Solution: (2) No. of mole of gas $=1$ so molar mass $=4 \mathrm{~g} / \mathrm{mole}$ $ \mathrm{V}=\sqrt{\frac{\mathrm{\gammaRT}}{\mathrm{m}}} \Rightarrow 952 \times 952=\frac{\gamma \times 3.3...
Light of wavelength is incident on a metal with work function . The de Broglie wavelength of the emitted electron is: (1) (2) (3) (4)
Solution: (4) $ \mathrm{KE}_{\max }=\frac{h c}{\lambda}-\Psi $ $\mathrm{KE}_{\max }=\frac{1240}{500}-2.82$ $\mathrm{KE}_{\max }=2.48-2.28=0.2 \mathrm{eV}$ $\lambda_{\min }=\frac{\mathrm{h}}{\sqrt{2...
Two metal wires of identical dimensions are connected in series. If and are the conductivities of the metal wires respectively, the effective conductivity if the combination is: (1) (2) (3) (4)
The Solution is (2) $\mathrm{R}_{\mathrm{ec}}=\frac{\ell}{\sigma_{1} \mathrm{~A}}+\frac{\ell}{\sigma_{1} \mathrm{~A}}=\frac{\ell_{\mathrm{eq}}}{\sigma_{\mathrm{eq}} \mathrm{A}_{\mathrm{eq}}}$...
A nucleus of uranium decays at rest into nuclei of thorium and helium. Then: (1) The helium nucleus has less kinetic energy than the thorium nucleus (2) The helium nucleus has more kinetic energy than the thorium nucleus (3) The helium nucleus has less momentum then the thorium nucleus. (4) The helium nucleus has more momentum than the thorium nucleus
The correct Solution is (2) $ \begin{array}{l} \mathrm{U} \rightarrow \mathrm{Th}+\alpha \\ \mathrm{KE}_{\mathrm{Th}}=\frac{\mathrm{P}^{2}}{2 \mathrm{~m}_{\mathrm{Th}}},...
Two particles A and B move with constant velocities and . At the initial moment their position vectors and respectively. The condition for particles and for their collision is: (1) (2) (3) (4)
The correct Solution is (2) For two particles to collide, the direction of the relative velocity of one with respect to other should be directed towards the relative position of the other particle...
A force is acting at a point . The value of for which angular momentum about origin is conserved is: (2) (3) 2 (4) Zero
The Solution is (2). If $\overrightarrow{\mathrm{L}}=$ constant then $\vec{\tau}=0$ So $\vec{r} \times \vec{F}=0 \Rightarrow \vec{F}$ should be parallel to $\vec{r}$ so coefficient should be in same...
At the first minimum adjacent to the central maximum of a single-slit diffraction pattern, the phase difference between the Huygen’s wavelet from the edge of the slit and the wavelet from the midpoint of the slit is: (1) radian (2) radian (3) radian (4)
The Solution is (4) For first minima $ \mathrm{AP}-\mathrm{BP}=\lambda $ $ A P-M P=\frac{\lambda}{2} $ So phase difference =$\pi$
Point masses and are placed at the opposite ends of rigid rod of length , and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity is minimum, is given by:(1) (2) (3) (4)
Solution: (1) $ \mathrm{K} . \mathrm{E} .=\frac{1}{2} \mathrm{I} \omega^{2} $ I is min. about the centre of mass $So,\left(m_{1}\right)(x)=\left(m_{2}\right)(L-x)$ $ \mathrm{x}=\frac{\mathrm{m}_{2}...
A string is stretched between fixed points separated by . It is observed to have resonant frequencies of and . There are no other resonant frequency for this string is: (1) , (2) (3) (4)
The correct Solution is (1) Two consecutive resonant frequencies for a string fixed at both ends will be $ \begin{array}{l} \frac{n v}{2 \ell} \text { and } \frac{(n+1) v}{2 \ell} \\ \Rightarrow...
The position vector of a particle as a function of time is given by: Where is in meters, is in seconds and Î and j denote unit vectors along – and -directions, respectively. Which one of the following statements is wrong for the motion of particle? (1) Patch of the particle is a circle of radius 4 meter (2) Acceleration vector is along (3) Magnitude of acceleration vector is , where is the velocity of particle (4) Magnitude of the velocity of particle is 8 meter/second,
The correct Solution is (4) $ \begin{array}{l} \mathrm{x}=45 \mathrm{~m} 2 \pi \mathrm{t} \\ \mathrm{y}=4 \cos (2 \pi \mathrm{t}) \end{array} $ On Squaring and adding. $\Rightarrow$ Circular motion...
A remote-sensing satellite of earth revolves in a circular orbit at a height of above the surface of earth. If earth’s radius is and , then the orbital speed of the satellite is: (1) (2) (3) (4)
The correct Solution is (2) $ \begin{aligned} & V_{0}=\sqrt{\frac{G M}{r}}=\sqrt{\frac{G M}{\overline{R^{2}}}, \frac{R^{2}}{r}} \\ =& \sqrt{\frac{9.8 \times 6.38 \times 6.38}{6.63 \times...
In the given figure, a diode is connected to an external resistance and an e.m.f. of . If the barrier potential developed across the diode is , the current in the circuit will be: (1) (2) (3) (4)
The correct Solution is (2) $ \begin{array}{l} \text { Current }=\frac{(3.5-0.5)}{100} \mathrm{~A} \\ =\frac{3}{100} \mathrm{~A}=30 \mathrm{~mA} \end{array} $
A satellite is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then, (1) The acceleration of is always directed towards the centre of the earth (2) The angular momentum of about the centre of the earth changes in direction, but its magnitude remains constant. (3) The total mechanical energy of S varies periodically with time (4) The linear momentum of S remains constant is magnitude
The correct Solution is (1) and (2) The gravitational pull on the satellite will be directed toward the centre of the earth, hence the satellite's acceleration will also be directed toward the...
Two vessels separately contain two ideal gases and at the same temperature, the pressure of a being twice that of . Under such conditions, the density of is found to be times the density if . The ratio of molecular weight of and is: (1) (2) (3) (4) 2
The Solution is (3) $ P_{A}=\frac{\rho_{A} M_{A}}{R T}, P_{B}=\frac{\rho_{B} M_{B}}{R T}=\frac{3}{2} \Rightarrow \frac{P_{A}}{P_{B}}=\frac{\rho_{A}}{\rho_{B}} \frac{M_{A}}{M_{B}}=2...
A parallel plate air capacitor has capacity ‘ , distance of separation between plates is ‘d’ and potential difference ‘ is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is: (1) (2) (3) (4)
The Solution is (3) Attraction between the plates $ \mathrm{F}=\frac{\mathrm{C}^{2} \mathrm{~V}^{2}}{2 \mathrm{Cd}}=\frac{\mathrm{CV}^{2}}{2 \mathrm{~d}} $ Force of attraction between the plates is...
A rectangular coil of length and width having 50 turns of wire is suspended vertically in a uniform magnetic field of strength Weber . The coil carries a current of . if the plane of the coil is inclined at an angle of with the direction of the field, the torque required to keep coil in stable equilibrium will be: (1) (2) (3) (4) .
The correct solution is (3) $ \begin{array}{l} \vec{\tau}=\overrightarrow{\mathrm{M}} \times \overline{\mathrm{B}}=\mathrm{MB} \sin 60^{\circ} \\ =\mathrm{Ni} \mathrm{AB} \sin 60^{\circ} \\ 50...
An automobile moves on a road with a speed of . The radius of its wheels is and the moment of inertia of the wheel about its axis of rotation is . If the vehicle is brought to rest in , the magnitude of average torque transmitted by its brakes to the wheel is: (1) (2) (3) (4)
The correct solution is (2) $ \begin{array}{l} \omega_{\mathrm{i}}=\frac{15}{0.45}=\frac{100}{3} \omega_{\mathrm{f}}=0 \\ \omega_{\mathrm{f}}=\omega_{\mathrm{i}}+\alpha \mathrm{t} \\...
A source of sound emitting waves of frequency and an observer are located at some distance from each other. The source is moving with a speed of at an angle of with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air ), is: (1) (2) (3) (4)
The correct solution is (3) $ \begin{array}{l} t^{1}=f_{0}\left(\frac{v-v}{v-v_{s}}\right) \\ f^{1}=100\left(\frac{v-0}{v-(+9.7)}\right) \\ f^{1}=100 \frac{v}{v\left(1-\frac{9.7}{V}\right)}...
A potentiometer wire of length and a resistance are connected in series with a battery of e.m.f. and a resistance . An unknown e.m.f. is balanced at a length of the potentiometer wire. The e.m.f. E will be given by: (1) (2) (3) (4)
The correct option is 3 $ K=\text { potential gradient }=\left(\frac{E_{e} r}{r+r_{1}}\right) \frac{1}{L} $ So $\mathrm{E}=\mathbb{K} \ell=\frac{\mathrm{E}_{0} r...
The energy of the em waves is of the order of 15 keV. To which part of the spectrum does it belong?
(1) γ-rays
(2) X-rays
(3) Infra-red rays
(4) Ultraviolet rays
The ray wavelength $ \begin{array}{l} \lambda=\frac{\mathrm{hc}}{\mathrm{E}} \\ =0.826 \AA \end{array} $ As $\lambda<100 \AA$ Hence it is X-ray
In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:
(1) 5/27
(2) 4/9
(3) 9/4
(4) 27/5
In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is: $ \begin{array}{l}...
A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively
$ (1)\,\,\frac{S}{4},\frac{3gS}{2} $ $ (2)\,\,\frac{S}{4},\frac{\sqrt{3gS}}{2} $ $ (3)\,\,\frac{S}{2},\frac{\sqrt{3gS}}{2} $ $ (4)\,\,\frac{S}{4},\sqrt{\frac{3gS}{2}} $ Solution: Answer (4) Let...
An electromagnetic wave of wavelength is incident on a photosensitive surface of negligible work function. If ‘m’ mass is of photoelectron emitted from the surface has de-Broglie wavelength, then
$ (1)\,\,\lambda =\left( \frac{2m}{hc} \right)\lambda _{d}^{2} $ $ (2)\,\,{{\lambda }_{d}}=\left( \frac{2mc}{h} \right){{\lambda }^{2}} $ $ (3)\,\,\lambda =\left( \frac{2mc}{h} \right)\lambda...
Column-I gives certain physical terms associated with flow of current through a metallic conductor. Column-II gives some mathematical relations involving electrical quantities. Match Column-I and Column-II with appropriate relations.
Solution: Answer (1) $ Drift\,velocity,\,{{v}_{d}}=\frac{eE\tau }{m} $ $ Elasticity\,\operatorname{Re}sistivity,\,\rho =\frac{1}{\sigma }=\frac{E}{J} $ $ \operatorname{Re}laxation\,period,\,\tau...
A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since
(1) A large aperture contributes to the quality and visibility of the images. (2) A large area of the objective ensures better light-gathering power. (3) A large aperture provides a better...
For a plane electromagnetic wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively?
$ (1)\,\,\hat{j}+\hat{k},\hat{j}+\hat{k} $ $ (2)\,\,-\hat{j}+\hat{k},-\hat{j}-\hat{k} $ $ (3)\,\,\hat{j}+\hat{k},-\hat{j}-\hat{k} $ $ (4)\,\,-\hat{j}+\hat{k},-\hat{j}+\hat{k} $ Solution: Answer (2)...
An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance ‘R’ are connected in series to an ac source of potential difference ‘V’ volts as shown in figure. Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is
A . The impedance of the circuit is
Solution: Answer (4)
A dipole is placed in an electric field as shown. In which direction will it move?
(1) Towards the left as its potential energy will increase. (2) Towards the right as its potential energy will decrease. (3) Towards the left as its potential energy will decrease. (4) Towards the...
An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of 105 m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.
(1) 4 × 10–20 N (2) 8π × 10–20 N (3) 4π × 10–20 N (4) 8 × 10–20 N Solution: Answer (4) The magnetic field produced due...
A Carnot engine having an efficiency of 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is
(1) 90 J (2) 99 J (3) 100 J (4) 1 J Solution: Answer (1)
A long solenoid of diameter 0.1 m has 2 × 104 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 1000 ohms, the total charge flowing through the coil during this time is
(1) 16 micro Columb (2) 32 micro Columb (3) 16 pi micro Columb (4) 32 pi micro Columb Solution: Answer (2) According to the question, Number of turns, n=100...
The x and y coordinates of the particle at any time are x = 5t – 2t2 and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is
(1) 5 m/s2 (2) –4 m/s2 (3) –8 m/s2 (4) 0 Solution: Answer (2) We have: x = 5t – 2t2 and y = 10t Therefore, dx/dt = 5 – 4t And dy/dt = 10 Or we can say that: Vx = 5 – 4t and Vy = 10 Similarly, we...
Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take g constant with a value 10 m/s2. The work done by the (i) gravitational force and the (ii) resistive force of air is
(1) (i) 1.25 J (ii) –8.25 J (2) (i) 100 J (ii) 8.75 J (3) (i) 10 J (ii) –8.75 J (4) (i) – 10 J (ii) –8.25 J Solution: Answer (3) wa = –8.75 J i.e. work done due to air resistance and work done due...
A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is
(1) 425 kg m–3 (2) 800 kg m–3 (3) 928 kg m–3 (4) 650 kg m–3 Solution: Answer (3) $ {{h}_{oil}}{{\rho }_{oil}}g={{h}_{water}}{{\rho }_{water}}g $ $ 140\times...
A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is
$ (1)\,\,\frac{\sqrt{5}}{2\pi } $ $ (2)\,\,\frac{4\pi }{\sqrt{5}} $ $ (3)\,\,\frac{2\pi }{\sqrt{3}} $ $ (4)\,\,\frac{\sqrt{5}}{\pi } $ Solution: Answer (2)
A physical quantity of the dimensions of length that can be formed out of c, G is [c is velocity of light, G is universal constant of gravitation and e is charge
Solution: Answer (4) According to the question, we have: on comparing we get, a = 3b + 3c =1, −b + c = 0 a + 2b + 2c = 0 On solving we get, a = −2, b = 21, c = 21 Thus, the answer...
Suppose the charge of a proton and an electron differ slightly. One of them is –e, the other is (e + e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then e is of the order of [Given mass of hydrogen mh = 1.67 × 10–27 kg]
(1) 10–23 C (2) 10–37 C (3) 10–47 C (4) 10–20 C Solution: Answer (2)...
The diagrams below show regions of equipotentials. A positive charge is moved from A to B in each diagram.
(1) In all the four cases the work done is the same. (2) Minimum work is required to move q in figure (a). (3) Maximum work is required to move q in figure (b). (4) Maximum work is required to move...
A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k’. Then they are connected in parallel and force constant is k”. Then k’ : k” is
(1) 1 : 9 (2) 1 : 11 (3) 1 : 14 (4) 1 : 6 Solution: Answer (2) We know that the Spring constant (k) is inversely proportional to the length. So, we have: k1 = 6k k2 = 3k k3 = 2k
A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle theta, the spot of the light is found to move through a distance y on the scale. The angle theta is given by
(1) y/x (2) x/2y (3) x/y (4) y/2x Solution: Answer (4) When mirror is rotated by an angle theta, reflected ray will be rotated by an angle twice that of theta. $ \frac{y}{x}=2\theta $ $ \theta...
The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is
(1) 1 (2) 4 (3) 0.5 (4) 2 Solution: Answer (2)
Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively
Solution: answer (1) Here block B free falls thus the acceleration of the block B is g Force change for block A is mg thus mg = 3ma a = g/3 Hence...
The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then
(1) d = 1 km (2) 3/2 km (3) d = 2 km (4) 1/2 km Solution: Answer (3) Above earth surface below Earth surface
Which of the following statements are correct?
(a) Centre of mass of a body always coincides with the centre of gravity of the body. (b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero (c) A...
The bulk modulus of a spherical object is ‘B’. If it is subjected to uniform pressure ‘p’, the fractional decrease in radius is
(1) B/3p (2) 3/Bp (3) p/3B (4) p/B Solution: Answer (3)
A gas mixture consists of 2 moles of O2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
(1) 15 RT (2) 9 RT (3) 11 RT (4) 4 RT Answer (3) Solution: $ U={{n}_{1}}\frac{{{f}_{1}}}{2}RT+{{n}_{2}}\frac{{{f}_{2}}}{2}RT $ $...
Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities 1 and 2. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is
Solution: C $ Let\text{ }the\text{ }angular\text{ }velocity\text{ }of\text{ }the\text{ }combination\text{ }be\text{ }W $ $ conservation\text{ }of\text{...
A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?
(1) 0.25 rad/s2 (2) 25 rad/s2 (3) 5 m/s2 (4) 25 m/s2 Answer (2) Solution:
A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be
(1) 450 (2) 1000 (3) 1800 (4) 225 Solution: Answer (3)
Figure shows a circuit contains three identical resistors with resistance R = 9.0 ohms each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf= 18 V. The current ‘i’ through the battery just after the switch closed is
(1) 0.2 A (2) 2 A (3) 0 ampere (4) 2 mA Solution: Answer (2) At t = 0, no current flows through R1 and R3 \ I = e/R2 =18 / 9 = 2...
The photoelectric threshold wavelength of silver is 3250 × 10–10 m. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength 2536 × 10–10 m is (Given h = 4.14 × 10–15 eVs and c = 3 × 108 ms–1)
(1) 0.6 × 106 ms–1 (2) 61 × 103 ms–1 (3) 0.3 × 106 ms–1 (4) 6 × 105 ms–1 Solution: Answer (1 & 4)* Both answers are correct.
The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?
(1) 20 Hz (2) 30 Hz (3) 40 Hz (4) 10 Hz Solution: Answer...
One end of string of length l is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ‘v’, the net force on the particle (directed towards center) will be (T represents the tension in the string)
$ (1)\,\,T+\frac{m{{v}^{2}}}{l} $ $ (2)\,\,T-\frac{m{{v}^{2}}}{l} $ $ (3)\,\,Zero $ $ (4)\,\,T $ Solution: Answer (4) N=mg & T is the tension. Because tension provides centripetal force, the net...
Thermodynamic processes are indicated in the following diagram.
Match the following Column-1 Column-2 Process I a. Adiabatic Process II b. Isobaric Process III c. Isochoric Process IV d. Isothermal Solution: Answer (1) Process...
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be
$ (1)\,\,\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{2}}-{{t}_{1}}} $ $ (2)\,\,\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{2}}+{{t}_{1}}} $ $ (3)\,\,{{t}_{1}}-{{t}_{2}} $ $ (4)\,\,\frac{{{t}_{1}}+{{t}_{2}}}{2} $ Solution:...
A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system
(1) Decreases by a factor of 2 (2) Remains the same (3) Increases by a factor of 2 (4) Increases by a factor of 4 Solution: Answer (1)
A thin prism having refracting angle 10° is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be
(1) 6° (2) 8° (3) 10° (4) 4° Sol. Answer (1) $ \left( \mu -1 \right)A+\left( \mu '-1 \right)A'=0 $ $ |\left( \mu -1 \right)A|=|\left( \mu '-1 \right)A'| $ $ (1.42-1)\times {{10}^{\circ }}=\left(...
The ratio of resolving powers of an optical microscope for two wavelengths λ1= 4000 Å and λ2=6000 Å is
(1) 9 : 4 (2) 3 : 2 (3) 16 : 81 (4) 8 : 27 Solution: Answer (2) We know that the resolving power is inversely...
A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F, because the method involves :
(1) Potential gradients (2) A condition of no current flow through the galvanometer (3) A combination of cells, galvanometer and resistances (4) Cells Solution: Answer (2) The reading of a...
If θ1 and θ2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by:
Solution: Option (4) is correct. Note that tan θ = V/H ...(1) where θ is true value of dip . Here we assumed θ=∝ Now, angle of dips, θ1 and θ2 have different formula tanθ1 = V/(H × cos∝ ...
A 250-Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 microA and subjected to a magnetic field of strength 0.85 T.Work done for rotating the coil by 180° against the torque is
(1) 4.55 micro Joule (2) 2.3 micro Joule (3) 1.15 micro Joule (4) 9.1 micro Joule Solution : Answer (4)
Which one of the following represents forward bias diode?
Solution: Answer B When the potential at A is higher (more positive) than the potential at B, the diode is said to be in forward bias, ie. Va > Vb
Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be
$ (1)\,\frac{3({{K}_{1}}+{{k}_{2}})}{2} $ $ (2)\,{{K}_{1}}+{{k}_{2}} $ $ (3)\,2({{K}_{1}}+{{k}_{2}}) $ $ (4)\,\frac{{{K}_{1}}+{{k}_{2}}}{2} $ Solution: Answer (4)
In an electromagnetic wave in free space the root mean square value of the electric field is Erms = 6 V/m. The peak value of the magnetic field is
(1) 2.83 × 10–8 T (2) 0.70 × 10–8 T (3) 4.23 × 10–8 T (4) 1.41 × 10–8 T Solution: Answer (1)
Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s]
(1) 361 Hz (2) 411 Hz (3) 448 Hz (4) 350 Hz Solution: Answer (3) $ {{f}_{A}}=f\left[ \frac{v+{{v}_{0}}}{v-{{v}_{0}}}...
The resistance of a wire is ‘R’ ohm. If it is melted and stretched to ‘n’ times its original length, its new resistance will be
$ (A)\,\frac{R}{{{n}^{2}}} $ $ (B)\,nR $ $ (C)\,\frac{R}{n} $ $ (D)\,{{n}^{2}}R $ Solution: Answer (D) Step 1: Resistance in terms of Volume and Length We know that Resistance is given by:...
The given electrical network is equivalent to
(1) OR Gate (2) NOR Gate (3) NOT Gate (4) AND Gate Solution: Answer (2) If we enter A=0 B=0 as input, we will get F=1 as output. Similarly, the following statements in the table are correct. The...
Radioactive material ‘A’ has decay constant ‘8‘ and material ‘B’ has decay constant ‘‘. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material ‘B’ to that ‘A’ will be
(1) 1/7$\lambda $ (2) 1/8$\lambda $ (3) 1/9$\lambda $ (4) 1/$\lambda $ Solution:
The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is
(A) $ \frac{h}{\sqrt{3mkT}} $ (B) $ \frac{3h}{\sqrt{3mkT}} $ (C) $ \frac{h}{\sqrt{mkT}} $ (D) $ \frac{2h}{\sqrt{mkT}} $ Solution: Answer (1) At thermal equilibrium with heavy water, we have: $...
An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current ‘I’ along the same direction is shown in Fig. Magnitude of force per unit length on the middle wire ‘B’ is given by
Solution: The correct answer is Answer (3). Magnetic field due to current-carrying wire $ =\frac{{{\mu }_{0}}~I}{2\pi d} $ force due to magnetic per field on current-carrying wire per unit length...
In a common emitter transistor amplifier the audio signal voltage across the collector is 3 V. The resistance of collector is 3 k. If current gain is 100 and the base resistance is 2 k, the voltage and power gain of the amplifier is
(1) 15 and 200 (2) 150 and 15000 (3) 20 and 2000 (4) 200 and 1000 Solution: Answer (2)
Young’s double slit experiment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly
(1) 1.59 (2) 1.69 (3) 1.78 (4) 1.25 Solution: Answer (3) μ =...
Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will
(1) move towards each other (2) Move away from each other (3) Will become stationary (4) Keep floating at the same distance between them Solution: The correct answer is option (1). Both astronauts...
Infinite number of bodies, each of mass 2kg are situated on x-axis at distance 1 m, 2m, 4m,8m…., respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
Option A -4 G Option B -G Option C -8/3 G Option D -4/3 G Solution: Correct Option A
The wettability of a surface by a liquid depends primarily on
Option A angle of contact between the surface and the liquid Option B viscosity Option C surface tension Option D density Solution: Correct Option A It depends on the angle of contact between the...
A uniform force of 3i + j newton acts on a particle of mass 2kg. Hence the particle is displaced from position2i + k meter to position 4i + 3j + k meter. The work done by the force on the particle is –
Option A 15 J Option B 9 J Option C 6 J Option D 13 J Solution: Correct Option B
A wire loop is rotated in magnetic field. The frequency of change of direction of the induced e. m. f. is
Option A six times per revolution Option B once per revolution Option C twice per revolution Option D four times per revolution Solution: Correct Option C...
When a proton is released from rest in a room, it starts with an initial acceleration a0 towards west. When it is projected towards north with a speed v0 it moves with an initial acceleration 3a0 towards west. The electric and magnetic fields in the room are:
Solution: The correct option is C.
If we study the vibration of a pipe open at both ends, then the following statements is not true:
Option A Pressure change will be maximum at both ends Option B Open end will be an antinode Option C Odd harmonics of the fundamental frequency will be generated Option D All harmonics of the...
Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is e. Now the strings are rigidly clamped at half the he ight. The equilibrium separation between the balls now become
Solution: The correct option is C.
A coil having self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decrease when
Option A and iron rod is inserted in the coil Option B frequency of the AC source is decreased Option C number of turns in the coil is reduced Option D A capacitance of reactance XC = XL is included...
A source of unknown frequency gives 4 beats / s, when sounded with a source of known frequency 250 Hz, the second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz, the unknown is
Option A 260 Hz Option B 254 Hz Option C 246 Hz Option D 240 Hz Solution: Correct Option B unknown source frequency f= 246 Hz or 254 Hz 492 Hz or 508 Hz is the source's second harmonic. When...
A wave travelling in the +ve x-direction having displacement along y-direction as 1 m, wavelength 2πm and frequency of 1/pi Hz is represented by:
Option A y = sin (2πx + 2πt) Option B y = sin (x - 2t) Option C y = sin (2πx - 2πt) Option D y = sin (10πx + 20πt) Solution: Correct Option B
The upper half of an inclined plane of inclination θ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by
Solution: The correct option is Option D. From the work-energy theorem W = change in KE, we have:
For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be –
Option A 1.5 cm Option B 5 cm Option C 2.5 cm Option D 1.67 cm Solution: Correct Option D...
A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct?
Option A The angular width of central maximum will be unaffected Option B Diffraction pattern is not observed on the screen in the case of electrons Option C The angular width of the central maximum...
A Plano convex lens fits exactly into a Plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices µ1 and µ2 and R is the radius of curvature of the curved surface of the lenses, then the focal length of combination is –
Solution: The correct option is Option D. Let the combined focal length be F, given as: where f1 and f2 are focal lengths of concave and convex lens respectively....
A small object of uniform density rolls up a curved surface with an initial velocity ‘v’. It reaches up to a maximum heights of 3v^2/4g with respect to the initial position. The object is
Option A Disc Option B Ring Option C Solid sphere Option D hollow sphere Solution:Correct Option A From the conservation of mechanical energy, we have:
In an experiment four quantities a, b, c, and d are measured with a percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows,error in P is
Option A 4 % Option B 14 % Option C 10 % Option D 7 % Solution: Correct Option B
An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms-1 and the second part of mass 2Kg moves with 8 ms-1 speed. If the third part files off with 4 ms-1 speed, then its mass is
Option A 17 kg Option B 3 kg Option C 5 kg Option D 7 kg Solution: Correct Option C Just before and after the explosion Momentum of the system will be conserved. This conclusion follows from the law...
The condition under which a microwave oven heats up a food item containing water molecules most efficiently is
Option A Infra-red waves produce heating in a microwave oven Option B The frequency of the microwaves must match the resonant frequency of the water molecules Option C The frequency of the...
A gas taken through the cycle A → B → C → A, as shown, what is the net work done by the gas?
Option A -2000 J Option B 2000 J Option C 1000 J Option D zero Solution: Correct Option C The total work done in a cyclic process equals the area of the triangle...
A piece of iron is heated in a flame. It first become dull red then becomes reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using:-
Option A Newton’s law of cooling Option B Stefan’s law Option C Wien’s law Option D Kirchhoff’s law Solution: The correct option is Option C. Temperature and wavelength are connected, according to...
The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from T1 K to T2 K is
Solution: The correct option is Option B According to the question, there are 1/4 moles in 1 g of He Then we can write the expression for the amount of heat energy required to raise its temperature...
The resistances of the four arms P,Q,R and S in a Wheatstone’s bridge are 10 ohm, 30 ohm, 30 ohm and 90 ohm, respectively. The e. m. f. and internal resistance of the cell are 7 volt and 5 ohm respectively. If the galvanometer resistance is 50 ohm, the current drawn from the cell will be
Option A 2.0 A Option B 1.0 A Option C 0.2 A Option D 0.1 A Solution: The correct option is Option C. Given circuit is a balanced Wheatstone bridge. Reff =...
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
Option A length = 300 cm, diameter = 3 mm Option B length = 50 cm, diameter = 0.5 mm Option C length = 100cm, diameter = 1 mm Option D length = 200 cm, diameter = 2 mm Solution The correct option is...
During an adiabatic process, the pressure of a gas found to be proportional to the cube of its temperature. The ratio of Cp/Cv for the gas is –
Option A 3/2 Option B 4/3 Option C 2 Option D 5/3 Solution: The correct option is Option A $ P\alpha {{T}^{3}} $ $ P{{V}^{\gamma }}=cons\tan t $ $ P{{\left( \frac{T}{P} \right)}^{\gamma }}=cons\tan...
For photoelectric emission from certain metal the cutoff frequency is v. If radiation of frequency 2v impinges on the metal plate, the maximum possible velocity of the emitted electron will be (m is the electron mass)-
The internal resistance of a 2.1 V cell which gives a current of 0.2 V cell which gives a current of 0.2 A through a resistance of 10Ω is
Option A 1.0 Ω Option B 0.2 Ω Option C 0.5 Ω Option D 0.8 Ω Solution: The correct option is Option. I = E/(R+r) 0.2 × (10+r) = 2.1 10 + r = 2.1/2 ×10 r = 10.5 − 10 r...
A bar magnet of length ‘ℓ’ and magnetic dipole moment ‘M’ is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be
Solution: The correct option is Option C. Let m represent the magnetic pole strength So, we have: M = mℓ In the new situation, we have:
A stone falls freely under gravity. It covers distances h1, h2 and h3 in the first 5 seconds, the next 5seconds and the next 5 seconds respectively. The relation between h1, h2 and h3 is
Solution: The correct option is Option C.
A body of mass ‘m’ is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be –
Option A 1/3 mgR Option B mg2R Option C 2/3 mgR Option D 3 mgR Solution: The correct option is Option C.
The velocity of a projectile at the initial point A is 2 i + 3 j m/s. It’s velocity (in m/s) at point B is
Solution: The correct option is D. The x-component of velocity will remain constant, but the y-component will fluctuate.
A wire of resistance 4Ω is stretched to twice its original length. The resistance of stretched wire would be
Option A 16 Ω Option B 2 Ω Option C 4 Ω Option D 8 Ω Solution: The correct option is option A. According to the question, the volume of the wire remains the same. Al = constant. So when the length...
A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is
Solution: The correct option is Option B
A, B and C are three points in a uniform electric field. The electric potential is
Option A Same at all the three points A, B and C Option B Maximum at A Option C Maximum at B Option D Maximum at C Solution: The correct option is Option C. Electric potential decrease as we move in...
A current loop in a magnetic field –
Option A Can be in equilibrium in two orientations, one stable while the other is unstable. Option B Experiences a torque whether the field is uniform or non-uniform in all orientation Option C Can...
Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is
Option A 9/31 Option B 5/27 Option C 3/23 Option D 7/29 Solution: We know that, E = hc/λ The energy difference should be minimal at the longest wavelength, and it becomes minimal when the...
The wavelength λe of an electron and λp of a photon of same energy E are related by:
The molar specific heats of an ideal gas at constant pressure and volume are denoted by Cp and Cv’ respectively. If and R is the universal gas constant, then Cv is equal to:
Solution: The correct option is option C. We know that, Cp − Cv = R It is also given that γ = Cp/Cv Therefore from the correlation of above two equations, we get CV...
The half-life of radioactive isotope ‘X’ is 20 years. It decays to another element ‘Y’ which is stable. The two elements ‘X’ and ‘Y’ were found to be in the ratio 1:7 in a sample of a given rock. The age of the rock is estimated to be:
Option A 100 years Option B 40 years Option C 60 years Option D 80 years Solution: The correct option is Option C
In a n-type semiconductor, which of the following statement is true:
Option A Holes are majority carriers and trivalent atoms are dopants Option B Electrons are majority carriers and trivalent atoms are dopants Option C Electron are minority carriers and pentavalent...
Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m? (g is the acceleration due to gravity)
Option A 6 mg Option B zero Option C 2 mg Option D 3 mg Solution: The correct option is Option B We know that, F = mass×acceleration According to the question, the...
The output (X) of the logic circuit shown in figure will be:
Solution: The correct option is Option D The first gate is the NAND gate and the second one is the NOT gate. So, their combination will result in AND gate.
In the given (V-T) diagram, what is the relation between pressure P1 and P2?
Option A Cannot be predicted Option B P2 =P1 Option C P2 > P1 Option D P2 < P1 Solution: The correct option is Option D According to the ideal gas equation, PV =nRT or we can write: V = nRT/P...