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Page 1 IITJAM 2022 Section A: Q.1Q.10 Carry ONE mark each. Q1. The equation 22 4 zz ? ? in the complex plane (where z is the complex conjugate of z ) represents (a) Ellipse (b) Hyperbola (c) Circle of radius 2 (d) Circle of radius 4 Ans. 1: (b) Q2. A rocket ? ? ' S moves at a speed / 2 c ms along the positive x axis, where c is the speed of light. When it crosses the origin, the clocks attached to the rocket and the one with a stationary observer ? ? S located at 0 x ? are both set to zero. If S observes an event at ?? , x t the same event occurs in the ' S frame at (a) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? (b) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? (c) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? (d) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? Ans. 2: (a) Q3. Consider a classical ideal gas of N molecules equilibrium at temperature T . Each molecule has two energy levels, ? ? and ?. The mean energy of the gas is (a) 0 (b) tanh B N kT ?? ? ? ?? ?? (c) tanh B N kT ?? ? ?? ?? ?? (d) 2 ? Ans. 3: (c) Page 2 IITJAM 2022 Section A: Q.1Q.10 Carry ONE mark each. Q1. The equation 22 4 zz ? ? in the complex plane (where z is the complex conjugate of z ) represents (a) Ellipse (b) Hyperbola (c) Circle of radius 2 (d) Circle of radius 4 Ans. 1: (b) Q2. A rocket ? ? ' S moves at a speed / 2 c ms along the positive x axis, where c is the speed of light. When it crosses the origin, the clocks attached to the rocket and the one with a stationary observer ? ? S located at 0 x ? are both set to zero. If S observes an event at ?? , x t the same event occurs in the ' S frame at (a) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? (b) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? (c) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? (d) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? Ans. 2: (a) Q3. Consider a classical ideal gas of N molecules equilibrium at temperature T . Each molecule has two energy levels, ? ? and ?. The mean energy of the gas is (a) 0 (b) tanh B N kT ?? ? ? ?? ?? (c) tanh B N kT ?? ? ?? ?? ?? (d) 2 ? Ans. 3: (c) Q4. At a temperature T, let ? and k denote the volume expansively and isothermal compressibility of a gas, respectively. Then k ? is equal to (a) V P T ? ?? ?? ? ?? (b) T P V ? ?? ?? ? ?? (c) V T P ? ?? ?? ? ?? (d) P T V ? ?? ?? ? ?? Ans. 4: (a) Q5. The resultant of the binary subtraction 1110101 0011110 ? is (a) 1001111 (b) 1010111 (c) 1010011 (d) 1010001 Ans. 5: (b) Q6. Consider a particle trapped in a threedimensional potential well such that ?? ,, 0 Uxyz ? for 0,0 ,0 xaya za ? ?? ?? ? and ? ? ,, Uxyz ? ? everywhere else. The degeneracy of the th 5 excited state is (a) 1 (b) 3 (c) 6 (d) 9 Ans. 6: (c) Q7. A particle of mass m and angular momentum L moves in space where its potential energy is ?? ? ? 2 0 Ur kr k ?? and r is the radial coordinate. If the particle moves in a circular orbit, then the radius of the orbit is (a) 1 2 4 L mk ?? ?? ?? (b) 1 2 4 2 L mk ?? ?? ?? (c) 1 2 4 2L mk ?? ?? ?? (d) 1 2 4 4L mk ?? ?? ?? Ans. 7: (b) Q8. Consider a twodimensional force field ????? ? 22 2 2 ˆˆ ,5 4 4 Fxy x ay bxyx x xy y y ?? ? ? ? ? ? If the force field is conservative, then the values of a and b are (a) 2 a ? and 4 b ? (b) 2 a ? and 8 b ? (c) 4 a ? and 2 b ? (d) 8 a ? and 2 b ? Ans. 8: (b) Page 3 IITJAM 2022 Section A: Q.1Q.10 Carry ONE mark each. Q1. The equation 22 4 zz ? ? in the complex plane (where z is the complex conjugate of z ) represents (a) Ellipse (b) Hyperbola (c) Circle of radius 2 (d) Circle of radius 4 Ans. 1: (b) Q2. A rocket ? ? ' S moves at a speed / 2 c ms along the positive x axis, where c is the speed of light. When it crosses the origin, the clocks attached to the rocket and the one with a stationary observer ? ? S located at 0 x ? are both set to zero. If S observes an event at ?? , x t the same event occurs in the ' S frame at (a) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? (b) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? (c) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? (d) 2 ' 2 3 ct xx ?? ?? ?? ?? and 2 ' 2 3 x tt c ?? ?? ?? ?? Ans. 2: (a) Q3. Consider a classical ideal gas of N molecules equilibrium at temperature T . Each molecule has two energy levels, ? ? and ?. The mean energy of the gas is (a) 0 (b) tanh B N kT ?? ? ? ?? ?? (c) tanh B N kT ?? ? ?? ?? ?? (d) 2 ? Ans. 3: (c) Q4. At a temperature T, let ? and k denote the volume expansively and isothermal compressibility of a gas, respectively. Then k ? is equal to (a) V P T ? ?? ?? ? ?? (b) T P V ? ?? ?? ? ?? (c) V T P ? ?? ?? ? ?? (d) P T V ? ?? ?? ? ?? Ans. 4: (a) Q5. The resultant of the binary subtraction 1110101 0011110 ? is (a) 1001111 (b) 1010111 (c) 1010011 (d) 1010001 Ans. 5: (b) Q6. Consider a particle trapped in a threedimensional potential well such that ?? ,, 0 Uxyz ? for 0,0 ,0 xaya za ? ?? ?? ? and ? ? ,, Uxyz ? ? everywhere else. The degeneracy of the th 5 excited state is (a) 1 (b) 3 (c) 6 (d) 9 Ans. 6: (c) Q7. A particle of mass m and angular momentum L moves in space where its potential energy is ?? ? ? 2 0 Ur kr k ?? and r is the radial coordinate. If the particle moves in a circular orbit, then the radius of the orbit is (a) 1 2 4 L mk ?? ?? ?? (b) 1 2 4 2 L mk ?? ?? ?? (c) 1 2 4 2L mk ?? ?? ?? (d) 1 2 4 4L mk ?? ?? ?? Ans. 7: (b) Q8. Consider a twodimensional force field ????? ? 22 2 2 ˆˆ ,5 4 4 Fxy x ay bxyx x xy y y ?? ? ? ? ? ? If the force field is conservative, then the values of a and b are (a) 2 a ? and 4 b ? (b) 2 a ? and 8 b ? (c) 4 a ? and 2 b ? (d) 8 a ? and 2 b ? Ans. 8: (b) Q9. Consider an electrostatic field E ? in a region of space. Identify the INCORRECT statement. (a) The work done in moving a charge in a closed path inside the region is zero (b) The curl of E ? is zero (c) The field can be expressed as the gradient of a scalar potential (d) The potential difference between any two points in the region is always zero Ans. 9: (d) Q10. Which one of the following figures correctly depicts the intensity distribution for Fraunhofer diffraction due to a single slit? Here, x denotes the distance from centre of the central fringe and I denotes the intensity. (a) (b) (c) (d) Ans. 10: (c) I x I x I x I xRead More
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