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# Question Paper (Section wise)

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Question 1
Positive Marks: 4 / Negative Marks: 1
•  1) A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60 J of heat flows into the system. If path ADB is used work down by the system is 10 J. the heat flow into the system in path ADB is 1. 40 J

2. 80 J

3. 100 J

4. 20 J

•  2) Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index µ. A student finds that, irrespective of what the incident angle I (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of µ is 1. 2. 3. 4. •  3) A heavy ball of mass M is suspended from the ceiling car by a light string of mass m (m<
1. 2. 3. 4. •  4) A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th  and Tc  respectively, then:
1. Th = Tc

2. Th = 2Tc

3. Th = 1.5Tc

4. Th = 0.5c

•  5) The actual value of resistance R, shown in the figure is 30 Ω. This is measured in an experiment as shown using the standard Formula where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is 5 % less, then the internal resistance of the voltmeter is: 1. 600 Ω

2. 570 Ω

3. 35 Ω

4. 350 Ω

•  6) A cylindrical plastic bottle of negligible mass of field with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic still motion at angular frequency ⍵. If the radius of the bottle is 2.5 cm then ⍵ is closed to: (density of water = 103 kg/m3)

•  7) In the given circuit the current through Zener Diode is close to: 1. 0.0 mA

2. 6.7 mA

3. 4.0 mA

4. 6.0 mA

•  8) An amplitude modulated signal is given by V (t) = 10 [1 + 0.6cos (2.2 × 104t) sin (5.5 × 105) t]. Here t is in seconds. The seconds. The sideband frequencies (in kHz) are. [Given π = 22/7]
1. 1785 and 1715

2. 1785 and 1715

3. 89.25 and 85.75

4. 892.5 and 857.5

•  9) A liquid of density ρ is coming out of a hose pipe of radius a with horizontal speed ν and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% losses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be:
1. 2. 3. 4. pv2

•  10) In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 µF. All values in the circuit are in µF. 1. 2. 3. 4. •  11) A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 × 103 kg/m3 and its Young’s modulus is 9.27 × 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations?
1. 7.5 kHz

2. 5 kHz

3. 2.5 kHz

4. 10 kHz

•  12) A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment is close to:
1. 322 ms-1

2. 341 ms-1

3. 335 ms-1

4. 328 ms-1

•  13) In the circuit shown, a four wire potentiometer is made of a 400 cm long wire, which extends between A and B. The resistance per unit length of the potentiometer wire is r = 0.01Ω/cm, If an ideal voltmeter is connected as shown with jockey J at 50 cm from end A, the expected reading of the voltmeter will be. 1. 0.75V

2. 0.20V

3. 0.25V

4. 0.50V

•  14) A common emitter amplifier circuit, built using an npn transistor, is shown in the figure. Its dc current gain is 250, Rc = 1kΩ and Vcc = 10V. What is the minimum base current for VCE to reach saturation? 1. 7 µA

2. 40 µA

3. 10 µA

4. 100 µA

•  15) 1. -106.5

2. -112.5

3. -118.5

4. -99.5

•  16) A system of three charges are placed as shown in the figure: If D >> d, the potential energy of the system is best given by:
1. 2. 3. 4. •  17) An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is ⊽, m is its mass and kB is Boltzmann constant, then its temperature will be:
1. 2. 3. 4. •  18) Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n =4 to n = 2) will be
1. 889.2 nm

2. 642.7 nm

3. 488.9 nm

4. 388.9 nm

•  19) In an experiment, brass and steel wires of length 1 m each with areas of cross section 1 mm2 are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produce a new elongation of 0.2 mm is [Given, the Young’s Modulus for steel and brass are respectively 120 × 109 N/m2 and 60 × 109 N/m2]
1. 8 × 106 N/m2

2. 0.2 × 106 N/m2

3. 1.2 × 106 N/m2

4. 4.0 × 106 N/m2

•  20) In Li++, electron in first Bohr orbit is excited to a level by a radiation of wavelength λ. When the ion gets deexcited to the ground state in all possible ways (including intermediate emission) a total of six spectral lines are observed. What is the value of λ? (Given: h = 6.63 × 1034 js; e = 3 × 108 ms–1)
1. 10.8 nm

2. 11.4 nm

3. 9.4 nm

4. 12.3 nm

•  21) A spaceship orbits around a planet at a height of 20 km from surface. Assuming that only gravitational field of the plant acts on the spaceship. What will be the number of complete revolutions made by the spaceship in 24 hours around the plane? [Given: Mass of plane = 8 × 1022 kg, Radius of planet = 2 × 106 m, Gravitational constant G = 6.67 × 10-11 Nm2/kg2]
•  22) The value of numerical aperture of the objective lens of a microscope is 1.25. If light of wavelength 5000 A is used, the minimum separation between two points, to be seen as distinct, will be _____× 10-7 m.
•  23) A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of 40 π rad s-1 about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8 × 10-9 T, then the charge carried by the ring is close to ________ μC. (µ0 = 4π × 10-7N/A2)
•  24) A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is – 180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is ______ J. •  25) In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of 5Ω, a balance is found when the cell is connected across 40 cm of the wire. The internal resistance of the cell is ______ Ω.
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