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Page 1 IIT-JAM 2020 SECTION – A MULTIPLE CHOICE QUESTIONS (MCQ) Q1 – Q10 carry one mark each. Q1. Which one of the following functions has a discontinuity in the second derivative at 0 x ? , where x is a real variable? (a) ?? 3 fxx ? (b) ?? fxxx ? (c) ? ? ? ? cos fxx ? (d) ?? 2 fxx ? Ans. : (b) Solution: ?? 2 2 2 dx xx dx x ? Assuming a function to be real. Plots: Q2. A collimated beam of laser light of wavelength 514nm is normally incident on a smooth glass slab placed in air. Given the refractive indices of glass and air are 1.47 and 1.0 , respectively, the percentage of light intensity reflected back is (a) 0 (b) 4.0 (c) 3.6 (d) 4.2 Ans. : (c) Solution: 2 12 12 11.47 0.036 0.036 100 3.6% 11.47 nn R nn ?? ?? ?? ?? ? ? ?? ???? ?? ?? ?? Q3. Two stationary point particles with equal and opposite charges are at some fixed distance from each other. The points having zero electric potential lie on: (a) A sphere (b) A plane (c) A cylinder (d) Two parallel planes Ans. : (b) Solution: All points on the plane are at equal distance from charges, so potential will be zero. y 2 1 1 ? 2 ? 1 2 x 1 ? 2 ? ? ? from 2 to 2 x ? Page 2 IIT-JAM 2020 SECTION – A MULTIPLE CHOICE QUESTIONS (MCQ) Q1 – Q10 carry one mark each. Q1. Which one of the following functions has a discontinuity in the second derivative at 0 x ? , where x is a real variable? (a) ?? 3 fxx ? (b) ?? fxxx ? (c) ? ? ? ? cos fxx ? (d) ?? 2 fxx ? Ans. : (b) Solution: ?? 2 2 2 dx xx dx x ? Assuming a function to be real. Plots: Q2. A collimated beam of laser light of wavelength 514nm is normally incident on a smooth glass slab placed in air. Given the refractive indices of glass and air are 1.47 and 1.0 , respectively, the percentage of light intensity reflected back is (a) 0 (b) 4.0 (c) 3.6 (d) 4.2 Ans. : (c) Solution: 2 12 12 11.47 0.036 0.036 100 3.6% 11.47 nn R nn ?? ?? ?? ?? ? ? ?? ???? ?? ?? ?? Q3. Two stationary point particles with equal and opposite charges are at some fixed distance from each other. The points having zero electric potential lie on: (a) A sphere (b) A plane (c) A cylinder (d) Two parallel planes Ans. : (b) Solution: All points on the plane are at equal distance from charges, so potential will be zero. y 2 1 1 ? 2 ? 1 2 x 1 ? 2 ? ? ? from 2 to 2 x ? Q4. For a system undergoing a first order phase transition at a temperature c T , which one of the following graphs best describes the variation of entropy (S ) as a function of temperature (T )? (a) (b) (c) (d) Ans. : (d) Solution: P g S T ? ?? ?? ?? ? ?? specific entropy. In first order Phase transition first order derivative of specific Gibbs free energy is discontinuous that is specific entropy. Q5. In a photoelectric effect experiment, a monochromatic light source emitting photon with energy greater than the work function of the metal under test is used. If the power of the light source is doubled, which one of the following statements is correct? (a) The number of emitted photoelectrons remains the same (b) The stopping potential remains the same (c) The number of emitted photoelectrons decreases (d) The stopping potential doubles Ans.: (b) Solution: Stopping potential is not defined at power of light source Q6. The figure below shows a cubic unit cell with lattice constant a . The shaded crystallographic plane intersects the x -axis at 0.5a . The Miller indices of the shaded plane are (a) ?? 210 (b) ?? 210 (c) ?? 110 (d) ?? 102 S c T T S c T T S c T T S c T T x y a z Page 3 IIT-JAM 2020 SECTION – A MULTIPLE CHOICE QUESTIONS (MCQ) Q1 – Q10 carry one mark each. Q1. Which one of the following functions has a discontinuity in the second derivative at 0 x ? , where x is a real variable? (a) ?? 3 fxx ? (b) ?? fxxx ? (c) ? ? ? ? cos fxx ? (d) ?? 2 fxx ? Ans. : (b) Solution: ?? 2 2 2 dx xx dx x ? Assuming a function to be real. Plots: Q2. A collimated beam of laser light of wavelength 514nm is normally incident on a smooth glass slab placed in air. Given the refractive indices of glass and air are 1.47 and 1.0 , respectively, the percentage of light intensity reflected back is (a) 0 (b) 4.0 (c) 3.6 (d) 4.2 Ans. : (c) Solution: 2 12 12 11.47 0.036 0.036 100 3.6% 11.47 nn R nn ?? ?? ?? ?? ? ? ?? ???? ?? ?? ?? Q3. Two stationary point particles with equal and opposite charges are at some fixed distance from each other. The points having zero electric potential lie on: (a) A sphere (b) A plane (c) A cylinder (d) Two parallel planes Ans. : (b) Solution: All points on the plane are at equal distance from charges, so potential will be zero. y 2 1 1 ? 2 ? 1 2 x 1 ? 2 ? ? ? from 2 to 2 x ? Q4. For a system undergoing a first order phase transition at a temperature c T , which one of the following graphs best describes the variation of entropy (S ) as a function of temperature (T )? (a) (b) (c) (d) Ans. : (d) Solution: P g S T ? ?? ?? ?? ? ?? specific entropy. In first order Phase transition first order derivative of specific Gibbs free energy is discontinuous that is specific entropy. Q5. In a photoelectric effect experiment, a monochromatic light source emitting photon with energy greater than the work function of the metal under test is used. If the power of the light source is doubled, which one of the following statements is correct? (a) The number of emitted photoelectrons remains the same (b) The stopping potential remains the same (c) The number of emitted photoelectrons decreases (d) The stopping potential doubles Ans.: (b) Solution: Stopping potential is not defined at power of light source Q6. The figure below shows a cubic unit cell with lattice constant a . The shaded crystallographic plane intersects the x -axis at 0.5a . The Miller indices of the shaded plane are (a) ?? 210 (b) ?? 210 (c) ?? 110 (d) ?? 102 S c T T S c T T S c T T S c T T x y a z Ans. : (a) Solution: (i) Intercepts along ,, xyz - axis ,, 2 a xyaz ?? ?? (ii) Divide by lattice parameters /2 1 ,, ,1, 2 aa aaa ? ?? (iii) Take reciprocal, 2,1,0 ? The Miller indices is ?? 210 Q7. For a particle moving in a central potential, which one of the following statements is correct? (a) The motion is restricted to a plane due to the conservation of angular momentum (b) The motion is restricted to a plane due to the conservation of energy only (c) The motion is restricted to a plane due to the conservation of linear momentum (d) The motion is not restricted to a plane Ans. : (a) Solution: For central force problem angular momentum J ? is conserved and .0 rJ ? ? ? which ensure that motion of particle is confined in plane Q8. Consider the motion of a quantum particle of mass m and energy E under the influence of a step potential of height 0 V . If R denotes the reflection coefficient, which one of the following statements is true? (a) If 0 4 ,1 3 EVR ?? (b) 0 4 ,0 3 EVR ? ? (c) 0 1 ,1 2 EVR ?? (d) 0 1 ,0.5 2 EVR ?? Ans. : (c) Solution: 0 2 V E ? 0 EV ?? , so 1 R ? Therefore, option (c) is correct x 0 V Page 4 IIT-JAM 2020 SECTION – A MULTIPLE CHOICE QUESTIONS (MCQ) Q1 – Q10 carry one mark each. Q1. Which one of the following functions has a discontinuity in the second derivative at 0 x ? , where x is a real variable? (a) ?? 3 fxx ? (b) ?? fxxx ? (c) ? ? ? ? cos fxx ? (d) ?? 2 fxx ? Ans. : (b) Solution: ?? 2 2 2 dx xx dx x ? Assuming a function to be real. Plots: Q2. A collimated beam of laser light of wavelength 514nm is normally incident on a smooth glass slab placed in air. Given the refractive indices of glass and air are 1.47 and 1.0 , respectively, the percentage of light intensity reflected back is (a) 0 (b) 4.0 (c) 3.6 (d) 4.2 Ans. : (c) Solution: 2 12 12 11.47 0.036 0.036 100 3.6% 11.47 nn R nn ?? ?? ?? ?? ? ? ?? ???? ?? ?? ?? Q3. Two stationary point particles with equal and opposite charges are at some fixed distance from each other. The points having zero electric potential lie on: (a) A sphere (b) A plane (c) A cylinder (d) Two parallel planes Ans. : (b) Solution: All points on the plane are at equal distance from charges, so potential will be zero. y 2 1 1 ? 2 ? 1 2 x 1 ? 2 ? ? ? from 2 to 2 x ? Q4. For a system undergoing a first order phase transition at a temperature c T , which one of the following graphs best describes the variation of entropy (S ) as a function of temperature (T )? (a) (b) (c) (d) Ans. : (d) Solution: P g S T ? ?? ?? ?? ? ?? specific entropy. In first order Phase transition first order derivative of specific Gibbs free energy is discontinuous that is specific entropy. Q5. In a photoelectric effect experiment, a monochromatic light source emitting photon with energy greater than the work function of the metal under test is used. If the power of the light source is doubled, which one of the following statements is correct? (a) The number of emitted photoelectrons remains the same (b) The stopping potential remains the same (c) The number of emitted photoelectrons decreases (d) The stopping potential doubles Ans.: (b) Solution: Stopping potential is not defined at power of light source Q6. The figure below shows a cubic unit cell with lattice constant a . The shaded crystallographic plane intersects the x -axis at 0.5a . The Miller indices of the shaded plane are (a) ?? 210 (b) ?? 210 (c) ?? 110 (d) ?? 102 S c T T S c T T S c T T S c T T x y a z Ans. : (a) Solution: (i) Intercepts along ,, xyz - axis ,, 2 a xyaz ?? ?? (ii) Divide by lattice parameters /2 1 ,, ,1, 2 aa aaa ? ?? (iii) Take reciprocal, 2,1,0 ? The Miller indices is ?? 210 Q7. For a particle moving in a central potential, which one of the following statements is correct? (a) The motion is restricted to a plane due to the conservation of angular momentum (b) The motion is restricted to a plane due to the conservation of energy only (c) The motion is restricted to a plane due to the conservation of linear momentum (d) The motion is not restricted to a plane Ans. : (a) Solution: For central force problem angular momentum J ? is conserved and .0 rJ ? ? ? which ensure that motion of particle is confined in plane Q8. Consider the motion of a quantum particle of mass m and energy E under the influence of a step potential of height 0 V . If R denotes the reflection coefficient, which one of the following statements is true? (a) If 0 4 ,1 3 EVR ?? (b) 0 4 ,0 3 EVR ? ? (c) 0 1 ,1 2 EVR ?? (d) 0 1 ,0.5 2 EVR ?? Ans. : (c) Solution: 0 2 V E ? 0 EV ?? , so 1 R ? Therefore, option (c) is correct x 0 V Q9. The Boolean function ?? ? ? PQ P Q Q Q ?? is equivalent to: (a) P (b) P (c) PQ (d) PQ Ans. : (b) Solution: ???? Y PQP QQQ ?? ? ? ? ? ? .1 YPQPQ PPQPQ ?? ? ? ? ? ? ?? ?? 11 YP Q PQ P Q P ?? ? ? ? ? ? Q10. Three point charges each carrying a charge q are placed on the vertices of an equilateral triangle of side L . The electrostatic potential energy of the configuration is: (a) 2 0 1 4 q L ?? (b) 2 0 2 4 q L ?? (c) 2 0 3 4 q L ?? (d) 2 0 1 q L ?? Ans. 10: (c) Solution: Work done in placing charges 1 0 W ? , 2 2 0 1 4 q W L ?? ? and 2 3 00 112 44 qq q Wq LL L ?? ?? ?? ??? ?? ?? Also Total work done ?? 22 12 3 00 13 12 44 qq WW W LL ?? ?? ? ??? ? ? q q q ? ? ? L L L 1 2 3 Page 5 IIT-JAM 2020 SECTION – A MULTIPLE CHOICE QUESTIONS (MCQ) Q1 – Q10 carry one mark each. Q1. Which one of the following functions has a discontinuity in the second derivative at 0 x ? , where x is a real variable? (a) ?? 3 fxx ? (b) ?? fxxx ? (c) ? ? ? ? cos fxx ? (d) ?? 2 fxx ? Ans. : (b) Solution: ?? 2 2 2 dx xx dx x ? Assuming a function to be real. Plots: Q2. A collimated beam of laser light of wavelength 514nm is normally incident on a smooth glass slab placed in air. Given the refractive indices of glass and air are 1.47 and 1.0 , respectively, the percentage of light intensity reflected back is (a) 0 (b) 4.0 (c) 3.6 (d) 4.2 Ans. : (c) Solution: 2 12 12 11.47 0.036 0.036 100 3.6% 11.47 nn R nn ?? ?? ?? ?? ? ? ?? ???? ?? ?? ?? Q3. Two stationary point particles with equal and opposite charges are at some fixed distance from each other. The points having zero electric potential lie on: (a) A sphere (b) A plane (c) A cylinder (d) Two parallel planes Ans. : (b) Solution: All points on the plane are at equal distance from charges, so potential will be zero. y 2 1 1 ? 2 ? 1 2 x 1 ? 2 ? ? ? from 2 to 2 x ? Q4. For a system undergoing a first order phase transition at a temperature c T , which one of the following graphs best describes the variation of entropy (S ) as a function of temperature (T )? (a) (b) (c) (d) Ans. : (d) Solution: P g S T ? ?? ?? ?? ? ?? specific entropy. In first order Phase transition first order derivative of specific Gibbs free energy is discontinuous that is specific entropy. Q5. In a photoelectric effect experiment, a monochromatic light source emitting photon with energy greater than the work function of the metal under test is used. If the power of the light source is doubled, which one of the following statements is correct? (a) The number of emitted photoelectrons remains the same (b) The stopping potential remains the same (c) The number of emitted photoelectrons decreases (d) The stopping potential doubles Ans.: (b) Solution: Stopping potential is not defined at power of light source Q6. The figure below shows a cubic unit cell with lattice constant a . The shaded crystallographic plane intersects the x -axis at 0.5a . The Miller indices of the shaded plane are (a) ?? 210 (b) ?? 210 (c) ?? 110 (d) ?? 102 S c T T S c T T S c T T S c T T x y a z Ans. : (a) Solution: (i) Intercepts along ,, xyz - axis ,, 2 a xyaz ?? ?? (ii) Divide by lattice parameters /2 1 ,, ,1, 2 aa aaa ? ?? (iii) Take reciprocal, 2,1,0 ? The Miller indices is ?? 210 Q7. For a particle moving in a central potential, which one of the following statements is correct? (a) The motion is restricted to a plane due to the conservation of angular momentum (b) The motion is restricted to a plane due to the conservation of energy only (c) The motion is restricted to a plane due to the conservation of linear momentum (d) The motion is not restricted to a plane Ans. : (a) Solution: For central force problem angular momentum J ? is conserved and .0 rJ ? ? ? which ensure that motion of particle is confined in plane Q8. Consider the motion of a quantum particle of mass m and energy E under the influence of a step potential of height 0 V . If R denotes the reflection coefficient, which one of the following statements is true? (a) If 0 4 ,1 3 EVR ?? (b) 0 4 ,0 3 EVR ? ? (c) 0 1 ,1 2 EVR ?? (d) 0 1 ,0.5 2 EVR ?? Ans. : (c) Solution: 0 2 V E ? 0 EV ?? , so 1 R ? Therefore, option (c) is correct x 0 V Q9. The Boolean function ?? ? ? PQ P Q Q Q ?? is equivalent to: (a) P (b) P (c) PQ (d) PQ Ans. : (b) Solution: ???? Y PQP QQQ ?? ? ? ? ? ? .1 YPQPQ PPQPQ ?? ? ? ? ? ? ?? ?? 11 YP Q PQ P Q P ?? ? ? ? ? ? Q10. Three point charges each carrying a charge q are placed on the vertices of an equilateral triangle of side L . The electrostatic potential energy of the configuration is: (a) 2 0 1 4 q L ?? (b) 2 0 2 4 q L ?? (c) 2 0 3 4 q L ?? (d) 2 0 1 q L ?? Ans. 10: (c) Solution: Work done in placing charges 1 0 W ? , 2 2 0 1 4 q W L ?? ? and 2 3 00 112 44 qq q Wq LL L ?? ?? ?? ??? ?? ?? Also Total work done ?? 22 12 3 00 13 12 44 qq WW W LL ?? ?? ? ??? ? ? q q q ? ? ? L L L 1 2 3 Q11 - Q30 carry two marks each. Q11. Which of the following statements is correct? Given ?? ! !! n n m mn m ?? ? ?? ? ?? is the binomial coefficient (a) 22 4 4 cos cos cos sin cos sin ... 24 nn n nn n?? ? ? ? ? ?? ?? ?? ?? ? ? ?? ?? ?? ?? (b) 133 sin cos sin cos sin ... 13 nn nn n??? ?? ?? ?? ?? ?? ? ?? ?? ?? ?? (c) 22 44 cos cos cos sin cos sin .... 24 nn n nn n? ? ?? ?? ?? ?? ?? ?? ? ? ?? ?? ?? ?? (d) 22 44 sin cos cos sin cos sin .... 24 nn n nn n?? ? ? ? ? ?? ?? ?? ?? ? ? ?? ?? ?? ?? Ans. : (a) Solution: Let’s invoke De Moivre’s theorem here. We have ?? ?? ? ? ? ? ? ? cos sin cos sin n ni n i ? ?? ? ?? ? Since n is a positive integer, the binomial theorem holds, ?? ?? ?? cos sin n i ? ? ? Hence, by expanding, we have ?? ?? ?? ?? ? ? ?? ? ? ?? ? ? 1222 1 cos sin cos cos sin cos sin .... 12 n nn n nn ini i ?? ? ? ? ? ? ?? ? ?? ? ? ? ? ? ? Since 23 4 5 1, , 1, ,.... ii ii ii ?? ?? ? ? , we have ?? ?? ?? ?? ? ? ?? ?? 22 1 cos sin cos cos sin 12 n nn nn i ? ?? ? ? ? ? ? ?? ? ? ? ? ? ??? ?? ? ?? ?? 44 12 3 cos sin .... 12 3 4 n nn n n ?? ? ? ?? ? ??? ? ?? ? ? ?? ?? ? ? ? ? ? ? ?? ? ? 133 12 3 cos sin cos sin .... 12 3 nn nn n n in ?? ? ? ?? ?? ?? ? ?? ? ? ? ?? ?? ?? By equating the real and imaginary parts, we obtainRead More

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