SPL Module-1

Class (XII) - [SPJ 2023 - Module - I] STUDY MATERIAL [SPJ 2023] CLASS (XII) Module - I PHYSICS CHEMISTRY MATHEMATICS 1

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Class (XII) - [SPJ 2023 - Module - I] CONTENTS Physics 1. Electrostatics ------------------------------------------------------------------- 05 2. Current electricity ------------------------------------------------------------- 22 3. Moving charges and magnetism ------------------------------------------- 37 Chemistry 1. Solid state ----------------------------------------------------------------------- 49 2. Solutions ------------------------------------------------------------------------- 59 3. Electrochemistry--------------------------------------------------------------- 69 Mathematics 1. Relations functions and binary optation -------------------------------- 83 2. Trigonometry-II ----------------------------------------------------------------- 99 3. Matrices and determinants------------------------------------------------- 121 3

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PHYSICS Class (XII) - [SPJ 2023 - Module - I] CHAPTER - 01 ELECTROSTATICS QUESTIONS HOME WORK 1. Which of the following is not true about the electric charge? A) Charge on a body is always an integral multiple of a certain charge known as the charge of an electron B) Charge is a scalar quantity C) Net charge on an isolated system is always conserved D) Charge can be converted into energy and energy can be converted into charge 2. A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium, if q is equal to : A) –Q/2 B) –Q/4 C) +Q/4 D) +Q/2 3. A particle having charge q1 exerts electrostatic force F on charge q2 at rest. If a particle having charge q1/4 is placed midway between the line joining the two charges q1 and q2 then electrostatic force on q2 due to q1 will become / remain A) 2 F B) F/2 C) F D) Zero 3R 4. The electric field at a distance 2 from the centre of a charged conducting spherical shell of radius R R is E. The electric field at a distance 2 from the centre of the sphere is E B) zero C) E E A) 2 D) 3 5. Two point charges placed at a certain distance r in air exert a force F on each other. Then the distance r at which these charges will exert the same force in a medium of dielectric constant K is given by : A) r B) r / K C) r / K D) r K 5

Class (XII) - [SPJ 2023 - Module - I] 6. Figure shows the electric lines of force emerging from a charged body. If the electric field at A and B are EA and EB respectively and if the displacement between A and B is r, then A) EA > EB B) EA < EB C) EA  EB D) EA  EB r r2 7. The electric field intensity which would be just sufficient to balance the weight of a particle of charge 10 C and mass 10 mg is (Take g = 10 m/s2) A) 10 N/C, in an upward direction B) 103N/C, in a downward direction C) 10 N/C, in a downward direction D) 104N/C, in an upward direction 8. Two equal negative charges –q are fixed at points (0, a) and (0, –a) on the y-axis. A positive charge ‘q’ is released from rest at the point (x<<a) on the x-axis. What is the magnitude of acceleration on the charge q? A) 2 kq2 x B) kq2 x C) 2 kq2 x D) kq2 x ma3 ma3 ma ma2 9. Total electric flux coming out of a unit positive charge put in air is : A) 0 B) 01 C) (40 )1 D) 40 10. In a region, the intensity of an electric field is given by  ˆi  2ˆj in NC–1. The electric flux through a E surface  5 ˆi m2 in the region is : S A) 5 Nm2C–1 B) 10 Nm2C–1 C) 15 Nm2C–1 D) 20 Nm2C–1 11. An electric dipole with dipole moment 4 × 10–9 Cm is aligned at 300 with the direction of a uniform electric field of magnitude 10 × 104 NC–1. The magnitude of the torque acting on the dipole is : A) 10–4 Nm B) 10–5 Nm C) 2 × 10–4 Nm D) 2 × 10–5 Nm 6

Class (XII) - [SPJ 2023 - Module - I] 12. The net dipole moment of the system is of the magnitude -2q 2a 1200 2a +q +q A) q × 2a B) 2q × 2a C) q × a D) 2 × 2q × 2a 13. A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in figure as : 1 2 3 4 A) 2 B) 3 C) 4 D) 1 14. Consider the charge configuration and spherical Gaussian surface as shown in figure. When calculating the flux of the electric field over the spherical surface, the electric field will be due to : + q1 q2 - q1 A) q2 B) Only the positive charges C) All the charges D) +q1 and –q1 15. Two parallel infinite line charges with linear charge densities  C / m and   C / m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges? A) Zero B) 2 N / C C)  N/C D)  N/C 0R 0R 20R 16. Electric field at a distance ‘r’ from infinitely long conducting sheet is proportional to :- A) r–1 B) r–2 C) r–3/2 D) Independent of r 7

Class (XII) - [SPJ 2023 - Module - I] 17. Which of the following graphs shows the variation of electric field E due to a hollow spherical conductor of radius R as a function of distance from the centre of the sphere A) B) C) D) 18. An electric dipole is in unstable equilibrium in the uniform electric field. The angle between its dipole moment and the electric field is : A) 900 B) 1200 C) 1800 D) 00 19. Two equal charges q are placed at a distance of 2a and a third charge –2q is placed at the midpoint. The potential energy of the system is : q2 6q2 7q2 9q2 A) 80a B) 80a C) 80a D) 80a 20. A uniform electric field pointing in positive x direction exist in a region. Let A be the origin, B be the point on the x-axis at X = +1 cm and C be the point on the y-axis at Y = +1 cm. Then the potentials at the points A, B and C satisfy A) VA < VB B) VA > VB C) VA < VC D) VA > VC 21. Four charges +Q, –Q, +Q, –Q are placed at the corners of a square taken in order. At the centre of the square A) E = 0, V = 0 B) E  0, V  0 C) E  0, V  0 D) E  0, V  0 22. The figure shows some of the equipotential surfaces. Magnitude and direction off the electric field is given by : A) 200 V/m, making an angle 1200 with the X-axis B) 100 V/m, pointing towards the negative x-axis C) 200 V/m, making an angle –600 with the x-axis D) 100 V/m, making an angle 300 with the x-axis 8

Class (XII) - [SPJ 2023 - Module - I] 23. Four point charges –Q, –q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is : A) Q = –q B) Q 1 C) Q = q D) Q 1 q q 24. Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of bigger drop compared to each individual small drop is : A) 8 times B) 4 times C) 2 times D) 32 times 25. Two charged spherical conductors of radii R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres 1 / 2 is : A) R1 B) R2 C)  R1  D) R12 R2 R1  R2    R 2 2 26. Four plates of equal area A are separated by equal distance d and are arranged as shown in the figure. The equivalent capacity is : A) 20 A B) 30 A C) 40 A D) 0A d d d d 27. Separation between the plates of a parallel plate capacitor is d and the area of each plate is A. When a slab of material of dielectric constant K and thickness t (t < d) is introduced between the plates, its capacitance becomes : A) 0 A B) 0 A C) 0 A D) 0 A d  t  1  1  d  t  1  1  d  t 1  1  d  t  1  1  K  K  K  K  28. An air capacitor of capacity C 10 F is connected to a constant voltage battery of 12 V. Now the space between the plates is filled with a liquid of dielectric constant 5. The charge that flows now from battery to the capacitor is : A) 120 C B) 699 C C) 480 C D) 24 C 29. A battery does 200 J of work in charging a capacitor. The energy stored in the capacitor is : A) 200 J B) 100 J C) 50 J D) 400 J 30. Two identical capacitors have the same capacitance C. One of them is charged to potential V1 and the other to V2. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is : A) 1 C ( V12  V22 ) B) 1 C (V12  V22 ) C) 1 C ( V1  V2 )2 D) 1 C (V1  V2 )2 4 4 4 4 9

Class (XII) - [SPJ 2023 - Module - I] 31. Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron) A) 40Fd2 B) 40 Fe 2 C) 40Fd2 D) 40Fd2 e2 d2 e2 q2 32. A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to A) -Q/4 B) Q/4 C) -Q/2 D) Q/2 33. A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is A) qEy B) qE2y C) qEy2 D) q2Ey 34. The given figure gives electric lines of force due to two charges q1 and q2. What are the signs of the two charged? A) q1 is positive but q2 is negative B) q1 is negative but q2 is positive C) both are negative D) both are positive 35. An electric dipole is placed at an angle of 30o with an electric field intensity 2 × 105N C-1. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2cm, is A) 8 mC B) 2 mC C) 5 mC D) 7C 36. A hollow cylinder has a charge q coulomb within it. If  is the electric flux in units of volt meter associated with the curved surface B, the flux linked with the plane surface A in units of V-m will be q  q  1 q  A) 20 B) 3 C) 0 D)    2  0  37. The electric potential at a point in free space due to charge Q coulomb is Q ×1011 volts. The electric field at that point is A) 40Q 1020 volt/m B) 120Q 1022 volt/m C) 40Q 1022 volt/m D) 120Q 1020 volt/m 10

Class (XII) - [SPJ 2023 - Module - I] 38. Four electric charges +q, +q, -q and -q are placed at the corners of a square of side 2L (see figure). The electric potential at point A, midway between the two charges +q and +q, is  A) 1 2q 1 5 B) 1 2q 1  1 40 L 40 L 5  C) 1 2q 1  1 D) Zero 40 L 5  39. Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2a. D and E are the mid points of BC and CA. The work done in taking a charge Q from D to E is 3qQ 3qQ qQ D) zero A) 40a B) 80a C) 40a 40. A network of four capacitors of capacity equal to C1  C, C2  2C, C3  3C and C4  4C are connected to a battery as shown in the figure. The ratio of the charges on C2 and C4 is A) 4/7 B) 3/22 C) 7/4 D) 22/3 11

Class (XII) - [SPJ 2023 - Module - I] 41. Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become A)  2r  B)  2r   3   3  C)  1 2 r  2  D)  3 2  42. Point charges +4q, -q and +4q are kept on the X-axis at point x=0, x=a and x=2a respectively. Then A) only -q is in stable equilibrium B) all the charges are in stable equilibrium C) all of the charges are in unstable equilibrium D) none of the charges is in equilibrium 43. A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E . Due to the force qE , its velocity increases from 0 to 6 ms-1 in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively A) 2 m s-1, 4 m s-1 B) 1 m s-1, 3 m s-1 C) 1 m s-1, 3.5 m s-1 D) 1.5 m s-1, 3 m s-1 44. Two parallel infinite line charges with linear charge densities  C / m and  C / m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges? A)  N/C B) Zero 20R C) 2 N/C D)  N/C 0R 0R 12

Class (XII) - [SPJ 2023 - Module - I] 45. An infinitely long thin non-conducting wire is parallel to the Z-axis and carries a uniform line charge density  . It pierces a thin non-conducting spherical shell of radius R in such a way that the arc PQ subtends an angle 120 at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is 0 . Which of the following statements is (are) true? A) The electric flux through the shell is 3 R / 0 B) The Z-component of the electric field is zero at all the points on the surface of the shell C) The electric flux through the shell is 2 R / 0 D) The electric field is normal to the surface of the shell at all points 46. A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with dielectric in between is C1. When the capacitor is charged, the plate area covered by the dielectric gets charge Q1 and the rest of the area gets charge Q2. The electric field in the dielectric is E1 and that in the other portion is E2. Choose the correct option/options, ignoring edge effects A) E1 1 B) E1  1 C) Q1  3 D) C  2 K E2 E2 K Q2 K C1 K 47. There are two small identical metallic spheres A and B each carrying same charge. These two spheres are found to repel each other with a force F. A third identical neutral metal sphere C is first brought in contact with A and then B. The sphere C is taken away from A and B. The magnitude of electric force now is found to be 3F/x. What is x? 13

Class (XII) - [SPJ 2023 - Module - I] 48. A parallel plate capacitor is connected to a battery and when it is fully charged, the energy stored in the capacitor is U1. Now it is disconnected from the battery and then reconnected to the same battery but with the polarity reversed. During the time capacitor is again charged, heat H is found to get dissipated from the capacitor. Calculate H/U1. 49. A parallel plate air capacitor has a capacitance of C0. Separation between the plates is reduced to one third and a slab of dielectric constant 3 is filled between the plates and thus the new capacitance becomes C. What will be C/C0? 50. Column - I Column - II A) Non-conducting solid sphere p) Uniform electric field B) Non-conducting solid cylinder of q) Electric field intensity is directly proportional to the large length distance from centre for points inside C) Uniformly charged large surface r) Electric field intensity is inversely proportional to the distance from centre for points outside it D) Point charge s) Electric field intensity in a region of space is inversely proportional to the square of distance from the centre LEVEL - I 1. In a neutral sphere, 5 × 1021 electrons are present. If 10 percent electrons are removed, then calculate the charge on the sphere. A) 60 C B) 70 C C) 80 C D) 90 C 2. Two identical metal spheres carry charges of +q and -2q respectively. When the spheres are separated by a large distance r, the force between them is F. Now the spheres are allowed to touch and then moved back to the same separation. Find the new force of repulsion between them A) F/4 B) F/6 C) F/8 D) F/10 3. ABC is a right angles triangle. Calculate the magnitude of force on charge -Q. A) k Q2 B) k Q2 2 C) k Q2 2 D) k Q2 3 a2 a2 a2 a2 4. Two charges 4C and36C are placed 60cm apart. At what distance from the larger charge is the electric field intensity is zero? A) 35 cm B) 45 cm C) 55 cm D) 65 cm 14

Class (XII) - [SPJ 2023 - Module - I] 5. A point charge of 2.0C is at the centre of a cubic Gaussian surface of edge 9.0 cm. What is the net electric flux through the surface? A) 2.25 105 Nm2 /C B) 3.25105 Nm2 /C C) 4.25 105 Nm2 /C D) None of these 6. Three charges -q, Q and -q are places at equal distances on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio Q:q? A) 1:2 B) 1:3 C) 1:4 D) 1:5 7. Three point charges q, -2q and -2q are placed at the vertices of an equilateral triangle of side a. find the work done by external forces to increase their separation to 2a? A) kq2 B) kq2 C) 2kq2 D) Zero a 2a a 8. Calculate the electric potential at the center of the square shown in figure. A) -0.6 × 103 V B) -1.3 × 103 V C) 1.8 × 103 V D) -2.4 × 103 V 9. An electric dipole is placed making at an angle 60o with an electric field of strength 4 × 105 N/C. It experiences a torque equal to 8 3 N-m . Calculate the charge on the dipole, if it is of length 4cm. A) 1 mC B) 2 mC C) 3 mC D) 4 mC 10. Four plates of the same area A are joined as shown in the figure. The distance between successive plates is d. Find the equivalent capacity across PQ will be A) 0A B) 20A C) 30A D) 40A d d d d 11. The distance between the plates of a parallel plate capacitor is ‘d’. Another thick metal plate of thickness d/2 and area same as that of plates is so placed between the plates, that it does not touch them. The capacity of the resulting capacitor: A) remains the same B) becomes double C) becomes half D) becomes one fourth 15

Class (XII) - [SPJ 2023 - Module - I] LEVEL - II 1. A polythene piece rubbed with wool is found to have a negative charge of 4 × 10-7 C. The mass transferred is: A) 1.8 × 10-18 kg from polythene to wool B) 1.8 × 10-18 kg from wool to polythene C) 3 × 10-16 kg from wool to polythene D) 22.75 × 10-19 kg from wool to polythene 2. Two equal and opposite charges are placed at a certain distance. The force between them is F. If 25% of one charge is transferred to other, then the force between them is: A) F B) 9F/16 C) 15F/16 D) 4F/5 3. When air is replaced by a dielectric medium of force constant K, the maximum force of attraction between two charges, separated by a distance A) decreases K-times B) increases K-times C) remains unchanged D) becomes 1 times K2 4. ABC is an equilateral triangle of side 1m. Charges of 1Cand 1C are placed at points B and C as shown in figure. The electric field at A is: A) 9 × 102 NC-1 B) 18 × 103 NC-1 C) 9 × 103 NC-1 parallel to BC D) 9 × 103 NC-1 parallel to CB 5. Two points charges q1  2C and q2  1C are placed at distances b = 1cm and a = 2 cm from the origin on the Y and X axes as shown in figure. The electric field vector at point P (a, b) will subtend and angle  with x-axis given by: A) tan   1 B) tan   2 C) tan   1 D) tan   1 16 2 4

Class (XII) - [SPJ 2023 - Module - I] A uniform electric field given by E  3ˆi  4ˆj  5kˆ N  6. C pierces the Gaussian cube as shown. The electric flux through the right face and top face in Nm2/c are: A) 12 and 20 B) Zero, Zero C) 16 and 20 D) 12 and 16 7. A charged ball B hangs from a silk thread S, which makes an angle  with a large charged conducting sheet P, as shown in the figure. The surface charge density  of the sheet is proportional to: A) cot  B) cos C) tan  D) sin  8. Two metal balls of radii 5cm and 4cm are charged to the same potential, the surface densities of charge on the two spheres are in the ratio: A) 4:5 B) 5:4 C) 16:25 D) 25:16 9. The electric field E between two points is constant in both magnitude and direction. Consider a path of length d at an angle   60o with respect to field lines shown in figure. The potential difference between points 1 and 2 is: E B) Ed cos 60o Ed D) E cos 60o A) d cos 60o C) cos 60o d 17

Class (XII) - [SPJ 2023 - Module - I] 10. Six equal capacitors each of capacitance C are connected as shown in the figure. Then the equivalent capacitance between X and Y is: A) 6C B) C C) 2C D) C/2 11. The equivalent capacitance of the arrangement shown in figure, if A is the area of each plate, is A) C  0A  K1  K2  K3  B) C 0A  K1  K2K3  d  2 K2K3  d  2 K2  K3      C) C 0A K1  K2K3  D) C 0A K1  K2K3  2d  K2  K3  d  K2  K3    LEVEL - III 1. A solid conducting sphere of radius a has a net positive charge 2Q. A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and has a net charge -Q. The surface charge density on the inner and outer surfaces of the spherical shell will be A) 2Q , Q B)  Q , Q C) 0, Q D) None of the above  4b2 4c2 4b2 4c2 4c2 18

Class (XII) - [SPJ 2023 - Module - I] 2. The electric field at a distance 3R from the centre of a charged conducting spherical shell of radius 2 R is E. The electric field at a distance R from the centre of the sphere is 2 A) E B) zero C) E D) E 2 2 3. A capacitor C is fully charged with voltage V0. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance C . The energy loss in the process after 2 the charge is distributed between the two capacitors is: A) 1 CV02 B) 1 CV02 C) 1 CV02 D) 1 CV02 2 3 4 6 Numerical Type 4. Determine the charge (in coulomb) on the capacitor in the following circuit: 5. The 1000 small droplets of water each of radius r and charge Q, make a big drop of spherical shape. The potential of big drop is how many times the potential of one small droplet? 6. Consider a sphere of radius R which carries a uniform charge density  . If a sphere of radius R is 2 carved out of it, as shown, the ratio EE AB of magnitude of electric field  and E B , respectively, at EA points A and B due to the remaining portion is: 19

Class (XII) - [SPJ 2023 - Module - I] 7. An electric dipole, consisting of two opposite charges of 2 × 10-6 C each separated by a distance 3 cm is placed in an electric field of 2 × 105 N/C. Maximum torque (in Nm) acting on the dipole is More than one correct 8. Figure shows a cross-section of a spherical metal shell of inner radius R and out radius 2R. A point charge q is located at a distance R/2 from the centre of the shell. If the shell is electrically neutral, then: A) the electrical field at some point insdie shell is zero B) the electrical field at point inside shell is non-zero C) the electrical field at the outer surface of the shell is E  1 q 22 40 3R / D) the electrical field at the outer surface is E  1 q 40 2R 2 9. A few electric field lines for a system of two charges Q1 and Q2 fixed at two different points on the x- axis are shown in the figure. These lines suggest that A) Q1  Q2 B) Q1  Q2 C) at a finite distance to the left of Q1 the electric field is zero D) at a finite distance to the right of Q2 the electric field is zero 20

Class (XII) - [SPJ 2023 - Module - I] 10. A ring with a uniform charge Q and radius R, is placed in the yz plane with its centre at the origin. A) the field at the origin is zero 1Q B) The potential at the origin is 40 R 1Q C) The field at the point (x, 0, 0) is 40 x2 1Q D) The field at the point (x, 0, 0) is 40 R2  x2 11. Figure shows three concentric spherical conducting shells A, B and C of radii R, 2R and 4R respectively. A and C are connected by a conducting wire and B is given charge Match the following columns: 1  K    4 0 Column-I Column-II A) Charge on shell A p) Q/3 B) Charge on shell C q) -Q/3 C) Potential of A r) Q D) Potential of C s) KQ 4R t) none 21

Class (XII) - [SPJ 2023 - Module - I] CHAPTER - 02 CURRENT ELECTRICITY QUESTIONS HOME WORK 1. There is a current of 3.2 A in a conductor. The number of electrons that cross any section normal to the direction of flow per second is A) 1019 B) 2 × 1019 C) 3 × 1019 D) 3.2 × 1019 E) 4.2 × 1019 2. When a potential difference v is applied across a conductor at temperature T, the drift velocity of electrons is proportional to A) V B) V C) T D) T E) T2 3. If the temperature is decreased, then relaxation time of electrons in metals will : A) increase B) decrease C) fluctuate D) remains constant E) none 4. Two wires A and B of the same material having radii in the ratio 1 : 2 and carry currents in the ratio 4 : 1. The ratio of drift speed of electrons in A and B is: A) 1 : 16 B) 16 : 1 C) 4 : 1 D) 1 : 4 E) 1 : 8 5. The speed at which the current travels, in a conductor, is nearly: A) 3 ´ 104 m/s B) 3 ´ 105 m/s C) 4 ´ 106 m/s D) 3 ´ 108 m/s E) 9 × 108 m/s 6. A steady current is passing through a linear conductor of non-uniform cross-section. The current in the conductor is: A) independent of area of cross-section B) directly proportional to length of the conductor C) directly proportional to area of cross-section D) inversely proportional to length of the conductor E) none 22

Class (XII) - [SPJ 2023 - Module - I] 7. A p.d. is applied across the ends of a metallic wire. If the p.d. is doubled, the drift velocity will be A) doubled B) halved C) quadrapled D) remains unchanged E) none of these 8. A current of 3.2A is flowing in a wire of area of cross section 1 10–7 m2. The number of free electrons in the wire is 2 1028 per m3. Determine the drift velocity of electrons. A) 102 m/s B) 10–2 m/s C) 3.2  10–3 m/s D) 2 1018 m/s E) none 9. Specific resistance of all metal is mostly affected by A) Magnetic field B) Volume C) Pressure D) Temperature E) None 10. Appropriate material to be used in the construction of resistance boxes out of the following is A) Copper B) Iron C) Manganin D) Aluminium E) None 11. The length and area of cross-section of a conductor are doubled, its resistance will be A) halved B) doubled C) tripled D) quadrupled E) unchanged 12. A resistance of 2  is to be made from a copper wire (specific resistance 1.7 × 10-8  m) using a wire of length 50 cm. The radius of the wire is A) 0.0116 mm B) 0.0367 mm C) 0.116 mm D) 0.367 mm E) 0.414 mm 13. A copper wire of cross - sectional area 2 mm2 resistivity = 1.7 × 10-8  m, carries a current of 1A. the electricfield in the copper wire is A) 8.5 × 10-5 V/m B) 8.5 × 10-4 V/m C) 8.5 × 10-3 V/m D) 8.5 × 10-2 V/m E) 8.5 × 10-1 V/m 14. 2, 4 and 6 S are the conductances of three conductors. When they are joined in parallel, their equivalent conductance will be A) 12 S 1 12 B) 12 S C) 11 S 11 E) 24 S D) 12 S 15. A given resistor has the following colour scheme of the various strips on it. Brown, Black, Green and Silver. Its value in ohm is: A) 1.0 × 104  10% B) 1.0 × 105  10% C) 1.0 × 106  10% D) 1.0 × 106  20% E) 1.0 × 104  20% 23

Class (XII) - [SPJ 2023 - Module - I] 16. Resistances 2ohm, 4ohm and 6ohm are connected in series with a battery of emf 6V. Find the current in the circuit. What is the current when the resistances are connected in parallel A) 1A, 2A B) 1.5 A, 3.5 A C) 0.5 A, 5.5 A D) 25A, 4.5 A E) 6A, 1A 17. The temperature coefficient of resistance of a wire is 0.00125 per degree. The resistance at 300K is 1  . At what temperature, its resistance become 2  A) 1154 K B) 1127 K C) 600 K D) 1400 K E) 1312 K 18. Two metal wires of idential dimensions are connected in series. If 1 and 2 are the conductivities of the metals respectively, the effective conductivity of the combination is: A) 1  2 B) 1  2 C) 12 2 D) 212 E) None 1  2 19. A piece of copper and silicon are cooled from room temperature to 100K. The resistance of : A) each of them increaes B) each of them decreases C) copper increases and that of silicon decreases D) copper decreases and that of silicon increases 20. A coil of wire has a resistance of 25 at 20oC and a resistance of 25.17 at 35oC. What is its temp coeff. A) 3104o C1 B) 8107o C1 C) 12104o C1 D) 6104o C1 E) 4.5104o C1 21. A wire of resistance 1W is stretched to double its length. The resistance will become: A) 1/4 W B) 1 W C) 4 W D) 2 W E) 5 W 22. Which of the following has negative temperature coefficient of resistance? A) Platinum B) Tungsten C) Carbon D) Nichrome E) None of these 23. A conductor with rectangular cross-section has dimensions (a x 2a x 4a) as shown in figure. Resistance across AB is x, across CD is y and across EF is z. Then A) x = y = z B) x > y > z C) y > z > x D) x > z > y E) z > x > y 24

Class (XII) - [SPJ 2023 - Module - I] 24. Rp is the equivalent resistance of n equal resistors connected in parallel and Rs the equivalent resistance when they are connected in series. Then Rs Rp is A) n B) 1 C) n3 n D) 1 E) n2 n2 25. The value of internal resistance of an ideal cell is A) High B) Low C) Infinite D) Zero E) None 26. A cell does 5 joules of work in carrying 2 coulomb of charge around a closed circuit. The electromotive force of the cell is A) 2 volt B) 2.5 volt C) 4 volt D) 5 volt E) 6 volt 27. A 50 V battery is connected across 10 ohm resistor and a current of 4.5 A flows. The internal resistance of the battery is A) 10 ohm B) 0.5 ohm C) 1.1 ohm D) 5 ohm E) 6 ohm 28. From the figure calculate the effective emf. of the cell A) 6V B) 2V C) 3V D) 8V E) 4V 29. n identical cells each of e.m.f E and internal resistance r are connected in parallel. An external resistance R is connected across the combination. The current through this resistance is: A) nE B) nE C) E D) E R  nr nR  r Rr nR  r 30. The circuit has a current of 0.5A when R is 10W and a current of 0.27A, when R is 20W. Internal resistance and emf of the battery are A) 2.76 & 7.2V B) 1.76 , 5V C) 1.76 and 5.88V D) 2 , 8V E) 6  3V 31. The terminal potential difference of a cell which draws 10A current from a charger is 6.8 V. If the cell has an open circuit voltage 5.6 V, the internal resistance of the cell is A) 0.1  B)0.5  C) 0.12  D) 0.2  E) 0.24  25

Class (XII) - [SPJ 2023 - Module - I] 32. The internal resistance of a cell of e.m.f. 2V is 0.1W. It is connected to a resistance of 3.9W. The voltage across the cell will be: A) 0.5 V B) 1.9 V C) 1.95 V D) 2 V E) 2.5 V 33. Kirchoff’s loop rule is based on the principle of conservation of A) Charge B) Energy C) Linear momentum D) Mass E) Angular momentum 34. Point out the right statements about the validity of kirchoff’s junction rule A) It is based on conservation of charge B) Outgoing currents add up and are equal to incoming currents at a junction C) Bending or reorienting the wire does not change the validity of kirchoff’s junction rule D) All of above E) None 35. Figure represents a part of closed circuit. The potential difference (VA - VB) is : A) 6 V B) 12 V C) 24 V D) 18 V 36. In the circuit figure if the resistance R2 is decreased: A) The current through R1 increases B) The current through R1 is constant C) The voltage drop across R2 decreases D) The power dissipation by R2 decreases 37. A, B and C are voltmeters of resistance R, 1.5 R and 3R respectively. When same potential difference is applied between x and y, the voltmeter readings are VA, VB and VC. Then : A) VB = VC B) VA  VB  VC C) VA  VB  VC D) VA  VB  VC 26

Class (XII) - [SPJ 2023 - Module - I] 38. In the given circuit the voltmeter reads 8 V. Assuming that the internal resistance of the cell is zero and the voltmeter is ideal, the emf of the cell is: A) 8V B) 10V C) 12V D) 15V E) 16V 39. In the adjoining figure, the reading of ammeter A is not zero while that of voltmeter V is zero. The substance C is V C A A) A semiconductor B) An insulator C) A superconductor D) A semi metal E) None 40. Let R1 be the resistance of 100 W, 250 V lamp and R2 be that of 200W, 250V lamp. Which of the following is correct? A) R1 = 4R2 B) R1 = R2 C) R1 = 2R2 D) 4R1 = 4R2 E) 2R1 = R2 41. Two electric lamps each of 100 watt 220 V are connected in series to a supply of 220 Volt. The power consumed would be: A) 100 W B) 200 W C) 25 W D) 50 W E) 75 W 42. Two heater wires of equal length are first connected in series and then in parallel. The ratio of heat produced in two cases is A) 2 : 1 B) 1 : 2 C) 4 : 1 D) 1 : 4 E) 1 : 1 43. The best instrument for accurate measurement of emf of a cell is: A) a voltmeter B) an ammeter C) a potentiometer D) wheatsone’s bridge E) galvanometer 44. A potentiometer is used for the comparison of emf of two cells E1 and E2. For cell E1 the no deflection point is obtained at 20 cm and for E2 the no deflection point is obtained at 30 cm. The ratio of their emf’s will be A) 2/3 B) 3/2 C) 1 D) 2 E) 4/3 27

Class (XII) - [SPJ 2023 - Module - I] 45. The metre-bridge wire AB shown in figure is 50 cm long. When AD = 30 cm, no deflection occurs in the galvanometer. Find R. A) 1 B) 2  C) 3  D) 4  46. The current through AD is A) 3 i B) 2 i i i 5 5 C) 2 D) 4 47. A current I varies with time in a coil of resistance R as shown in the graph. The average heat produced in the coil is A) 5 I20 RT B) 1 I02 RT 6 6 C) 1 I02RT D) 2 I02 RT 3 5 28

Class (XII) - [SPJ 2023 - Module - I] 48. During an experiment with a meter bridge, the galvanometer shows a null point when the jockey is pressed at 40cm using a standard resistance of 90cm as show in the scale used in the meter bridge is 1mm. The unknown resistance is A) 60  0.15 B) 135  0.56 C) 60  0.25 D) 135  0.23 49. In the circuit shown, each resisitance is 2 . The potential V1 is as indicated in the circuit. What is the magnitude of V1 in volt ? 50. In the circuit shown in figure, the battery, ammeter, and voltmeter are ideal and the switch S is initially closed as shown. When S is opened, match the parameters of column I with the effects in column II Column I Column II i. Equivalent resistance across the battery a. Remains same ii. Power dissipated by left resistance R b. Increases iii. Voltmeter reading c. Decreases iv. Ammeter reading d. Becomes zero 29

Class (XII) - [SPJ 2023 - Module - I] LEVEL - I 1. A current of 3.2 A is flowing in a wire of area of cross section 1 107 m2 . The number of free electrons in the wire is 2 1028 / m3 . Determine the drift velocity of electrons. A) 102 m/s B) 10–2 m/s C) 3.2  103 m / s D) 2 108 m / s 2. A given resistor has the following colour scheme of the various strips on it. Brown, Black, Green and Silver. Its value in ohm is, A) 1.0 104  10% B) 1.0  105  10% C) 1.0  106  10% D) 1.0 106  20% 3. The total current supplied to the circuit by the battery in the given circuit is A) 1 A B) 2 A C) 4 A D) 6 A 4. The terminal potential difference of a cell which draws 10 A current from a charger is 6.8 V. If the cell has an open circuit voltage 5.6 V, the internal resistance of the cell is A) 0.1 B) 0.5 C) 0.12 D) 0.2 5. How much time heater will take to increase the temperature of 100 g water by 50oC, if resistance of heating coil is 484 and supply voltage is 220 V. A) 210 S B) 42 S C) 200 S D) 50 S 6. Current passing through 1 resistance is zero, then the value of emf ‘E’ is 1 6V 2  E A) 8 V B) 12 V C) 4 V D) 6 V 7. Flow would you arrange 48 cells each of emf 1.8 V and internal resistance 1 . So as to get strongest possible current in a resistance of 3 A) 4 × 12 B) 24 × 2 C) 2 × 24 D) 6 × 8 30

Class (XII) - [SPJ 2023 - Module - I] 8. The metre-bridge wire AB shown in figure is 50 cm long. When AD = 30 cm, no deflection occurs in the galvanometer. Find R A) 1 B) 2  C) 3  D) 4  9. In a potentiometer experiment, the galvanometer shows no deflection when a cell is connected across 60 cm of the potentiometer wire. If the cell is shunted by a resistance of 6  , the balance is obtained across 50 cm of the wire. The internal resistance of the cell is A) 1.2  B) 0.5  C) 0.6  D) 1.5  10. The figure below shows currents in a part of electric circuit. The current i is: A) 1.7 amp B) 3.7 amp C) 1.3 amp D) 1 amp LEVEL - II 1. The total momentum of electrons in a straight wire of copper of length 1 m carrying a current of 16 A is A) 91 × 10–15 kg m/s B) 91 × 10–16 kg m/s C) 91 × 10–14 kg m/s D) 91 × 10–12 kg m/s 2. When is a 5 V potential difference is applied a wire of length 0.1 m, the drift speed of electrons is 2.5 104 m / s . If the electron density in the wire is 8 1028 m / s the resistivity of the material is close to A) 1.6 108 m B) 1.6 107 m C) 1.6 105 m D) 1.6 106 m 3. The net Resistance between points P and Q is: A) R B) 5R C) 2R D) R 2 2 5 5 31

Class (XII) - [SPJ 2023 - Module - I] 4. In the given circuit, the voltmeter reads 30 V. The resistance of voltmeter is A) 750 ohm B) 200 ohm C) 100 ohm D) 3000 ohm 5. Eight cells marked 1 to 8 each of emf 5 V and internal resistance 0.2 are connected as shown in the figure. What is the reading of the ideal voltmeter v? A) 40 V B) 20 V C) 5 V D) zero 6. Four resistance of 15, 12, 4 and 0 respectively are connected in cyclic order to form Wheatstone network. Calculate the resistance to be connected in parallel with the resistance of 10  to balance the network. A) 4 B) 10  C) 12  D) 15 7. See the electrical circuit shown in this figure. Which of the following equations is a correct equation for it? A) 2  i2r2  1  i1r1  0 B) 2  i1  i2  R  i2r2  0 D) 1  i1  i2  R  i1r1  0 C) 1  i1  i2  R  i1r1  0 32

Class (XII) - [SPJ 2023 - Module - I] 8. A filament bulb (500 W, 100 V) is to be used in 230 V main supply. When a resistance ‘R’ is connected in series, it works perfectly and the bulb consumes 500 W. The value of R is : A) 26  B) 13  C) 230  D) 46  9. All bulbs in figure below are identical. Which bulb (s) light (s) most brightly? A) 1 only B) 2 only C) 3 and 4 only D) 1 and 5 10. What will happen when a 40 W, 220 V lamp and 100 W, 220 V lamp are connected in series across 440 V supply? A) 100 W lamp will fuse B) 40 W lamp will fuse C) Both lamps will fuse D) Neither lamp will fuse LEVEL - III 1. In an electrolyte 3.2 1018 bivalent positive ions drift to the right per second while 3.2 1018 monovalent negative ions drift to left per second. Then the current is: A) 1.6 amp to the left B) 1.6 amp to the right C) 0.45 amp to the right D) 0.45 amp to the left 2. The reading of the ammeter as per figure shown is: A) 1 A B) 3 A 8 4 C) 1 A D) 2A 2 33

Class (XII) - [SPJ 2023 - Module - I] 3. In the circuit shown, a meter bridge is in its balnaced state. The meter bridge wire has a resistance 0.1 ohm/cm. The value of unknown resistance X and the current drawn from the battery of negligible resistance is: A) 6, 5amp B) 10, 0.1amp C) 4,1.0amp D) 12, 0.5amp 4. In the network shown in figure, points A, B and C are at potentials of 70V, 0, and 10V, respectively A) Point D is at a potential of 40V B) The currents in the sections AD, DB, DC are in the ratio 3:2:1 C) The currents in the sections AD, DB, DC are in the ratio 1:2:3 D) The network draws a total power of 200W 5. When some potential difference is maintained between A and B, current I enters the network at A and leaves at B A) The equivalent resistance between A and B is 8 B) C and D are at the same potential C) No current flows between C and D D) Current 3I 5 flows from D to C 34

Class (XII) - [SPJ 2023 - Module - I] 6. In the circuit shown in figure, the cell has emf 10V and internal resistance 1 A) The current through the 3  resistor is 1A B) The current through the 3  resistor is 0.5A C) The current through the 4  resistor is 0.5A D) The current through the 3  resistor is 0.25A 7. In the circuit shown in figure A) Power supplied by the battery is 200W B) current flowing in the circuit is 5A C) potential difference across the 4 resistance is equal to the potential difference across the 6 resistance D) current in wire AB is zero Integer Type 8. Nine wires each of resistance r  5 are connected to make a prism as shown in figure. Find the equivalent resistance of the arrangement across AB (in  ) 35

Class (XII) - [SPJ 2023 - Module - I] 9. Find the potential differenfe (in V) between points A and B shown in the circuit 10. If in the circuit shown in figure, power dissipation is 150W, then find the value of R (in  ) Matching Column 11. Match the column I with column II Column I Column II a. dimensions i. Electrical conductivity of conductor depends on (length, area of cross section etc.) ii. Conductance of a conductor depends on b. temperature iii. For a given conductor of given c. nature of conductor dimensions and at a given temperature, current density depends on d. electric field strength iv. For a given potential difference applied across a conductor of given length, current in it will depend on 36

Class (XII) - [SPJ 2023 - Module - I] CHAPTER - 03 MOVING CHARGES AND MAGNETISM QUESTIONS HOME WORK 1. An electron is travelling along X-direction. It encounters a magnetic field in the Y-direction. Its subsequent motion will be A) Straight line along X-direction B) a circle in XZ-plane C) a circle in YZ-plane D) a circle in XY-plane 2. A charged particle moves with velocity v in a uniform magnetic field B . The magnetic force experienced by the particle is A) always zero B) never zero C) zero, if  and v are perpendicular D) zero, if  and v are parallel B B 3. Lorentz force can be calculated by using the formula A) F  q E  v  B B) F  q E  v  B C) F  q E  v.B D) F  q E  v  B 4. A strong magnetic field is applied on a stationary electron, then the electron A) moves in the direction of the field B) moves in an opposite direction of the field C) remains stationary D) starts spinning 5. If a charged particle enters perpendicularly in the uniform magnetic field then A) energy remains constant but momentum changes B) energy and momentum both remains constant C) momentum tremains constant but energy changes D) neither energy nor momentum remains constant 6. A beam of protons with a velocity of 4 105 ms1 enters a uniform magnetic field of 0.3 T at an angle of 60o to the magnetic field. The radius of helical path taken by proton beam is A) 0.36 m B) 0.012 m C) 0.024 m D) 0.048 m 7. A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to A) the velocity B) the momentum C) the kinetic energy D) none of these 37

Class (XII) - [SPJ 2023 - Module - I] 8. A beam of ions with velocity 2 105 m / s enters normally into a uniform magnetic field of 4 102 T . If the specific charge of the ion is 5107 C / kg , then the radius of the circular path described will be A) 0.1m B) 0.16m C) 0.2m D) 0.25m 9. Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius R with constant speed v. The time period of the motion. A) depends on both R and V B) Is independent of both R and V C) depends on R but not on V D) depends on V but not on R 10. A proton and a deutron with the same initial kinetic energy enter in a magnetic field in a direction perpendicular to the direction of the field. The ratio of the radii of the circular trajectories described by them is A) 1: 4 B) 1: 2 C) 1:1 D)1:2 11. A particle of mass m , charge Q and kinetic energy T enters a transverse uniform magnetic field of induction B . After 3 seconds the kinetic energy of the particle will be: A) T B) 4T C) 3T D) 2T 12. Electron moves at right angle to a magnetic field of 1.5 102 tesla with speed of 6 107 m / s . If the specific charge of the electron is 1.7 1011C / Kg . The radius of circular path will be; A) 3.31 cm B) 4.31 cm C) 1.31 cm D) 2.35 cm 13. An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 102 T, if the value of (e/m) is 1.76 1011C / kg, the frequency of revolution of the electron is A) 6.82MHz B) 1GHz C) 100MHz D) 62.8MHz 14. Electron of mass m and charge e is travelling with a speed V along the circular path of radius r at right angle to uniform magnetic field B. If the speed of electron is doubled and magnetic field is halved, the resulting path would have a radius A) 4r B) 2r r r C) 4 D) 2 15. Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular path of radii R1 and R2 respectively, then ratio of masses of X to that of Y A)  R1 2 B) R 2 R1 C) R1 R 2 D)  R2 2  R2  R1         16. In a region, steady and uniform electric and magnetic fields are present. These 2 fields are parallel to each other. A charged particle is released from rest in the region. The path of the particle will be: A) ellipse B) circle C) helix D) straight line 17. An electric field of 1500 V/m and a magnetic field of 0.4 weber/m2 act on a moving electron. The minimum uniform speed along a straight line the electron could have is A) 1.6 105 m / s B) 6 106 m / s C) 3.75103 m / s D) 3.75102 m / s 38

Class (XII) - [SPJ 2023 - Module - I] 18. A cyclotron can be used to accelerate A)  -particle B)  - particle C) neutrons D) neutrino 19. The magnetic field  due to small current element  at a distance r from an element carrying dB d current i is: A) dB  0 i2  d  r  B) dB  0 i  d  r  4   4  r3   r2    C) dB  0 i2  d  r  D) dB  0 i  d  r  4   4  r2   r3    20. A moving electric charge produces A) An electric field only B) A magnetic field only C) Both electric and magnetic field D) An electric field in Vacuum only 21. The direction of induced magnetic field dB due to a current element  at a point of distance r from id it, when a current i passes through a long conductor is in the direction A) of positive vector r of the point B) of current element  d C) perpendicular to both  and r D) perpendicular to  only d d 22. The magnetic field at a distance r from a long wire carrying current I is 0.4 tesla. The magnetic field at a distance 2 r is A) 0.1 tesla B) 0.2 tesla C) 0.8 tesla D) 1.6 tesla 23. If a long straight wire carries a current of 40 A, then the magnitude of the field B at a point 15 cm away from the wire is A) 5.34 105 T B) 8.34 105 T C) 9.6 105 T D) 10.2 105 T 24. Two long parallel wires a distance ‘d’ apart carry currents of 1A and 3A in the same direction. The wire carrying 1A current lies to left of the other wire. The point at which their magnetic fields cancel are locate at A) A distance of d/4 to the right of the first wire having current 1 A B) A distance of d/4 to the right of the second wire having current 3 A C) A distance of d/4 to the left of the second wire having current 3 A D) A distance of 3d/4 to the right of the second wire having current 3 A 25. A current of 0.1A circulates around a coil of 100 turns and having a radius equal to 5cm. The magnetic  field set up at the centre of the coil is 0  4 107 Wb / A  m A) 4 105 T B) 8 105 T C) 4 105 T D) 2 105 T 26. Two concentric coils of 10 turns each are situated in the same plane. Their radii are 2cm and 4cm and they carry respectively 0.2 and 0.3A current in opposite directions. The magnetic field (in Wb/ m2) at the centre is  A) 35 4 0 B)  0 80  C) 780 0  D) 25 2 0 39

Class (XII) - [SPJ 2023 - Module - I] 27. A circular coil of radius 4cm and of 20 turns carries a current of 3A. It is placed in a magnetic field of 0.5T. The magnetic dipole moment of the coil is A) 0.15 A-m2 B) 0.3 A-m2 C) 0.45 A-m2 D) 0.6 A-m2 28. A current of I ampere flows in a circular arc of wire which subtends an angle of 3 / 2 radius at its centre, whose radius is R. The magnetic induction B at the centre is: A) oI / R B) oI / 2R C) 2oI / R D) 3oI / 8R 29. If B1 is the magnetic field induction at a point on the axis of a circular coil of radius R situated at a distance R 3 and B2 is the magnetic field at the centre of the coil, then ratio of B1 / B2 is equal to A1) 1/3 B) 1/8 C) 1/4 D) 1/2 30. If the current is flowing clockwise in a circular coil, the direction of magnetic lines of force inside the coil is A) towards you B) away from you C) towards the centre along the radius D) away from the centre along the radius 31. Magnetic field induction at the point O due to current flowing in an infinite wire shaped as shown in the figure is A) 0I B) 0I  0I C) 0I  0I D) 0I  0I 4R 4R 4R 4R 2R 4R 4R 32. Two wires with currents 24  2A are enclosed in a circular loop. Another wire with current 3A is situated outside the loop as show Q. The  B.dI around the loop is; A) o B) 3o C) 6o D) 2o 40

Class (XII) - [SPJ 2023 - Module - I] 33. The magnetic field due to a straight conductor of uniform cross-section of radius a and carrying a steady current is represented by A) B) C) D) 34. If a long hollow copper pipe carries a direct current, the magnetic field associated with the current will be: A) Only inside the pipe B) Only outside the pipe C) both inside and outside the pipe D) neither inside nor outside the pipe 35. A solenoid of length 0.6 m has a radius of 2cm and is made up of 600 turns. If it carries a current of 4A, then the magnitude of the magnetic field inside the solenoid is A) 6.024 103 T B) 8.024 103 T C) 5.024 103 T D) 7.024 103 T 36. A straight wire of length 0.5m and carrying a current of 1.2 ampere is placed in a uniform magnetic field of induction 2 tesla. The magnetic field is perpendicular to the length of the wire. The force on the wire is A) 2.4N B) 1.2 N C) 3.0 N D) 2N 37. A straight wire of mass 200 g and length 1.5 m carries a current of 2A. It is suspended in mid-air by a uniform horizontal magnetic field B. The magnitude of B(in tesla) is: (assume g = 9.8 ms–2) A) 2 B) 1.5 C) 0.55 D) 0.66 38. Current is flowing in two long parallel conductors in the same direction. The conductors A) Attract each other B) Repel each other C) Neither attract nor repel D) Get perpendicular to each other 39. Two long conductors, separated by a distance d carry currents I1 and I2 in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3d. The new value of the force between them is A) -F/3 B) F/3 C) 2F/3 D) –2F/3 40. A galvanometer of 50 resistance has 25 divisions. A current of 4 104 Ampere gives a deflection of one division. To convert this galvanometer into a voltmeter having a range of 25 volts, it should be connected with a resistance of: A) 2500 as a shunt B) 2450 as shunt C) 2550 in series D) 2450 in series 41. A galvanometer of resistance 100 contain 25 divisions. It gives a deflection of one division on passing a current of 4 104 A . The resistance in ohm to be added to it, so that it may become a voltmeter of range 2.5V is A) 100 B) 150 C) 250 D) 300 41

Class (XII) - [SPJ 2023 - Module - I] 42. A voltmeter which can measure 2V is constructed by using a galvanometer of resistance 12  and that produces maximum deflection for the current of 2mA, then the resistance R is A) 888  B) 988  C) 898  D) 999  Numerical Type 43. A proton with kinetic energy 8 eV is moving in a uniform magnetic field. The kinetic energy of a deutron moving in the same path in the same magnetic field in the units of eV will be 44. An alpha particle is accelerated by a potential difference of 104V. Find the change in its direction of motion in degree if it enters normally in a region of thickness 0.1m having transverse magnetic induction 0.1T (Given mass of  -particle 6.41027 kg ) 45. A conducting rod of 1m length and 1kg mass is suspended by two vertical wires through the ends. An external magnetic field of 2T is applied normal to the rod. Now the current to be passed through the rod so as to make the tension in the wires zero is [in ampere, take g = 10 ms–2] 46. A moving coil galvanometer has resistance of 900  . In order to send only 10% of the main current through this galvanometer, the resistance of required shunt is (in  ) 47. The deflection in moving coil galvanometer is reduced to half, when it is shunted with a 40 coil. The resistance of the galvanometer is (in  ) 48. Electron move at right angle to a magnetic field of 1.5102 tesla with speed of 6107 m / s . If the specific charge of the electron is 1.7 1011C / kg . The radius of circular path will be (in cm) 49. A, B and C wires are given below. Find the ratio of total magnetic field due to A, B and C at points X and Y 50. A 200 turn solenoid having a length of 25cm and a diameter of 10cm carries a current of 0.30A. Calculate the magnitude of the magnetic field B inside the solenoid in mT is LEVEL - I 1. A positive charge is moving upward in a magnetic field which is towards north. The particle will be deflected towards A) east B) west C) north D) south 2. A proton and an  -particle moving with the same velocity enter into a uniform magnetic field, acting normal to the plane of their motion. The ratio of the radii of the circular paths described by the proton and  -particle is A) 1 : 2 B) 1 : 4 C) 1 : 16 D) 4 : 1 42

Class (XII) - [SPJ 2023 - Module - I] 3. A current i ampere flows in a circular arc of wire whose radius is R, which subtend an angle 3 2 radian at its centre. The magnetic induction B at the centre is A) 0i B) 0i C) 20i D) 30i R 2R R 8R 4. The magnetic field at a point at a large distance x from the axis of a circular coil of small radius is proportional to A) x2 B) 1 C) x3 D) 1 x2 x3 5. A long straight wire AB carries a current of 4A. A proton P travels at 4 × 106 m/s parallel to the wire, 0.2m from it and in a direction opposite to the current. The force with which the magnetic field of current exerts on the proton is A) 1.6 × 10-18 N B) 16 × 10-18 N C) 6.4 × 10-18 N D) 2.56 × 10-18N 6. A long solenoid has 800 turns per metre length of solenoid. A current of 1.6 A flows through it. The magnetic induction at the end of the solenoid on its axis is approximately A) 16 × 10-4 Tesla B) 8 × 10-4 Tesla C) 32 × 10-4 Tesla D) 4 × 10-4 Tesla 7. A wire of 60 cm length and mass 10g is suspended by a pair of flexible leads in a magnetic field of induction 0.4 Wb/m2. The magnitude and direction of the current required to remove the tension in the supporting leads is: A) 0.41 A from right to left B) 0.2 A from right to left C) 0.41 A from left to right D) 0.2 A from left to right 8. In the hydrogen atom the electron revolves around the nucleus in a circle of radius 5.11011m at a frequency of 6.8 1015 rev / s . The magnetic field at the centre of the orbit is A) 6.7T B) 13.4 T C) 20.1 T D) 26.8 T 43

Class (XII) - [SPJ 2023 - Module - I] 9. Two particles, each of mass m and charge q, are attached to the two ends of a light rigid rod of length 2 R. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is: A) zero B) q C) 2q D) q m m 2m 10. An ammeter is obtained by shunting a 30  galvanometer with 30  resistance. What additional shunt should be connected across it to double the range A) 15  B) 10  C) 5  D) 25  LEVEL - II 1. An electron moving with a speed u along positive x-axis at y = 0 enters a region of uniform magnetic  field B  B0kˆ which exists to the right of y-axis. The electron exits from the region after some time with speed v at c-ordinate y, then A) v > u, y < 0 B) v = u, y > 0 C) v > u, y > 0 D) v = u, y < 0 2. The acceleration of an electron at a certain moment in a magnetic field B  2ˆi  3ˆj  4kˆ is a  xˆi  ˆj  kˆ . The value of x is A) 0.5 B) 1 C) 2.5 D) 1.5 3. An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +X direction and a magnetic field along the +Z direction then: A) Positive ions deflect towards +Y direction and negative ions towards –Y direction B) All ions deflect towards +Y direction C) All ions deflect towards –Y direction D) Positive ions deflect towards –Y direction and negative ions towards + Y direction 4. A potential difference of 600 V is applied across the plates of a parallel plate capacitor. The separation between the plates is 3 mm. An electron is projected vertically, parallel to the plates, with a velocity of 2 × 106 m/s moves undeflected between the plates. The magnitude and direction of magnetic field in the region between the capacitor plates is: A) 1 T , into the plane of paper B) 1 T, out of plane of paper C) 0.1 T, into the plane of paper D) 0.1 T out of plane of paper 44

Class (XII) - [SPJ 2023 - Module - I] 5. Two long straight wires are connected by a circular section that has a radius r as shown in the figure. All segments of the wire lie in the same plane and carry steady current I. The magnetic field at centre O of the circular segment is A) 0I B) 0I C) 0I D) 0I 4r 4r r 2r 6. The figure shows a wire frame in xy-plane carrying a current I. The magnetic field at the point O is A) 0I  1  1  kˆ B) 0I  1  1  kˆ 8 a b  8  b a  C) 0I  1  1  kˆ D) 0I 1  1 kˆ 4  a b  4 b a  7. A current carrying wire PQ is placed near an another long current carrying wire RS. If free to move with PQ will have A) translational motion only B) Rotational motion only C) Translational as well as rotational motion D) neither translational nor rotational motion 45

Class (XII) - [SPJ 2023 - Module - I] 8. A conducting wire bent in the form of a parabola y2 = 2x carries a current I = 2A as shown in figure.  The wire is placed in a uniform magnetic field B  4kˆ tesla. The magnetic force on the wire (in newton) A) 16 ˆi B) 32 ˆi C) 32 ˆi D) 16 ˆi 9. A uniform magnetic field of 3000 G is established along the positive Z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. The torque on the loop in the two cases shown are A) (i) Zero (ii) 1.8 × 10–2 Nm along positive y-axis B) (i) 1.8 × 10–2 Nm along negative y-axis (ii) zero C) (i) zero (ii) 1.8 × 10–2 Nm along negative y-axis D) (i) 1.8 × 10–2 Nm long negative z-axis (ii) zero 10. A galvanometer of resistance 100  gives full scale deflection for 20 mV. The resistance to be attached, so that it gives full deflection of 5 V is A) 24.9 103  in series B) 24.9 103  in parallel C) 49.3  103  in series D) 49.3  103  in parallel LEVEL - III 1. A galvanometer whose resistance is 120 give full scale deflection with a current of 0.05A. So that it can read a maximum current of 10A. A shunt resistance is added in parallel with it. The resistance of the ammeter so formed is: A) 0.06 B) 0.006 C) 0.6 D) 6 2. A galvanometer of 50 resistance has 25 divisions. A current of 4 104 Ampere gives a deflection of one division. To convert this galvanometer into a voltmeter having a range of 25 volts, it should be connected with a resistance of: A) 2500 as a shunt B) 2450 as shunt C) 2550 in series D) 2450 in series 46

Class (XII) - [SPJ 2023 - Module - I] 3. A long straight wire of radius ‘a’ carries a steady current I . The current is uniformly distributed a across its cross-section. The ratio of the magnetic field at 2 and 2a is (the distance is measured from axis) 11 A) 2 B) 1 C) 2 D) 4 Numerical 4. A conducting rod of 1m length and 1kg mass is suspended by two vertical wires through the ends. An external magnetic field of 2T is applied normal to the rod. Now the current to be passed through the rod so as to make the tension in the wires zero is [in ampere, take g = 10 ms–2] 5. The deflection in moving coil galvanometer is reduced to half, when it is shunted with a 40 coil. The resistance of the galvanometer is (in  ) 6. A galvanometer has sensitivity of 60 divisions / ampere. When a shunt is used, its sensitivity becomes 10 divisions / ampere. What is the value of shunt (in ohm) used if the resistance of the galvanometer is 20 7. A moving coil galvanometer has a rectangular coil of 10 turns and length and breadth 5cm and 2cm respectively situated in a radial magnetic field of 0.4T. The coil is suspended by a torsion wire of torsional rigidity 2 × 10–6 N-m/degree. The current sensitivity is x degree per mA, where x is Matching Type 8. A square loop of side ‘a’ and carrying current i as shown in the figure is placed in gravity free space having magnetic field B  B0kˆ . Now match the following Column I Column II A) Torque on loop p) is zero B) Net force on loop  q) is in direction kˆ C) Potential energy of loop r) has minimum magnitudes D) Magnetic moment of loop s) has maximum magnitudes A) A-p; B-p; C-s; D-q B) A-p,s; B-p; C-s; D-q C) A-p; B-p,s; C-s; D-q D) A-p,s; B-p,s; C-s; D-q 47

Class (XII) - [SPJ 2023 - Module - I] 9. Equal currents are flowing in two infinitely long wires lying along x and y axes in the directions shown in figure. Match the following two column Column I Column II a) Magnetic field at (a,a) p) along positive y-axis b) Magnetic field at (–a, –a) q) along positive z-axis c) Magnetic field at (a, –a) r) along negative z-axis d) Magnetic field at (–a, a) s) zero A) a  p; b  q; c  r; d  p B) a  q; b  r; c  s; d  s C) a  q; b  r; c  q; d  p D) a  p; b  q; c  r; d  q More than one correct answer 10. If a charged particle kept at rest experiences an electromagnetic force A) the electric field must be there B) the magnetic field must be there C) the magnetic field may or may not be there D) the electric field may or may not be there 11. If a charged particle goes without any acceleration in a region containing electric and magnetic fields A) E must be perpendicular to B B) V must be perpendicular to E C) V must be perpendicular to B D) E must be parallel to B 48

CHEMISTRY Class (XII) - [SPJ 2023 - Module - I] CHAPTER - 01 SOLID STATE QUESTIONS [HOMEWORK] Single Correct 1. Which one of the following is INCORRECT about crystals ? A) They are isotropic B) They show sharp melting point C) They are true solids D) They show long range order 2. A particular solid is very hard and has a high melting point. In solid state, it is a non-conductor and its melt is a conductor of electricity. Classify the solid A) Metallic B) Molecular C) Network D) Ionic 3. Graphite is a A) Molecular solid B) Covalent solid C) Ionic solid D) Metallic solid 4. Solid x is a very hard solid which is electrical insulator in solid as well as in molten state and has extremely high melting point what type of a solid is it ? A) Ionic solid B) Covalent solid C) Metallic solid D) Molecular solid 5. Possible unit cells in two dimensional and three dimensional lattices respectively are A) 2, 14 B) 5, 14 C) 14, 5 D) 2, 5 6. Crystal structure of Na2SO4 . 10H2O is B) Rhombic A) Monoclinic C) Cubic D) Tetragonal 7. The crystal system present in TiO2 is B) Triclinic A) Hexagonal C) Tetragonal D) Orthorhombic 49

Class (XII) - [SPJ 2023 - Module - I] 8. The contribution of particle at the edge centre of a particular unit cell is 1 11 A) 2 B) 1 C) 4 D) 8 9. The number of atoms per unit cell of bcc structure is A) 1 B) 2 C) 4 D) 6 10. In a face centred lattice of X and Y, X atoms are present at the corners while ‘Y’ atoms are at face centres. Then formula of the compound is A) XY3 B) X2Y3 C) X3Y D) XY 11. A atoms at the corner, B atoms at the faces. One of the axis facial atoms are removed, formula of the compound is A) A1B5 B) A2B5 C) AB2 D) A2B 12. Which of the following describes the hexagonal close packed arrangement of spheres? A) ABCABA B) ABCABC C) ABABAB D) AAAAAA 13. Co-ordination number of simple cubic lattice is A) 8 B) 3 C) 4 D) 6 14. A metallic solid crystallises into a lattice containing a sequence of layers ABABAB ................... What % by volume of this lattice is empty? A) 50% B) 45% C) 40% D) 26% 15. Percentage of free space in cubic close packed structure and in body centred packed structure are respectively A) 48% and 26% B) 30% and 26% C) 26% and 32% D) 32% and 48% 16. Which of the following statements is not correct? A) The fraction of the total volume occupied by the atoms in a primitive cell is 0.48 B) Molecular solids are generally volatile C) The number of carbon atoms in a unit cell of diamond is 8 D) The number of Bravais lattices in which a crystal can be categorised is 14 17. Total volume of atoms present in a face centered unit cell of a metal is (r = atomic radius) A) 20 r 3 B) 24 r 3 3 3 C) 12 r 3 D) 16 r 3 3 3 50