacity C 2 ) is charged to potential difference ‘V’. The total energy stored in both the combinations is same. The value of C 1 in terms of C 2 is

Solution: The correct answer is A. $ For\,series\,combination,\,equivalence\,capacitance\,=\,\frac{{{C}_{1}}}{{{N}_{1}}} $ $ ch\arg e,\,\,q=(3V)\frac{{{C}_{1}}}{{{N}_{1}}} $ $...

### A body is thrown from the surface of the earth with velocity ‘u’ m/s. The maximum height in m above the surface of the earth upto which it will reach is (R = radius of earth, g = acceleration due to gravity)

Solution: The correct answer is D. $ We\,have:\,\,g=\frac{G{{M}_{e}}}{{{R}^{2}}} $ $ Applying\text{ }law\text{ }of\text{ }conservation\text{ }of\text{ }mechanical\text{ }energy:- $ $...

### The deflection in galvanometer falls to [1/4]th when it is shunted by 3Ω. If additional shunt of 2Ω is connected to earlier shunt, the deflection in galvanometer falls to

1/2 (1/3)rd (1/4)th (1/8.5)th Solution: The correct answer is The current through the galvanometer is given by $ {{i}_{1}}=\frac{{{R}_{s}}}{{{R}_{s}}+{{R}_{g}}}i $ where Rs = resistance of shunt...

### When source of sound moves towards a stationary observer, the wavelength of sound received by him

(A) decreases while frequency increases (B) remains the same whereas frequency increases (C) increases and frequency also increases (D) decreases while frequency remains the same Solution; The...

### The expression for electric field intensity at a point outside uniformly charged thin place sheet is (d is the distance of point from plane sheet)

independent of d directly proportional to d directly proportional to 1/√d directly proportional to √d Solution: The correct answer is A. independent of d The required electric field for the point...

### A mass attached to once end of a string crosses top-most point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be (g = gravitational acceleration)

g 3g 6g 4g Solution: The correct answer is B. 3g $ The\text{ }speed\text{ }when\text{ }a\text{ }string\text{ }is\text{ }horizontal,~\,v=\sqrt{3gr} $ $ Hence,\text{ }centripetal\text{...

### In a photocell, frequency of incident radiation is increased by keeping other factors constant the stopping potential

(A) decreases (B) increases (C) becomes zero (D) first decreases and then increases Solution: The correct answer is (B) increases We know: eVo = hν − ϕ where Vo gives the stopping potential, ν is...

### A bomb at rest explodes into 3 parts on same mass. The momentum of two parts is −3P^i and 2P^j respectively. The magnitude of the momentum of the third part is.

P √5P √11P √13P Solution: The correct answer is √13P P1 = −3Pi and P2 = 2Pj And m1 = m2 = m3 = m/3 And Pinitial = 0 Let the momentum of the third part be P3 Making use of the principle of...

### The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is ‘I’. It is rotating with angular velocity ′ω′. Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis then loss is kinetic energy is

Iω2/2 Iω2/4 Iω2/6 Iω2/8 Solution: The correct answer is Iω2/4 $ Initial\text{ }angular\text{ }momentum,\,{{L}_{1}}=I\omega $ $ {{K}_{1}}=\frac{1}{2}I{{\omega }^{2}} $ We know that the block's...

### A mass is suspended from a vertical spring which is executing S.H.M of frequency 5 Hz. The spring is unstretched at the highest point of oscillation. Maximum speed of the mass is [acceleration due to gravity g = 10m/s2]

2πm/s πm/s 1/2πm/s 1/πm/s Solution: The correct answer is 1/πm/s We know that the block's greatest speed occurs when it is in balance. Applying mechanical energy conservation at the equilibrium...

### Magnetic susceptibility for a paramagnetic and diamagnetic material is respectively

(A) small, positive and small, positive (B) large, positive and small, negative (C) small, positive and small, negative (D) large, negative and large, positive Solution: The correct answer is (C)...

### A unit vector is represented as ( 0.8i+bj+0.4k ) . Hence the value of ‘b’ must be

√0.6 0.4 0.2 √0.2 Solution: The correct answer is

### A square frame ABCD is formed by four identical rods each of mass ‘m’ and length ‘T’. This frame is in X – Y plane such that side AB coincides with X – axis and side AD along Y – axis. The moment of inertia of the frame about X – axis is

2ml2/3 4ml2/3 5ml2/3 ml2/12 Solution: The correct answer is The inertia moments of rods AD and BC are as follows: $ \frac{1}{3}m{{T}^{2}} $ Because rod AB is on the X-axis, its moment of inertia...

### If A = 3i−2j +k, B=i−3j+5k and C=2i+ j−4k form a right angled triangle then out of the following which one is satisfied?

Solution: The correct answer is A.

### A string is vibrating in its fifth overtone between two rigid supports 2.4m apart. The distance between successive node and antinode is

0.1m 0.2m 0.6m 0.8m Solution: The correct answer is There are six loops in the fifth overtone, each of which is half wavelength long. $ 6\frac{\lambda }{2}=L=2.4\,m $ $ \lambda =0.8\,m $ Now,...

### A ray of light is incident normally on a glass slab of thickness 5 cm and refractive index 1.6. The time taken to travel by a ray from source to surface of slab is same as to travel through glass slab. The distance of source from the surface is :

4 cm 8 cm 12 cm 16 cm Solution: the correct answer is B. 8cm We know, $ v=\frac{c}{\mu }\,\,where\,\,\mu =1.6 $ Let T1 represent the time it takes to travel from the source to the surface, and T2...

### An alternating electric field of frequency ‘y’ is applied across the dees (radius R) of a cyclotron to accelerate protons (mass m). The operating magnetic field ‘B’ used and K.E. of the proton beam produced by it are respectively (e = charge of proton).

Solution: The correct answer is C. $ Time,\,\,T=\frac{1}{y} $ $ speed\,of\,proton,\,v=\frac{2\pi R}{T}=2\pi Ry $ $ For\text{ }circular\text{ }motion\text{ }in\text{ }the\text{ }dees- $ $...

### With forward biased mode, the junction diode

(A) is one in which width of depletion layer increases (B) is one in which potenital barrier increases (C) acts as closed switch (D) acts as open switch Solution: The correct answer is (C) acts as...

### In a capillary tube having area of cross-section ‘A’, water rises to a height ‘h’. If cross-sectional area is reduced to A9. the rise of water in the capillary tube is

3h 4h 2h h Solution: The correct answer is A. 3h $ h=\frac{2T\cos \theta }{r\rho g} $ $ \Rightarrow h\,\alpha \,\frac{1}{r} $ $ A=\pi {{r}^{2}},\,here\,\,r\,\alpha \,\sqrt{A} $ $ \therefore...

### The molar specific heat of an ideal gas at constant pressure and constant volume is ‘ C p ‘ and C v ‘ respectively. If ‘R’ is the universal gas constant and the ratio of C p to C v is ′ γ ′ then C v =

Solution; The correct answer is D. $ \frac{{{C}_{p}}}{{{C}_{v}}}=\gamma $ $ {{C}_{p}}=\gamma {{C}_{v}} $ $ {{C}_{p}}-{{C}_{v}}=R $ $ \gamma {{C}_{v}}-{{C}_{v}}=R $ $ {{C}_{v}}=\frac{R}{\gamma -1}...

### A conducting wire has length ′L′1 and diameter ′d′1. After stretching the same wire length becomes ′L′2 and diameter ′d′2. The ratio of resistances before and after stretching is

Solution: The correct answer is A. The resistance of a body is related to its length and material resistivity, and inversely proportional to its cross-sectional area. $ {{R}_{1}}=\rho...

### An ideal transformer converts 220Va.c. to 3.3 k.V a.c to transmit a power of 4.4 kW. If primary coil has 600 turns, then alternating current in secondary coil is

1/3A 4/3A 5/3A 7/3A Solution; The correct answer is B. 4/3 A Suppose that there is no loss in power transmission: $ {{E}_{1}}{{I}_{1}}={{E}_{2}}{{I}_{2}} $ $...

### For a particle performing linear S.H.M. Its average speed over one oscillation is (a = amplitude of S.H.M, n = frequency of oscillation)

2an 4an 8an 6an Solution; the correct answer is In SHM:- Distance covered per oscillation, s = 4a Time taken for one oscillation, T = 1/n Hence, the average speed per oscillation, v(avg) = S/T =...

### A sphere of mass ′m′ moving with velocity ′v′ collides head-on on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is (e is coefficient of restitution and collision is inelastic)

(e−1)/2 (e+1)/2 e e/2 Solution: the correct answer is (e+1)/2 $ coefficient\text{ }of\text{ }restitution,\,\,e=\frac{{{v}_{2}}-{{v}_{1}}}{u} $ $...

### A metal wire of density ′ ρ ′ floats on water surface horizontally. If it is NOT to sink in water the maximum radius of wire is proportional to

Solution: The correct answer is B. $\sqrt{\frac{T}{\pi \rho g}} $ $ W={{F}_{s}} $ $ \pi {{r}^{2}}L\rho g=LT $ $ r=\sqrt{\frac{T}{\pi \rho g}} $

### An electron of stationary hydrogen atom jumps from 4th energy level to ground level. The velocity that the photon acquired as a result of electron transition will be (h = Planck’s constant, R = Rydberg’s constant, m = mass of photon)

9Rh/16m 11hR/16m 13hR/16m 15hR/16m Solution: the correct answer is 4. 15hR/16m The change in energy is given by: $ \Delta E=Rhc\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right) $ $ \Delta...

### If M2=magnetization of a paramagnetic sample, B = external magnetic field, T = absolute temperature, C = curie constant then according to Curie’s law in magnetism, the correct relation is

Solution: The correct answer is B. Mz = CB/T $ According\text{ }to\text{ }Curie's\text{ }law:- $ $ X\,\alpha \,\frac{1}{T'} $ $ \Rightarrow X=\frac{C}{T'} $ $ Magnetization,\,{{M}_{z}}=XB $ $...

### If numerical aperture of a microscope is increased then its

(A) resolving power remains constant (B) resolving power becomes zero (C) limit of resolution is decreased (D) limit of resolution is increased Solution; The correct answer is (D) limit of...

### In non-uniform circular motion, the ratio of tangential to radial acceleration is (r =radius of a circle, v = speed of the particle, α = angular acceleration)

1. α2r2 / v 2. α2r2 / v2 3. v2r2 / α 4. α2r/v2 Solution: The correct answer is 2. α2r2 / v2 $ Tangential\text{ }acceleration,~\text{ }~{{a}_{t}}=\alpha .r~ $ $ {{a}_{r}}=\frac{{{v}^{2}}}{r} $ $...

### The angle made by incident ray of light with the reflecting surface is called

(A) glancing angle (B) angle of incidence (C) angle of deviation (D) angle of refraction Solution: The correct answer is (A) glancing angle The angle formed by the incident beam ray and the...

### In the following network, the current flowing through 15ohm resistance is

0.8A 1.0A 1.2A 1.4A Solution: The correct answer is In the circuit above, we have 15/3 = 20/4 As a result, the wheat-stone bridge is balanced, and the galvanometer has no current flowing through...

### An alternating voltage e = 200√2 sin (100t) volt is connected to 1μF capacitor through a.c. ammeter. The reading of ammeter is

5 mA 20 mA 10 mA 15 mA Solution: The correct answer is 20mA $ E=200\sqrt{2}sin(100t) $ $ {{E}_{rms}}=\frac{{{E}_{0}}}{\sqrt{2}}=200V\,and\,\omega =100\,{{s}^{-1}} $ $ {{X}_{C}}=\frac{1}{{{\omega...

### Two light waves of intensities ′ I ′ 1 and ′ I ′ 2 having same frequency pass through same medium at a time in same direction and interfere. The sum of the minimum and maximum intensities is

Solution: The correct answer is B. 2 × (I1+I2) since the frequencies are the same so the maximum intensity will be I = (√I1+√I2 )2 minimum intensity is i = (√I1-√I2 )2 adding both we get, I + I =...

### A circular coil carrying current ‘I’ has a radius ‘R’ and magnetic field at the center is ‘B’. At what distance from the center along the axis of the same coil, the magnetic field will be B8?

R√3 2R 3R R√2 Solution: The correct answer is A. R√3 We know that the magnetic field B is given by at a distance x from the center of a current-carrying coil's axis. $ {{B}_{1}}=\frac{{{\mu...

### A disc has ‘M’ and radius ‘R’. How much tangential force should be applied to the rim of the disc so as to rotate with angular velocity ‘\omega’ in time ‘t’?

A) MRω/4t B) MRω/2t C) MRω/t D) MRωt Solution: The correct answer is B) MRω/2t $ \alpha =\frac{\omega }{t} $ $ moment\text{ }of\text{ }inertia\text{ }of\text{ }disc,\,I=\frac{1}{2}M{{R}^{2}} $ $...

### A transistor is used as a common emitter amplifier with a load resistance 2 kohms. The input resistance is 150 ohms. Base current is changed by 20 micro amperes. which results in a change in collector current by 1.5mA. The voltage gain of the amplifier is

1000 1100 900 1200 Solution: The correct answer is A. 1000 $ \frac{{{V}_{0}}}{{{V}_{i}}}=\beta \frac{{{R}_{L}}}{{{R}_{I}}} $ $ \beta =\frac{{{I}_{C}}}{{{I}_{B}}}=\frac{1.5mA}{20\mu A}=75 $ $...

### A vessel completely filled with water has holes and at depths and from the top respectively. Hole is a square of side and is circle of radius The water flowing out per secound from both the holes is same. Then is equal to

r.(π)1/4(3)1/4 r.(π)1/2(3)1/4 r12(π)1/3(3)1/2 r12(π)1/2(3)1/2 Solution: The correct answer is 2. r.(π)1/2(3)1/4 $ velocity\text{ }of\text{ }efflux\text{ }at\text{ }depth~d~is\,v=\sqrt{2gd} $ $...

### The path of oscillation of simple pendulum of length 1 meter is 16cm. Its maximum velocity is (g = π2m/s2)

A) 2πcm/s B) 4πcm/s C) 16πcm/s D) 8πcm/s Solution: the correct answer is D) 8πcm/s $ l=1m=100cm~and~s=16cm $ $ l\times (2\theta )=s $ $ 2\theta =\frac{s}{l}=0.16 $ $ \theta =0.08 $ Applying the Law...

### Sensitivity of a moving coil galvanometer can be increased by

A) decreasing the number of turns of coil B) increasing the number of turns of coil C) decreasing the area of a coil D) by using a weak magnet Solution: The answer is B) increasing the number of...

### The electric field intensity at a point near and outside the surface of a charged conductor of any shape is ‘E1’. The electric field intensity due to uniformly charged infinite thin plane sheet is ‘E2’. The relation between ‘E1’ and ‘E2’ is

A) 2E1 = E2 B) E1 = E2 C) E1 = 2E2 D) E1 = 4E2 Solution: The answer is C) E1 = 2E2 The electric field...

### A light is travelling from air into a medium. Velocity of light in a medium is reduced to 0.75 times the velocity in air. Assume that angle of incidence ‘i’ is very small, the deviation of the ray is

A) i B) i/3 C) i/4 D) 3i/4 Solution; the answer is C) i/4 $ speed\text{ }of\text{ }light\text{ }in\text{ }medium\text{ }~v=\frac{3c}{4} $ $ Using~c\,sinr=v\,sini $ $ As~i~and~r~are\text{ }very\text{...

### An electron of mass ‘m’ and charge ‘q’ is accelerated from rest in a uniform electric field of strength ‘E’. The velocity acquired by it as it travels a distance ‘l’ is

Solution; The answer is A) $ We\,know\,that:\,\,F=qE $ $ Thus\text{ }acceleration\text{ }of\text{ }the\text{ }electron~a=\frac{F}{m}=\frac{qE}{m} $ $ and\,here\,a=0 $ $ Using\text{...

### Which logic gate produces ‘LOW’ output when any of the inputs is ‘HIGH’ ?

A) AND B) OR C) NAND D) NOR Solution: The answer is D) NOR The truth table for the NOR gate is shown above, indicating that it is a logic gate that...

### A satellite of mass ‘m’ is revolving in circular orbit of radius ‘r’ round the earth. Its angular momentum w.r.t. the centre of its orbit is (M = mass of earth, G = universal gravitational constant)

Solution: The answer is B) Assume the satellite is in a circular orbit with a radius of r and a linear velocity of v. The gravitational force of the earth balances the centripetal force acting on...

### A mass is suspended from a spring having spring constant ‘K’ is displaced vertically and released, it oscillates with period ‘T’. The weight of the mass suspended is (g = gravitational acceleration)

KTg/4π2 KT2g/4π2 KTg2/π2 KT2g2/π2 Solution: The answer is 2. KT2g/4π2 $ Time\text{ }period\text{ }of\text{ }the\text{ }suspended\text{ }mass\text{ }executing\text{ }SHM\,Is: $ $ T=2\pi...

### In a pipe open at both ends, ‘n1’ and ‘n2’ be the frequencies corresponding to vibrating lengths ‘l 1’ and ‘l 2’ respectively. The end correction is

Solution: The correct answer is (c) $ {{n}_{1}}=\frac{pv}{2\left( {{l}_{1}}+2e \right)}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1) $ $ {{n}_{2}}=\frac{pv}{2\left( {{l}_{2}}+2e...

### A toy cart is tied to the end of an unstretched string of length ‘l’. When revolved, the toy cart moves in horizontal circle with radius ‘2l’ and time period T. If it is speeded untill it moves in horizontal circle of radius ‘3l’ with period T1, relation between T and T1 is (Hooke’s law is obeyed)

Solution: The correct answer is D) $ T=\frac{m{{v}^{2}}}{r} $ $ Time~Period=\frac{2\pi r}{v} $ $ ~\Delta L=\frac{Fl}{AY} $ $ ~\Rightarrow T=\frac{\Delta lAY}{l} $ $ v=\sqrt{\frac{\Delta lAYr}{lm}} $...

### A cord is wound around the circumference of wheel of radius ‘r’. The axis of the wheel is horizontal and moment of inertia about it is ‘I’. The weight ‘mg’ is attached to the end of the cord and falls from rest. After falling through a distance ‘h’, the angular velocity of the wheel will be

Solution: The correct answer is (c) $ Using\text{ }law\text{ }of\text{ }conservation\text{ }of\text{ }energy.\, $ $ At\text{ }height\text{ }h:~Mechanical\text{ }Energy=~M.{{E}_{1}}=mgh $ $...

### A black body radiates heat at temperatures ‘T1’ and ‘T2’ (T2 > T1). The frequency corresponding to maximum energy is

A) more at T1 B) more at T2 C) equal for T1 and T2 D) independent of T1 and T2 Solution; the correct answer is B) more at T2 The expression for heat radiated per unit time is P = σAeT4 where σ...

### A large number of liquid drops each of radius ‘a’ are merged to form a single spherical drop of radius ‘b’. The energy released in the process is converted into kinetic energy of the big drop formed. The speed of the big drop is [ρ = density of liquid, T = surface tension of liquid]

Solution: The correct answer is (A) Let's say there are n little drops that have fused to produce one larger drop. Before and after the merging, the liquid's mass is conserved. $ \therefore \rho...

### A hollow sphere of mass ‘M’ and radius ‘R’ is rotating with angular frequency ‘ω’. It suddenly stops rotating and 75% of kinetic energy is converted to heat. If ‘S’ is the specific heat of the material in J K kg then rise in temperature of the sphere is (M.I. of hollow sphere = 2/3 MR2)

A) Rω/4S B) R2 ω2/4S C) Rω/2S D) R2 ω2/2S Solution: The correct answer is R2 ω2/4S $ Moment\text{ }of\text{ }inertia\text{ }of\text{ }hollow\text{ }sphere~I=\frac{2}{3}M{{R}^{2}} $ $ Kinetic\text{...

### The length and diameter of a metal wire is doubled. The fundamental frequency of vibration will change from ‘n’ to (Tension being kept constant and material of both the wires is same)

A) n/4 B) n/8 C) n/12 D) n/16 Solution: The correct answer is $f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$ According to the question, we have: T2 = T1, μ2 = 4μ1, L2 = 2L1 [∵ A2...

### A rope 1 cm in diameter breaks if tension in it exceeds 500 N. The maximum tension that may be given to a similar rope of diameter 2 cm is

A) 2000 N B) 1000 N C) 500 N D) 250 N Solution: The correct answer is A) 2000N We know that tension in a rope is directly proportional to r2, thus doubling the diameter doubles the radius, and the...

### An open and closed organ pipe have the same length. The ratio of ‘p’th mode of frequency of vibration of air in two pipes is

A) p(2p + 1) B) 2p/(2p - 1) C) p D) 1 Solution: The correct answer is B) 2p/(2p - 1) Let v and L stand for the velocity of the sound wave and the length of the organ pipes, respectively. The...

### The dimensions of Stefan’s constant are

A) [M0 L1 T–3 K–4] B) [M1 L1 T–3 K–3] C) [M1 L2 T–3 K–4] D) [M1 L0 T–3 K–4] Solution: The correct option is D) [M1 L0 T–3 K–4] Expression of power radiated by a body is: P = σAeT4 where σ represents...

### A particle is executing S.H.M. of periodic time ‘T’. The time taken by a particle in moving from mean position to half the maximum displacement is (sin30°= 0.5)

A) T/2 B) T/4 C) T/8 D) T/12 Solution: The correct answer is D) T/12 Let's say the particle is in the mean position at time t = 0. As a result, the particle executing S H M has the following...

### A solid cylinder has mass ‘M’, radius ‘R’ and length ‘l’. Its moment of inertia about an axis passing through its centre and perpendicular to its own axis is

$ A.\,\,\frac{2M{{R}^{2}}}{3}+\frac{M{{l}^{2}}}{12} $ $ B.\,\,\frac{M{{R}^{2}}}{3}+\frac{M{{l}^{2}}}{12} $ $ C.\,\,\frac{3M{{R}^{2}}}{4}+\frac{M{{l}^{2}}}{12} $ $...

### The pitch of the whistle of an engine appears to drop to (5/6)th of original value when it passes a stationary observer. If the speed of sound in air is 350 m/s then the speed of engine is

A) 35 m/s B) 70 m/s C) 105 m/s D) 140 m/s Solution: The correct option is According to the question, the speed of sound in air, v...

### Let ‘gh’ and ‘gd’ be the acceleration due to gravity at height ‘h’ above the earth’s surface and at depth ‘d’ below the earth’s surface respectively. If gh = gd then the relation between ‘h’ and ‘d’ is

A) d = h B) d= h/2 C) d = h/4 D) d = 2h Solution: The correct option is D) d = 2h Let R be the earth's radius and g be the acceleration due to gravity at the surface. The following is the...

### The equation of the progressive wave is . The ratio of maximum particle velocity to wave velocity is

πa/5 3πa/5 2πa/5 4πa/5 Solution; The correct answer is C. 2πa/5

### A simple pendulum is oscillating with amplitude ‘A’ and angular frequency ‘ω’. At displacement ‘x’ from mean position, the ratio of kinetic energy to potential energy is

$ A.\,\,\frac{{{x}^{2}}}{{{A}^{2}}-{{x}^{2}}} $ $ B.\,\,\frac{{{x}^{2}}-{{A}^{2}}}{{{x}^{2}}} $ $ C.\,\,\frac{{{A}^{2}}-{{x}^{2}}}{{{x}^{2}}} $ $ D.\,\,\frac{A-x}{x} $ Solution: The correct option...

### A particle of mass ‘m’ is moving in circular path of constant radius ‘r’ such that centripetal acceleration is varying with time ‘t’ as K2 r t2 where K is a constant. The power delivered to the particle by the force acting on it is

A) m2 K2 r2 t2 B) mK2 r2 t C) m K2 r t2 D) m K r2 t Solution: The correct answer is B) mK2 r2 t $ Since\,~{{a}_{c}}={{k}^{2}}r{{t}^{2}} $ $ \frac{{{v}^{2}}}{r}={{k}^{2}}r{{t}^{2}} $ $...

### A liquid rises to a height of 1.8 cm in a glass capillary ‘A’. Another glass capillary ‘B’ having diameter 90% of capillary ‘A’ is immersed in the same liquid. The rise of liquid in capillary ‘B’ is

A) 1.4 cm B) 1.8 cm C) 2.0 cm D) 2.2 cm Solution: The correct answer is C) 2.0 cm The equation for capillary action is given as follows: 2S cosθ = ρgrh Or, we can say that: rh=constant r2 h2 = r1 h1...

### A range of galvanometer is ‘V’, when 50Ω resistance is connected in series. Its range gets doubled when 500Ω resistance is connected in series. Galvanometer resistance is

A) 100Ω B) 200Ω C) 300Ω D) 400Ω Solution: The correct answer is D) 400Ω $ Galvanometer\text{ }resistance=~G $ $ Current\,=\,{{I}_{G}} $ $ Then,\,the\,potential\,difference: $ $ V={{I}_{G}}\left( G+R...

### In Young’s double slit experiment, the ratio of intensities of bright and dark bands is 16 which means

A) the ratio of their amplitudes is 5 B) intensities of individual sources are 25 and 9 units respectively C) the ratio of their amplitudes is 4 D) intensities of individual sources are 4 and 3...

### For a transistor, the current ratio α(dc) = 69/70 . The current gain β(dc) is

A) 66 B) 67 C) 69 D) 71 Solution: The correct answer is C) 69 $ {{\alpha }_{dc}}=\frac{69}{70} $ $ {{\beta...

### Two coils A and B have mutual inductance henry. If the current in the primary is i = 5 sin (10π t) then the maximum value of e.m.f. induced in coil B is

A) π volt B) π/2 volt C) π/3 volt D) π/4 volt Solution: The correct answer is A) π volt $ emf=-M\frac{df}{dt}=-2\times \frac{1}{100}\times \frac{d}{dt}(5sin10\pi t) $ $ emf=-2\times...

### A potentiometer wire of length 10 m is connected in series with a battery. The e.m.f. of a cell balances against 250 cm length of wire. If length of potentiometer wire is increased by 1 m, the new balancing length of wire will be

A) 2.00 m B) 2.25 m C) 2.50 m D) 2.75 m Solution: The correct answer is D 2.75m According to the question, l=10m Balancing...

### A particle performs S.H.M. with amplitude 25 cm and period 3 s. The minimum time required for it to move between two points 12.5 cm on either side of the mean position is

A) 0.6 s B) 0.5 s C) 0.4 s D) 0.2 s Solution: The correct option is B) 0.5 s sinθ = 12.5/25 θ = 6π So, the total angle to move is...

### In sonometer experiment, the bridges are separated by a fixed distance. The wire which is slightly elastic, emits a tone of frequency ‘n’ when held by tension ‘T’. If the tension is increased to ‘4T’, the tone emitted by the wire will be of frequency

A) n B) 2n C) Slightly greater than 2n D) Slightly less than 2n Solution: The correct option is C) Slightly...

### A metal rod of length ‘L’, cross-sectional area ‘A’, Young’s modulus ‘Y’ and coefficient of linear expansion ‘α’ is heated to ‘t’ °C. The work that can be performed by the rod when heated is

$ A.\,\,\frac{YA\alpha L{{t}^{2}}}{2} $ $ B.\,\,\frac{YA{{\alpha }^{2}}L{{t}^{2}}}{2} $ $ C.\,\,\frac{YA{{\alpha }^{2}}{{L}^{2}}{{t}^{2}}}{2} $ $ D.\,\,\frac{YA\alpha Lt}{2} $ Solution: The correct...

### The difference between angular speed of minute hand and second hand of a clock is

A. 59π/900 rad/s B. 59π/1800 rad/s C. 59π/3600 rad/s D. 59π/24000 rad/s Solution: The correct option is B. 59π/1800 rad/s The time taken by minute hand to rotate by an angle of 2π radian is given...

### In the expression for Boyle’s law, the product ‘PV’ has dimensions of

A) force B) impulse C) energy D) momentum Solution: C) energy PV=nRT, where n is the number of moles, is the ideal gas equation. The...

### The process of regaining of information from carrier wave at the receiver is termed as

A) demodulation B) modulation C) attenuation D) amplification Solution: The correct option is A) demodulation Modulation is the process of superimposing...

### For the same angle of incidence, the angles of refraction in media ‘P’, ‘Q’, ‘R’ and ‘S’ are 50°, 40°, 30°, 20° respectively. The speed of light is minimum in medium

A) P B) Q C) R D) S Solution: The velocity of light in air is c ∴ The velocity of light in a medium, v =...

### The resistances in left and right gap of a meter bridge are 20Ω and 30Ω respectively. When the resistance in the left gap is reduced to half its value, the balance point shifts by

A) 15 cm to the right B) 15 cm to the left C) 20 cm to the right D) 20 cm to the left Solution: The correct option is A) 15 cm...

### Two coherent monochromatic light beams of intensities ‘4 I’ and ‘9 I’ are superimposed. The maximum and minimum possible intensities in the resulting beam are

A) 3 I and 2 I B) 9 I and 5 I C) 16 I and 3 I D) 25 I and I Solution: The correct option is D) 25 I and I $ Imax={{(\surd I1+\surd...

### For the hydrogen atom, the energy of radiation emitted in the transition from 4th excited state to 2nd excited state, according to Bohr’s theory is

A) 0.567 eV B) 0.667 eV C) 0.967 eV D) 1.267 eV Solution: The correct option is C) 0.967 eV $ Energy\text{ }of~nth~state\text{ }of\text{...

### The difference in the effective capacity of two similar capacitors when joined in series and then in parallel is 6μF . The capacity of each capacitor is

A) 2μF B) 4μF C) 8μF D) 16μF Solution: The correct option is B) 4μF Let the capacitance of each capacitor be given by C For series...

### Same current is flowing in two a.c. circuits. First contains only inductance and second contains only capacitance. If frequency of a.c. is increased for both, the current will

A) increase in first circuit and decrease in second B) increase in both circuits C) decrease in both circuits D) decrease in first circuit and increase in second Solution: The correct option is D)...

### The distance of a point on the screen from two slits in biprism experiment is m and m. If wavelength of light used is 6000 Å, the fringe formed at that point is

A) 10th bright B) 10th dark C) 9th bright D) 9th dark Solution: The correct answer is option(D). The two images of slit act as two new...

### For the Balmer series, wavelength of first line is ‘λ1 ’ and for Brackett series, wavelength of first line is ‘λ2 ’ then λ1/λ2 is

A) 0.081 B) 0.162 C) 0.198 D) 0.238 Solution: The correct option is B) 0.162 $ The\,wavelength\text{ }for\text{...

### For diamagnetic materials, magnetic susceptibility is

A) small and negative B) small and positive C) large and negative D) large and positive Solution: The correct option is A)...

### The de-Broglie wavelength ‘λ’ of a particle

A) is proportional to mass B) is proportional to impulse C) is inversely proportional to impulse D) does not depend on impulse Solution: The correct option is C) is inversely proportional to impulse...

### A coil carrying current ‘I’ has radius ‘r’ and number of turns ‘n’. It is rewound so that radius of new the coil is r/4and it carries current ‘I’. The ratio of the magnetic moment of the new coil to that of the original coil is

A) 1 B) 1/2 C) 1/4 D) 1/8 Solution: The correct option is C) 1/4 Initially, the radius of the coil is r1 = r The area of the coil initially is A = πr2 Thus initial magnetic moment of the coil μ1...

### When monochromatic light of wavelength ‘λ’ is incident on a metallic surface, the stopping potential for photoelectric current is ‘3V0’. When same surface is illuminated with light of wavelength ‘2λ’, the stopping potential is ‘V0’. The threshold wavelength for this surface when photoelectric effect takes place is

A) λ B) 2λ C) 3λ D) 4λ Solution: The correct option is D) 4λ $ Kinetic\text{ }energy\text{ }of\text{ }photoelectrons,~K.E=\frac{hc}{\lambda }-\phi ~ $ $ where\text{ }work\text{ }function,~\phi...

### A capacitor C1 = 4μF is connected in series with another capacitor C2 = 1μF. The combination is connected across d.c. source of 200 V. The ratio of potential across C2 to C1 is

A) 2 : 1 B) 4 : 1 C) 8 : 1 D) 16 : 1 Solution: The correct option is B) 4 : 1 According to the question: C1=4μF, C2=1μF and V=200 volts The equivalent capacitance for series combination is given...

### The capacity of a parallel plate air capacitor is 2μF and voltage between the plates is changing at the rate of 3 V/S. The displacement current in the capacitor is

A) 2μF B) 3μF C) 5μF D) 6μF Solution: The correct option is (D) 6μF Expression for the displacement current in the capacitor is, $ i=A{{\varepsilon...

### A series LCR circuit containing 5.0 H inductor, 80 micro F capacitor and 40 ohms resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be

(1) 25 rad/s and 75 rad/s (2) 50 rad/s and 25 rad/s (3) 46 rad/s and 54 rad/s (4) 42 rad/s and 58 rad/s Solution: Answer (3)

### From a circular ring of mass ‘M’ and radius ‘R’ an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is ‘K’ times ‘MR2’. Then the value of ‘K’ is

(1) 3/4 (2) 7/8 (3) 1/4 (4) 1/8 Solution; Answer (1) M(remain) = 3/4M I = Mremain R2 I = ¾ MR2 So, the correct option is 3/4

### Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 > > R2, the mutual inductance M between them will be directly proportional to

(a) R1/R2 (b) R2/R1 (c) R12/R2 (d) R22/R1 Solution: Answer (4) The magnetic field at the centre of the primary coil is given by: $B=\frac{{{\mu }_{0}}I}{2{{R}_{1}}}$ Considering it to be uniform,...

### A uniform conducting wire of length 12a and resistance ‘R’ is wound up as a current carrying coil in the shape of, (i) an equilateral triangle of side ‘a’. (ii) a square of side ‘a’. The magnetic dipole moments of the coil in each case respectively are

(1) √3Ia2 and 3Ia2 (2) 3 Ia2 and Ia2 (3) 3 Ia2 and Ia2 (4) 4 Ia2 and 3 Ia2 Solution: Answer (1) Current in the loop will be I=V/R which is the same for both loops. Now the magnetic moment of...

### A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass ‘m’ is suspended from the rod at 160 cm mark as shown in the figure. Find the value of ‘m’ such that the rod is in equilibrium. (g = 10 m/s2)

(1) 1/2kg (2) 1/3kg (3) 1/6kg (4) 1/12kg Solution: Answer (4) By balancing torque, 2g x 20 = 0.5g x 60 + mg x 120 m = 0.5/6 kg = 1/12kg

### For the given circuit, the input digital signals are applied at the terminals A, B and C. What would be the output at the terminal y?

Solution: Answer (3)

### In the product

$ \vec{F}=q(\vec{v}\times \vec{B}) $ $ \vec{F}=q\vec{v}(B\hat{i}+B\hat{j}+{{B}_{0}}\hat{k}) $ $ For\,q=1\,and\,\vec{v}=2\hat{i}+4\hat{j}+6\hat{k}\,and\, $ $ \vec{F}=4\hat{i}-20\hat{j}+12\hat{k} $ $...

### Twenty seven drops of same size are charged at 200 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

(1) 660 V (2) 1320 V (3) 1520 V (4) 1980 V Solution: Answer (4)

### A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of 60 cm 40 cm

(1) 20 cm from the lens, it would be a real image (2) 30 cm from the lens, it would be a real image (3) 30 cm from the plane mirror, it would be a virtual image (4) 20 cm from the plane mirror, it...

### A car starts from rest and accelerates at 5 m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s?

(1) 20 m/s, 5 m/s2 (2) 20 m/s, 0 (3) 20 2 m/s, 0 (4) 20 2 m/s, 10 m/s2 Solution: Answer (4) Initial velocity of car = 0 Acceleration of car = 5 m/s2 Velocity of car at t = 4 s; v = u + at Therefore,...

### A particle of mass ‘m’ is projected with a velocity v = kVe (k < 1) from the surface of the earth. (Ve = escape velocity) The maximum height above the surface reached by the particle is

Solution: Answer (4)\ given v = kVe where, k < 1 Thus, v < Ve From conservation of mechanical energy

### A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ‘’ to the horizontal, the maximum height attained by it equals 4R. The angle of projection, , is then given by :

Solution; Answer (4) T = 2πR/v ⇒ v = 2πR/T

### A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is

(g = 10 m/s2) nearly (1) 0 kg m/s (2) 4.2 kg m/s (3) 2.1 kg m/s (4) 1.4 kg m/s Solution; Answer (2) According to the question, the mass of the ball =...

### A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?

(1) 0.2 A (2) 0.4 A (3) 2 A (4) 4 A Solution: Answer (1) In ideal transformer, we know that: Input power = Output power 220 ×...

### If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

(1) [F][A][T] (2) [F][A][T2] (3) [F][A][T–1] (4) [F][A–1][T] Solution: Answer (2) We know that, [E] = [Fa][Ab][Tc] => [ML2T–2] = [MLT–2]a [LT–2]b...

### A convex lens ‘A’ of focal length 20 cm and a concave lens ‘B’ of focal length 5 cm are kept along the same axis with a distance ‘d’ between them. If a parallel beam of light falling on ‘A’ leaves ‘B’ as a parallel beam, then the distance ‘d’ in cm will be

(1) 25 (2) 15 (3) 50 (4) 30 Solution: Answer (2) After refraction by a convex lens, parallel beams of light...

### If E and G respectively denote energy and gravitational constant, then E/G has the dimensions o

(1) [M2] [L–1] [T0] (2) [M] [L–1] [T–1] (3) [M] [L0] [T0] (4) [M2] [L–2] [T–1] Solution: Answer (1) Dimensional formula of energy [E] = [M1 L2 T–2] ...(I) Dimensional formula of gravitational...

### A capacitor of capacitance ′C′, is connected across an ac source of voltage V, given by V=V0sinωtV The displacement current between the plates of the capacitor, would then be given by:

$ (1)\,\,{{I}_{d}}={{V}_{0}}\omega C\cos \omega t $ $ (2)\,\,{{I}_{d}}=\frac{{{V}_{0}}}{\omega C}\cos \omega t $ $ (3)\,\,{{I}_{d}}=\frac{{{V}_{0}}}{\omega C}\sin \omega t $ $...

### A solid cylinder of mass 2 kg and radius rolls up an inclined plane of angle of inclination . The centre of mass of the cylinder has speed of . The distance travelled by the cylinder on the inclined surface will be, [take ] (1) (2) (3) (4)

Answer (1) SoI. As $v=\sqrt{\frac{2 g h}{1+\frac{K^{2}}{\mathbf{R}^{2}}}}$ $v^{2}=\frac{2 g h}{1+\frac{1}{2}} \quad\left[\frac{K^{2}}{R^{2}}=\frac{1}{2}\right.$ for solid cylinder $]$ $...

### An object of mass , initially at rest, is acted upon by a variable force whose X-component varies with in the manner shown. The velocities of the object at the points and , would have the respective values of (nearly) (1) and (2) and (3) and (4) and

Answer (4) Sol. Using work-energy theorem $\Delta K=$ work $=$ area under $F=x$ graph From $x=0$ to $x=8 m$ $ \begin{array}{l} \frac{1}{2} m v^{2}=100+30 \\ v^{2}=520 \\ v=\sqrt{520}=23 \mathrm{~m}...

### A particle of mass at rest suddenly breaks on its own into three fragments. Two fragments of mass each move along mutually perpendicular direction with speed v each. The energy released during the process is, (1) (2) (3) (4)

Answer (1) Sol. From conservation of linear momentum. $0=m v \hat{j}+m v \hat{i}+3 m v_{1}$ $\vec{v}_{1}=-\frac{v}{3}(\hat{i}+\hat{j})$ $v_{1}=\frac{\sqrt{2}}{3} v$ $K E_{i}=0$ $K E_{f}=\frac{1}{2}...

### A body of mass is kept on a rough horizontal surface (coefficient of friction ). A horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by F, where is, (1) (2) (3) (4)

Answer (4) Sol. Since body does not move hence it is in equilibrium. $\mathrm{f}_{\mathrm{r}}=$ frictional force which is less than or equal to limiting friction. Now $\mathrm{N}=\mathrm{mg}$ Hence...

### The stress-strain curves are drawn for two different materials and . It is observed that the ultimate strength point and the fracture point are close to each other for material but are far apart for material . We can say that materials and are likely to be (respectively), (1) Plastic and ductile (2) Ductile and brittle (3) Brittle and ductile (4) Brittle and plastic

Answer (3) Sol. As given that fracture point and ultimate strength point is close for material $\mathrm{X}$, So, $\mathrm{X}$ is brittle in nature and both points are far apart for material $Y$...

### Consider the following statements (A) and (B) and identify the correct answer. (A) A zener diode is connected in reverse bias, when used as a voltage regulator. (B) The potential barrier of p-n junction lies between 0.1 V to 0.3 V.

(1) (A) and (B) both are correct. (2) (A) and (B) both are incorrect (3) (A) is correct and (B) is incorrect. (4) (A) is incorrect but (B) is correct. Solution: Answer (3) When reverse biassed, the...

### Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings apart and of same height of , with the same velocity of . When and where will the two bullets collide? (1) They will not collide (2) After at a height of (3) After at a height of (4) After at a height of

Answer (2) Sol. Let bullets collide at time t $ \begin{array}{l} x_{1}+x_{2}=100 \mathrm{~m} \\ 25 t+25 t=100 \\ t=2 s \\ \begin{array}{r} y=\frac{1}{2} g t^{2}=\frac{1}{2} \times 10 \times 2^{2} \\...

### A double convex lens has focal length . The radius of curvature of one of the surfaces is double of the other. Find the radii if the refractive index of the material of the lens is 1.5. (1) (2) (3) (4)

Answer (4) Sol. Focal length of lens is $\frac{1}{f}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$, $ \begin{array}{l} \frac{1}{25}=(1.5-1)\left(\frac{1}{R}+\frac{1}{2 R}\right) \\...

### A radioactive nucleus Z undergoes spontaneous decay in the sequence in following manner where Z is the atomic number of element X. The possible decay particles in the sequence are

Solution : Answer 3 β+ decreases the atomic number by 1, α decreases the atomic number by 2, and the β- decreases the atomic number by 1. Hence the correct order is given by the option 3

### In a Young’s double slit experiment, if there is no initial phase difference between the light from the two slits, a point on the screen corresponding to the fifth minimum has path difference (1) (2) (3) (4)

Answer (4) Sol. Path difference for destructive interference in YDSE $ \begin{array}{c} \Rightarrow \Delta X_{n}=\frac{(2 n-1)}{2} \lambda \quad n=1,2,3 \ldots . \\ \Delta X_{5^{k+}}=\left(\frac{2...

### An equiconvex lens has power . It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be, (1) (2) 0 (3) (4)

Answer (1) When a lens is cut in half as illustrated in the diagram, the power of each half is the same. i.e. P, because the focal length is the same.

### Two identical capacitors and of equal capacitance are connected as shown in the circuit. Terminals a and of the key are connected to charge capacitor using battery of emf V volt. Now disconnecting a and the terminals and are connected. Due to this, what will be the percentage loss of energy? (1) (2) (3) (4)

Answer (4) $\mathrm{Sol}$, Switch the key at point $c$ $ \begin{array}{l} \frac{q_{0}-q}{C}=\frac{q}{C} \\ 2 q=q_{0} \\ q=\left(\frac{q_{0}}{2}\right) \\...

### A sphere encloses an electric dipole with charges C. What is the total electric flux across the sphere? (1) (2) (3) Zero (4)

Answer (3) Sol. $\phi_{\text {Total }}=\frac{\mathbf{q}_{\text {enclosed }}}{\varepsilon_{0}}$ Because dipoles have equal and opposing charges, there will be no net charge inside the sphere....

### Polar molecules are the molecules

(1) Having zero dipole moment (2) Acquire a dipole moment only in the presence of electric field due to displacement of charges (3) Acquire a dipole moment only when magnetic field is absent (4)...

### For a transparent medium, relative permeability and permittivity, and are and respectively. The velocity of light in this medium would be, (1) (2) (3) (4)

Answer (2) Sol. $v=\frac{1}{\sqrt{\mu \in}}=\frac{\mathbf{c}}{\sqrt{\mu_{r} \in_{r}}}$ $ \begin{array}{l} =\frac{3 \times 10^{8}}{\sqrt{1 \times 1.44}} \\ =2.5 \times 10^{8} \mathrm{~m} / \mathrm{s}...

### A cycle wheel of radius is rotated with. constant angular velocity of 10 rad/s in a region of magnetic field of 0.1 T which is perpendicular to the plane of the wheel. The EMF generated between its centre and the rim is, (1) Zero (2) (3) (4)

Answer (3) Solution: $ \begin{array}{l} e=\frac{B 1^{2} \omega}{2} \\ =\frac{1}{2} \times 0.1 \times\left(\frac{1}{2}\right)^{2} \times 10 \\ =\frac{1}{8} \\ =0.125 \mathrm{~V} \end{array}...

### A parallel plate capacitor has a uniform electric field ‘ E ‘ in the space between the plates. If the distance between the plates is ‘d’ and the area of each plate is ‘A’, the energy stored in the capacitor is (Epsillon = permittivity of free space)

The capacitance of a parallel plate capacitor is $ C=\frac{{{\in }_{0}}A}{d} $ Potential difference between the plates is V = Ed ........ (ii) Then, the energy stored in the capacitor is given...

### A circuit when connected to an AC source of gives a current of . The same circuit when connected to a DC source of , gives a current of . The circuit is (1) Series LCR (2) Series LR (3) Series RC (4) Series LC

Answer (2) Sol. $I_{1}=\frac{V}{Z}$ $ I_{1}=\frac{12}{\sqrt{R^{2}+\left(X_{I}-X_{c}\right)^{2}}}=0.2 \mathrm{~A} $ In the second situation, the capacitor would give infinite resistance, but since...

### The time period of a geostationary satellite is , at a height is radius of earth) from surface of earth. The time period of another satellite whose height is from surface will be, (1) (2) (3) (4)

Answer (2) Sol. $T^{2} \propto r^{3}$ $\mathbf{T}^{2} \propto\left(\mathbf{R}_{\mathrm{E}}+\mathbf{h}\right)^{3}$...

### The rate of radioactive disintegration at an instant for a radioactive sample of half life is . The number of radioactive atoms in that sample at that instant is, (1) (2) (3) (4)

Answer (1) Sol. $T_{1 / 2}=\frac{\ln 2}{\lambda}=\frac{0.693}{\lambda}$ $ \begin{array}{l} 2.2 \times 10^{9}=\frac{0.693}{\lambda} \\ \lambda=\frac{0.693}{2.2 \times 10^{9}}=3.15 \times 10^{-10} \\...

### An object flying in air with velocity suddenly breaks into two pieces whose masses are in the ratio . The smaller mass flies off with a velocity The velocity of the larger piece will be, (1) (2) (3) (4)

Answer (2) Sol. By conservation of linear momentum $\overline{\mathbf{P}}=\overrightarrow{\mathbf{P}}_{\mathrm{f}}$ $\mathrm{mv}_{1}=\left(\frac{\mathrm{m}}{6} \overline{\mathrm{v}}_{1}+\frac{5...

### A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is

(1) 0.9 MeV (2) 9.4 MeV (3) 804 MeV (4) 216 MeV Solution: Answer (4) Reactant mass number = 240 Reactant mass number = 240 The total number of products is 120. BE per product nucleon = 8.5 MeV Total...

### A tuning fork with frequency 800 Hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonance are observed at lengths and . The speed of sound in air is, (1) (2) (3) (4)

Answer (4) $ \begin{array}{l} I_{1}=9.75 \mathrm{~cm} \\ I_{2}=31.25 \mathrm{~cm} \\ I_{3}=52.75 \mathrm{~cm} \\ e=\text { end correction } \end{array} $ $ \frac{3 \lambda}{4}+e=31.25 \mathrm{~cm} $...