4.Subject Test 1 - 2

SUBJECT TEST - 1 (ST-1) PHYSICS Duration : 1 Hour Max. Marks : 60 GENERAL INSTRUCTIONS 1. There are 20 Questions. 2. In Section 1 (Total Marks: 20), for each question you will be awarded 2 marks if you give the correct answer and zero mark otherwise. There are no negative marks in this section. 3. In Section 2 (Total Marks: 20), for each question you will be awarded 4 marks if you give the correct answer and zero mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 4. In Section 3 (Total Marks: 20), for each question you will be awarded 4 marks if you give the correct answer and zero mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. SECTION-1 : (Only One option correct type) This section contains 10 multiple choice qustions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. Figure shows three circular arcs, each of radius R and total charge as indicated. The net elecric potential at the centre of curvature is : +Q –2Q (A) (C) Q 20R 2Q 0R (B) (D) Q 40R Q 0R 2. A graph of the x component of the electric field as a function of x in a region of space is shown. The Y and Z components of the electric field are zero in this region. If the electric potential is 10 V at the origin, then potential at x = 2.0 m is : (A) 10 V (B) 40 V (C) – 10 V (D) 30 V 3. A metallic charged ring is placed in a uniform magnetic field with its plane perpendicular to the field. If the magnitude of field starts increasing with time, then : (A) the ring starts translating (B) the ring starts rotating about its axis (C) the ring starts rotating about a diameter (D) current starts flowing in the ring 4. A U-shaped conducting frame is fixed in space. A conducting rod CD lies at rest on the smooth frame as shown. The frame is in uniform magnetic field B0, which is perpendicular to the plane of frame. At time t = 0, the magnitude of magnetic field begins to change with time t as, B = B0 , where k is a positive constant. For no current to be ever 1 kt induced in frame, the speed with which rod should be pulled starting from time t = 0 is (the rod CD should be moved such that its velocity must lie in the plane of frame and perpendicular to rod CD) (A) ak (B) bk (C) a(1 + kt) (D) b(1 + kt) 6. Two particles having positive charges +Q and +2Q are fixed at equal distance x from centre of a conducting sphere having zero net charge and radius r as shown. Initially the switch S is open. After the switch S is closed, the net charge flowing out of sphere is (A) (C) Qr x 3Qr x (B)  Qr x (D)  3Qr x 7. The magnetic flux  through a metal ring varies with time t according to :  = 3(at3 – bt2)Tm2, with a = 2s–3 and b = 6 s–2. The resistance of the ring is 3 . The maximum current induced in the ring during the interval t = 0 to t = 2s, is - (A) 1 A (B) 2A (C) 3A (D) 6 A 8. Three equal charges Q are placed at the three vertices of an equilateral triangle. What should be the value of a charge, that when placed at the centroid, reduces the interaction energy of the system to zero : Q (A) 2 Q (B) 3 (C) (D) 9. A point charge Q is placed at a distance d from the centre of an uncharged conducting sphere of radius R. The potential of the sphere is (d > R) : (A) 1 4 0 . Q (d  R) (B) 1 . Q 4 0 d (C) 1 . Q 4 0 R (D) zero 10. Switch S is closed for a long time at t = 0. It is opened, then : (A) total heat produced in resistor R after opening the switch is 1 2 L 2 R2 1 L 2  R1  (B) total heat produced in resistor R1 after opening the switch is 2 R2   R1   R2  (C) heat produced in resistor R after opening the switch is 1 1 2 (D) no heat will be produced in R1. R2 L 2 (R1  R2 ) R2 SECTION-2 : (One or more option correct type) This section contains 5 multiple choice qustions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 11. A wire having a positive uniform linear charge density , is bent in the form of a ring of radius R. Point A as shown in the figure, is in the plane of the ring but not at the centre. Two elements of the ring of lengths a1 and a2 subtend very small same angle at the point A. They are at distances r1 and r2 from the point A respectively. (A) The ratio of charge of elements a1 and a2 is r1/r2. a2 (B) The element a1 produced greater magnitude of electric field at A than element a2. (C) The elements a1 and a2 produce same potential at A. (D) The direction of net electric field at A is towards element a2. 12. The plates of a parallel plate capacitor with no dielectric are connected to a voltage source. Now a dielectric of dielectric constant K is inserted to fill the whole space between the plates with voltage source remaining connected to the capacitor. (A) the energy stored in the capacitor will become K-times (B) the electric field inside the capacitor will decrease K-times (C) the force of attraction between the plates will become K2 -times (D) the charge on the capacitor will become K-times. 13. At distance of 5cm and 10cm outwards from the surface of a uniformly charged solid sphere, the potentials are 100V and 75V respectively. Then (A) potential at its surface is 150V. (B) the charge on the sphere is (5/3) × 1010C. (C) the electric field on the surface is 1500 V/m. (D) the electric potential at its centre is 225V. 14. A conducting rod of length 𝑙 is moved at constant velocity ‘v0’ on two parallel, conducting, smooth, fixed rails, that are placed in a uniform constant magnetic field B perpendicular to the plane of the rails as shown in figure. A resistance R R is connected between the two ends of the rail. Then which of the following is are correct : (A) The thermal power dissipated in the resistor is equal to rate of work done by external person pulling the rod. (B) If applied external force is doubled than a part of external power increases the velocity of rod. (C) Lenz’s Law is not satisfied if the rod is accelerated by external force (D) If resistance R is doubled then power required to maintain the constant velocity v 0 becomes half. 15. A charged particle of charge +q, mass m is moving with initial velocity 'v' as shown in figure in a uniform magnetic field B(kˆ) . Select the correct alternative/alternatives :- (A) Velocity of particle when it comes out from magnetic field is m (B) Time for which the particle was in magnetic field is 3 qB mv y → v  v cos 30 i  v sin 30 j extend upto a large distance X (C) Distance travelled in magnetic field is 3qB (D) The particle will never come out of magnetic field SECTION-3 : (Integer value correct Type) This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive) 16. In the circuit shown, current through the resistance 2 is i1 and current i1 through the resistance 30 is i2. Find the ratio i2 . 17. In the figure shown the switch S1 remains connected for long time and the switch S2 remains opened. Now the switch S2 is closed. Assuming that  = 10 volt and L = 1H, the magnitude of rate of change of current is 2X (in Amp/sec.) in the inductor  just after the switch S2 is closed then find X . R 2R 18. A point source of radiation power P is placed on the axis of completely absorbing disc. The distance between the source and the disc is 2 times the radius of the disc. The force that light exerts on the disc is P 4ac then find a (c = speed of light). 19. In the figure, a conducting rod of length 𝑙 = 1 meter and mass m = 1 kg moves with initial velocity u = 5 m/s. on a fixed horizontal frame containing inductor L = 2 H and resistance R = 1 . PQ and MN are smooth, conducting wires. There is a uniform magnetic field of strength B = 1T. Initially there is no current in the inductor. Find the total charge in coulomb, flown through the inductor by the time velocity of rod becomes vf = 1 m/s and the rod has travelled a distance x= 3 meter. 20. In a YDSE arrangement composite lights of different wavelengths  = 560 nm and  = 400 nm are used. If D = 1m, d = 0.1 mm. If the distance between two nearest completely dark regions is 7X mm then X is : A nswers 1. (A) 2. (D) 3. (D) 4. (A) 6. (C) 7. (D) 8. (D) 9. (B) 10. (C) 11. (A,B,C,D) 12. (A,C,D) 13. (A,C,D) 14. (A,B,D) 15. (B,C) 16. 9 17. 5 18. 5 19. 20. 4 SUBJECT TEST - 2 (ST-2) PHYSICS Duration : 1 Hour Max. Marks : 60 GENERAL INSTRUCTIONS 1. There are 20 Questions. Marking Scheme 2. In Section 1 (Total Marks: 24), for each question you will be awarded 3 marks if you give the correct answer and zero mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 3. In Section 2 (Total Marks: 24) and 3 (Total Marks: 12), for each question you will be awarded 3 marks if you give the correct answer and zero mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. SECTION – 1 : (One or more options correct Type) This section contains 8 multiple coice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 1. A parallel plate capacitor of capacitance 10 F is connected to a cell of emf 10 Volt and is fully charged.Now a dielectric slab (k = 3) of thickness equal to the gap between the plates, is very slowly inserted to completely fill in the gap, keeping the cell connected.During the filling process : (A) the increase in charge on the capacitor is 200 C. (B) the heat produced is zero. (C) energy supplied by the cell = increase in stored potential energy + work done on the person who is filling the dielectric slab. (D) energy supplied by the cell = increase in stored potential energy + work done on the person who is filling the dielectric slab + heat produced. 2. In the figure shown: (All batteries are ideal) (A) current through 25 V cell is 20 A (B) current through 25 V cell is 12.5 A (C) power supplied by 20 V cell is 20 W (D) power supplied by 20 V cell is  20 W  3. A coil of radius R carries a current . Another concentric coil of radius r (r << R) carries current 2 . Initially planes of the two coils are mutually perpendicular and both the coils are free to rotate about common diameter. They are released from rest from this position. The masses of the coils are M and m respectively (m < M). During the subsequent motion let K1 and K2 be the maximum kinetic energies of the two coils respectively and let U be the magnitude of maximum potential energy of magnetic interaction of the system of the coils. Choose the correct options. K1 M  R 2 Umr 2 UMR2 (A) =   (B) K = K = K 2 m  r  0  2 r 2 1 mr 2  MR2 2 mr 2  MR2 (C) U = 4R (D) K2 >> K1 4. The circuit shown is in steady state Choose the correct options : (A) charge on 1F capacitor is same as charge on 3 F capacitor (B) charge on 2F capacitor is 2 C (C) current through the battery is 2A (D) current is same in each external resistance 5. The light shines the object, which is lying on the bottom of the pool, when the flashlight is held 1.2 m above the water surface and is directed at the surface a horizontal distance of 1.6 m from the edge. Refractive index of water is 4/3. If the water here is 4m deep, then : (A) the angle of incidence of light at the surface of water is 53° (B) the angle of refraction of light is 37° (C) the distance of object from the edge of the pool (x) is 4.6 m (D) the angle of refraction of light should be greater than 37° 6. A conducting ring is placed in a uniform external magnetic field which is changing in magnitude with time as shown. The resistances of the parts ACD and AED are 2  and 4  respectively.The current in the ring is found to be 2 Amp.Mark the correct options. (A) The emf induced in the ring is 12 V (B) The potential difference between the points A and D is 2V. (C) Potential difference between the points A and D is zero as the electric field induced is nonconservative. (D) the potential difference given by V=iR across the two resistors must be same as they are in parallel. 7. In a series L,C,R circuit with an ac source, VR=4volt,VL=3volt and VC=4volt and I=2 amp. Mark the correct options, assuming that the values given are rms values. (A) The power factor of the circuit is (B)The average power consumption is 8 Watts. (C)The reactance of the circuit is 1  (D)The impedance of the circuit is . 2 8. Choose the right statement from the following (A) In an X ray tube , if the accelerating voltage is 30 KV, the cutoff wavelength ,in one significant digit, will be 0 0.4 A . (B) In photoelectric effect experiment if the wavelength of the incident photon is 500nm,electrons will be ejected out of a metal having work function 3 eV. V0 (C) According to the Bohr’s theory the speed of the electron in  excited state is 3 of the electron in the ground state. where V0 is the speed (D) A beam of photons emitted by the excited H atoms is passed through a prism and then let fall on a screen. Only Balmer series will be seen on the screen by a student who is performing the experiment SECTION – 2 : (Paragraph Type) This section contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices (A), (B), (C) and (D). Paragraph for Question Nos. 9 to 10 A thin ring of radius R metres is placed in x-y plane such that its centre lies on origin. The half ring in region x< 0 carries uniform linear charge density + C/m and the remaining half ring in region x> 0 carries uniform linear charge density – C/m. y´ R 9. Then the electric potential (in volts) at point P whose coordinates are (0m, + 2 m) is - 1  (A) 4o 2 (B) 0 (C) 1  (D) cannot be determined 4o 4 10. Then the dipole moment of the ring in C–m is (A) – (2R2) ˆi (C) – (4R2) ˆi (B) (2R2) ˆi (D) (4R2) ˆi Paragraph for Question Nos. 11 to 12 Rutherford's calculations used the inverse-square law of repulsive force between an -particle (Z = 2) and a gold nucleus (Z = 79) ignoring multiple scattering. The scattering angle  of the -particle is related to the impact parameter b through the relation Ze2 cot(/ 2) b = 40E . Where E is the kinetic energy of the incident -particle. The impact parameter b is the perpendicular distance of the initial velocity vector of the -particle at different angles agreed with Rutherford's calculations based on the nuclear model of an atom. Ze2 cot(/ 2) b = 40E . 11. For impact parameter (b = 0) scattering angle will be : (A)  = 00 (B)  =  (C)  = /2 (D) None of these 12. If for the +(positron) emission from a nucleus, there is another competing process known as electron capture, then which of the following is correct : (A) if + emission is energetically allowed then electron capture is necessarily allowed (B) if electron capture is energetically allowed then + emission is necessarily allowed (C) both processes are independent from each other (D) none of these Paragraph for Question Nos. 13 to 14 In the circuit shown, switch K is initially open. Both the cells are ideal and C = 30 F, E = 1V, R1 = 2, E2 = 3V, R2 = 4. At t = 0 second, the switch K is closed. A and B are two points on circuit as shown. 13. Just after the switch K is closed, the magnitude of current in amperes through resistance R1 is - 1 (A) 3 4 (B) 3 (C) 1 (D) 2 14. Long after the switch K is closed, the magnitude of charge on the capacitor in steady state is - (A) 10 C (B) 30 C (C) 50 C (D) 90 C Paragraph for Question Nos. 15 to 16 In a series L-R circuit, connected with a sinusoidal ac source, the maximum potential difference across L and R are respectively 3 volts and 4 volts. 15. At an instant the potential difference across resistor is 2 volts. The potential difference in volt, across the inductor at the same instant will be : (A) 3 cos 30° (B) 3 cos 60° (C) 6 cos 45° (D) 6 16. At the same instant, the magnitude of the potential difference in volt, across the ac source will be - (A) 3 cos 67° (B) 5 cos 83° (C) 6 cos 97° (D) 0 SECTION – 3 : (Matching List Type) This section contains 4 multiple choice questions. Each questions has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 17. Figure shows activities A of three different radioactive material’s samples (labelled as I, II and III) versus time. Using the given information, correctly match the requisite parameter in the left List with the options given in right List. Consider only their natural decay as the cause of rate of change of no. of parent nuclei A 0 List-I t List -II P Disintegration constant () has maximum value for the 1  material of sample ... Q Half life is maximum for the material of the sample .... 2  R Initially if samples of all three materials have same 3  number of atoms then number of parent atoms will be maximum at a later time in the sample ..... S Suppose all the materials decay by emitting -particles 4 it is not possible of same energy and initially all three samples contain to compare with the same amount (in gm) of the materials. Till the end of help of data available time span equal to their respective half lives, maximum energy is radiated by the sample Codes : P Q R S (A) 1 2 3 4 (B) 2 3 4 1 (C) 2 3 3 4 (D) 2 4 4 3 18. In each situation of List-I, some charge distributions are given with all details explained. In List -II the electrostatic potential energy, electric field and its nature is given situation in List -II. Then match situation in List-I with the corresponding results in List-II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the OMR. List-I List -II P. A thin shell of radius a and having a charge – Q uniformly distributed 1. Electric potential energy of the over its surface as shown system is Q. A thin shell of radius 5a and having 2 1 Q2 8 0 a in magnitude a charge – Q uniformly distributed 2. Electric potential energy of the over its surface and a point charge system is magnitude – Q placed at its centre as shown. R. A solid sphere of radius a and having 3 Q2 20 0 a in a charge – Q uniformly distributed 3. Electric potential energy of the throughout its volume as shown. system is S. A solid sphere of radius a and having a charge – Q uniformly distributed 2 Q2 5 0 a in magnitude throughout its volume. The solid sphere 4. Electric potential energy of the is surrounded by a concentric thin system is positive in sign uniformly charged spherical shell of radius 2a and carrying charge –Q as shown Codes: P Q R S (A) 1 2 3 4 (B) 1 3 3 4 (C) 4 3 2 1 (D) 1 2 2 4 19. The energy, the magnitude of linear momentum, magnitude of angular momentum and orbital radius of an electron in a hydrogen like atom corresponding to the quantum number n and nuclear charge Z are E, p, L and r respectively. Then according to Bohr's theory of hydrogen atom, match the expressions in List-I with statement in List-II. List-I List -II P. Epr 1. is independent of n. Q. p 2. is directly proportional to n E R. Er S. pr Codes : 3. is inversely proportional to n. 4. is directly proportional to L. P Q R S (A) 3 4 1 2 (B) 3 1 4 2 (C) 1 4 3 2 (D) 1 2 3 4 20. Four different circuit components are given in each situation of column-I and all the components are connected across an ac source of same angular frequency  = 200rad/sec. The information of phase difference between the current and source voltage in each situation of List-I is given in List-II. Match the circuit components in List-I with corresponding results in List-II.  2  4 A nswers 1. (A,B,C,D) 2. (B,D) 3. (B,C,D) 4. (A,B,C,D) 5. (A,B,C) 6. (A,B,) 7. (A,B,D) 8. (A,C,D) 9. (B) 10. (C) 11. (B) 12. (A) 13. (C) 14. (C) 15. (A) 16. (B) 27 (C) 28. (D) 29. (A) 30. (B)