2. One end of a taut string of length 3m along the x axis is fixed at x=0.The speed of the waves in the string is 100 πππ π β1. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is(are) A) (π‘π‘) = π΄π΄ sin ππππ 6 cos 50ππππ 3 B) (π‘π‘) = π΄π΄ sin ππππ 3 cos 100ππππ 3 C) (π‘π‘) = π΄π΄ sin5ππππ 6 cos 250ππππ 3 D) (π‘π‘) = π΄π΄ sin5ππππ 2 cos 250ππππ
Ans: (A), (C) and (D)
3. LetπΈπΈ1(ππ), πΈπΈ2(ππ) and πΈπΈ3(ππ) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density Ξ», and an infinite plane with uniform surface charge density Ο. If πΈπΈ1(ππ0) = πΈπΈ2(ππ0) = πΈπΈ3(ππ0) at a given distance r0, then A) ππ = 4ππππππ0 2 B) ππ0 = ππ 2ππππ C) πΈπΈ1 (ππ0β2) = 2πΈπΈ2 (ππ0β2) D) πΈπΈ2 (ππ0β2) =4πΈπΈ3 (ππ0β2)
Ans: (C)
4. Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5kgwater by 40K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K? A) 4 if wires are in parallel B) 2 if wires are in series C) 1 if wires are in series D) 0.5 if wires are in parallel
Ans: (B) and (D)
5. Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio: A) 4: 1 B) 25: 9 C) 16: 9 D) 5: 3
Ans: (B)
6. Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is1019mβ3 and their mobility is 1.6 m2/ (V.s) then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored) is close to: A) 2οm B) 0.4οm C) 4οm D) 0.2οm
Ans: (B)
7. A sample of radioactive material A, that has an activity of 10 mCi (l Ci = 3.7 Γ l010 decays/s), has twice the number of nuclei as another sample of a different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively: A) 20 days and 5 days B) 20 days and 10days C) 5 days and 10 days D) 10days and 40 days
Ans. (A)
8. A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is: A) 0.55 cm away from the lens B) 1.1 cm away from the lens C) 0.55 cm towards the lens D) 0
Ans: (A)
9. Two plane mirrors arc inclined to each other such that a ray of light incident on the first mirror (M1) and parallel to the second mirror (M2) is finally reflected from the second mirror (M2) parallel to the first mirror (M1). The angle between the two mirrors will be: A) 90Β° B) 45Β° C) 75Β° D) 60Β°
Ans: (D)
10. In a Young’s double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength = 500 nm is incident on the slits. The total number of bright fringes that are observed in the angular range β30Β°β€αΆΏβ€30Β°is: A) 320 B) 641 C) 321 D) 640
Ans: (B)
11. A rod of mass ‘M’ and length ‘2L’ is suspended at its middle by a wire. It exhibits torsional oscillations; if two masses each of ‘m’ are attached at distance ‘L/2’ from its center on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is close to: A) 0.17 B) 0.37 C) 0.57 D) 0.77
Ans: (B)
12. A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27Β°C. Amount of heat transferred to the gas, so that rams velocity of molecules is doubled, is about: [Take R = 8.3 J/ K mole] A) 10 k B) 0.9 kJ C) 6 kJ D) 14 Ki
Ans: (A)
13. In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of band width 6 MHz are (Take velocity of light c = 3 Γ 108m/s, h = 6.6 Γ 10β34 J-s) A) 3.75 Γ 106 B) 4.87 Γ 105 C) 3.86 Γ 106 D) 6.25 Γ 105
Ans: (D)
14. The energy required to take a satellite to a height ‘h’ above Earth surface (radius of Earth = 6.4 Γ 103 km) is E1 and kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for which E1 and E2 are equal, is: A) 1.28 Γ 104 km B) 6.4 Γ 103 km C) 3.2 Γ 103 k D) 1.6 Γ 103 km
Ans: (C)
15. A series AC circuit containing an inductor (20 MH), a capacitor (120 Β΅F) and a resistor (60ο) is driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is: A) 2.26 Γ 103 J B) 3.39 Γ 103 J C) 5.65 Γ 102 J D) 5.17 Γ 102 J
Ans: (D)
16. The magnetic field associated with a light wave is given, at the origin, by B = B0 [sin (3.14 Γ 107) ct + sin (6.28 Γ 107) ct]. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons? (c = 3 Γ l08msβ1, h = 6.6 Γ 10β34 J-s) A) 7.72 eV B) 8.52 eV C) 12.5 eV D) 6.82 eV
Ans: (A)
17. Two forces P and Q of magnitude 2F and 3F, respectively, are at an angle ΞΈ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle is: A) 30Β° B) 60Β° C) 90Β° D) 120Β°
Ans: (D)
18. The self-induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is: A) 437.5 J B) 637.5 J C) 740 J D) 540 J
Ans: (A)
19. A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11V is connected across it is: A) 11 Γ 10β5 W B) 11 Γ 10β4 W C) 11 Γ 105 W D) 11 Γ 10β3 W
Ans: (A)
20. The diameter and height of a cylinder are measured by a meter scale to be 12.6 Β± 0.1 cm and 34.2 Β± 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures? A) 4260 Β± 80 cm3 B) 4300 Β± 80 cm3 C) 4264.4 Β± 81.0 cm3 D) 4264 Β± 81 cm3
Ans: (A)
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