4. Subject Test

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. A curve is plotted to represent the dependence of the ratio of the received frequency  to the frequency  emitted by the source on the ratio of the speed of observer Vob to the speed of sound Vsound in a situation in which an observer is moving towards a stationary sound source. The curve is best represented by : f/f0 2 (A) (B) 1 0 Vob/Vsound (C) (D) 2. A pendulum of length L and bob of mass M has a spring of force constant k connected horizontally to it at a distance h below its point of suspension. The rod is in equilibrium in vertical position. The rod of length L used for vertical suspension is rigid and massless. The frequency of vibration of the system for small values of  is : (A) (B) (C) 2 (D) 3. A long capillary tube of mass '' gm, radius 2mm and negligible thickness, is partially immersed in a liquid of surface tension 0.1 N/m. Take angle of contact zero and neglect buoyant force of liquid. The force required to hold the tube vertically, will be - (g = 10 m/s2) (A) 10.4  mN (B) 10.8  mN (C) 0.8  mN (D) 4.8  mN 4. AB is an L shaped obstacle fixed on a horizontal smooth table. A ball strikes it at A, gets deflected and restrikes it at B. If the velocity vector before collision is → and coefficient of restitution of each collision is 'e', then the velocity of ball after its second collision at B is - (A) 2 → (B) e → (C)  → (D) data insufficient 5. A nonuniform sphere at rest on a rough horizontal surface is acted upon by a force F as shown. The friction force acting on it is (1) towards left (2) towards right (3) zero (A) 1 or 2 (B) 1 or 3 (C) 2 or 3 (D) 1or 2 or 3 6. AOB is a swing suspended from vertical poles AA´ and BB´ as shown. If ropes AO and OB of length l1 and l2 respectively are massless and are perpendicular to each other with a point mass m hanging from O, the time period of the swing for small oscillations perpendicular to the plane of paper is: 2 F ///////////////////// (A) (B) 2 (C) 2 (D) 2 7. A particle is executing SHM according to the equation x = A cos t. Average speed of the particle during the  interval 0  t  6  . (A) 2 3A (B) 4 3A (C)  (D)  2  3 8. Mass m shown in figure is in equilibrium. If it is displaced further by x and released find its acceleration just after it is released. Take pulleys to be light & smooth and strings light. (A) 4kx 5m (B) 2kx 5m (C) 4kx m (D) none of these 9. Consider a boy on a trolley who throws a ball with speed 20 m/s at an angle 37° with respect to trolley in direction of motion of trolley which moves horizontally with speed 10 m/s then what will be distance travelled by ball parallel to road : (A) 20.2 m (B) 12 m (C) 31.2 m (D) 62.4 m 10. One mole of an ideal gas at pressure P0 and temperature T0 is expanded isothermally to twice its volume and then compressed at constant pressure to (V0/2) and the gas is brought back to original state by a process in which P  V (Pressure is directly proportional to volume). The correct representation of process is - (A) (B) (C) (D) 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. Heat is supplied to a certain homogeneous sample of matter at a uniform rate. Its temperature is plotted against time as shown in the figure. Which of the following conclusions can be drawn? (A) its specific heat capacity is greater in the solid state than in the liquid state. (B) its specific heat capacity is greater in the liquid state than in the solid state. (C) its latent heat of vaporization is greater than its latent heat of fusion. (D) its latent heat of vaporization is smaller than its latent heat of fusion. 12. A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : (A) Average kinetic energy per molecule of gas A is equal to that of gas B. (B) Root mean square value of translational velocity of gas B is four times that of A. (C) Pressure exerted by gas B is eight times of that exerted by gas A. (D) Number of molecules of gas B in the cylinder is eight times that of gas A. 13. A partition divides a container having insulated walls into two compartments  and . The same gas fills the two compartments whose initial parameters are given. The partition is a conducting wall which can move freely without friction. Which of the following statements is/are correct, with reference to the final equilibrium position? 3V (A) The Pressure in the two compartments are equal. (B) Volume of compartment  is 5 12V (C) Volume of compartment  is 5 (D) Final pressure in compartment  is 5P 3 14. In a resonance tube experiment, a closed organ pipe of length 120 cm resonates when tuned with a tuning fork of frequency 340 Hz. If water is poured in the pipe then (given vair = 340 m/sec.) : (A) minimum length of water column to have the resonance is 45 cm. (B) the distance between two succesive nodes is 50 cm. (C) the maximum length of water column to create the resonance is 95 cm. (D) none of these. 15. A wire, under tension between two fixed points A and B, executes transverse vibrations in 2nd harmonium. Then : (A) All points of wire between A and B are in the same phase (B) All points between A and O are in the same phase (C) A point between A and O and a point between O and B may have a phase difference of /2 (D) A point between A and O and a point between O and B may have a phase difference of  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. A particle moving on a smooth horizontal surface strikes a stationary wall. The angle of strike is equal to the angle of rebound & is equal to 37° and the coefficient of restitution with wall is e = X 1 . Find the friction coefficient between 5 wall and the particle in the form 10 and fill value of X. 17. A spool of mass M = 3 kg and radius R = 20 cm has an axle of radius r = 10 cm around which a string is wrapped. The moment of inertia about an axis R MR2 perpendicular to the plane of the spool and passing through the centre is . 2 r Coefficient of friction between the surface and the spool is 0.4. If the maximum M T value of the tension is T (in N) that can be applied so that the spool rolls without slipping, then find T/2 [Take g = 10 m/s2.] 18. A particle is projected at an angle 60º with speed 10 3, from the point ' A ' as shown in the fig. At the same time the wedge is made to move with speed 10 3 towards right as shown in the figure. Then the time (in seconds) after which particle will strike the wedge is : 19. In a tank of horizontal cross-sectional area 1m2, a spring with force constant 2000 Nm–1 is fixed in vertical position upto the height of the water as shown in figure 1. A block of mass 180 kg is gently placed over the spring and it attains the equilibrium position as shown in figure 2. If base area of the block is 0.2m2 and height 60 cm, then compression in the spring is 5X (in cm) in equilibrium position. Then find X (take g = 10 m/s2;  = 1000 kg/m3) (Fig.1) (Fig. 2) 20. A planet revolves about the sun in elliptical orbit of semimajor axis 2 × 1012 m. The areal velocity of the planet when it is nearest to the sun is 4.4 × 1016 m2/s. The least distance between planet and the sun is 1.8 × 1012 m. The minimum speed of the planet is a × 101 (in km/sec) then find a A nswers 1. (A) 2. (D) 3. (B) 4. (C) 5. (D) 6. (D) 7. (D) 8. (C) 9. (D) 10. (C) 11. (A,C) 12. (A,B,C,D) 3. (A,B,C,D) 14. (A,B,C) 15. (B,D) 16. 5 17. 9 18. 2 sec 19. 8 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. The two blocks A and B of equal mass are initially in contact when released from rest on the inclined plane. The coefficients of friction between the inclined plane and A and B are  and  respectively : (Assume tan  >  and  ) (A) If  >  , the blocks will always remains in contact. (B) If  <  , the blocks will slide down with different accelerations (C) If  >  , the blocks will have a common acceleration 1 (   ) gsin  1 2 2 1 2 12 (D) If  <  , the blocks will have a common acceleration gsin 1 2 1  2 2. A particle P of mass m attached to a vertical axis by two light strings AP and BP of length L each. The separation AB = L, P rotates around the axis in a horizontal plane with a constant angular velocity . The tension in the strings AP and BP are T1 and T2 respectively, then: (take acceleration due to gravity g) (A) T1 = T2 (B) T1 + T2 = m2L (C) T1 – T2 = 2mg (D) BP will remain tight only if   3. In each of three figures shown, two blocks are connected by a light spring and the system is placed on smooth horizontal surface. A constant horizontal force of magnitude F is applied to left block as shown. Assuming spring constant in all three cases to be same, which of the following statements is/are true. fig.-1 fig.-2 fig.-3 (A) maximum compression in spring 1 is greater than that in spring 2. (B) maximum compression in spring 3 is greater than that in spring 1. (C) maximum compression in spring 3 is greater than that in spring 2. (D) maximum compression in all springs is equal. 4. A uniform disc of mass m and radius R is free to rotate about its fixed horizontal axis without friction. There is sufficient friction between the inextensible light string and disc to prevent slipping of string over disc. At the shown instant extension in light spring is 3mg, where m is mass of block, g is acceleration K due to gravity and K is spring constant. 4 g (A) Acceleration of block just after it is released is 3 (B) Tension in the string continuously increases till extension in the spring reaches maximum value. (C) maximum extension in the spring is 2mg K (D) Maximum extension in the spring is mg K 5. A particle moving with kinetic energy = 4J makes an elastic head on collision with a stationary particle which has thrice its mass. During the impact: (A) Kinetic energy of the system is 4J at all instant (B) The maximum elastic potential energy of the system is 3J (C) Momentum and total energy of system are conserved at every instant (D) The ratio of kinetic energy to elastic potential energy of the system first decrease and then increases 6. A wire of density 9  103 kg/m3 is stretched between two clamps 1 m apart and is stretched to an extension of 4.9  10 -4 metre. Young's modulus of material is 9  1010 N/m2. Then (A) The lowest frequency of standing wave is 35 Hz (B) The frequency of 1st overtone is 70 Hz (C) The frequency of 1st overtone is 105 Hz (D) The stress in the wire is 4.41 × 107 N/m2 7. A metal wire of length L, area of cross-section A and Young’s modulus Y is stretched by a variable force F such that F is always slightly greater than the elastic force of resistance in the wire. When the elongation of the wire is 𝑙 : (A) the work done by F is (B) the work done by F is YA2 L YA𝑙2 2L YA𝑙2 (C) the elastic potential energy stored in the wire is 2L (D) heat is produced during the elongation 8. A gaseous mixture consists of equal number of moles of two ideal gases having adiabatic exponents 1 and 2 and molar specific heats at constant volume Cv and Cv statements is/are correct ? respectively. Which of the following (A) Adiabatic exponent for gaseous mixture is equal to 1   2 2 Cv  Cv (B) Molar specific heat at constant volume for gaseous mixture is equal to 1 2 2 Cv  Cv  R (C) Molar specific heat at constant pressure for gaseous mixture is equal to 1 2 2 (D) Adiabatic exponent for gaseous mixture is 1 + 2R C  C 1 2 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 quantity of an ideal monoatomic gas consists of n moles initially at temperature T1. The pressure and volume are then slowly doubled in such a manner so as to trace out a straight line on a P-V diagram. W 9. For this process, the ratio nRT is equal to (where W is work done by the gas) : (A) 1.5 (B) 3 (C) 4.5 (D) 6 10. If C is defined as the average molar specific heat for the process then C has value R (A) 1.5 (B) 2 (C) 3 (D) 6 Paragraph for Question Nos. 11 to 12 Figure shows an electrical calorimeter to determine specific heat capacity of an unknown liquid. First of all, the mass of empty calorimeter (a copper container) is measured and suppose it is 'm1'. Then the unknown liquid is poured in it. Now the combined mass of calorimeter + liquid system is measured and let it be 'm2'. So the mass of liquid is (m – m ). Initially both were at room temperature ( ). 2 1 0 Now a heater is immersed in it for time interval 't'. The voltage drop across the heater is 'V' and current passing through it is ''. Due to heat supplied, the temperature of both the liquid and calorimeter will rise simultaneously. After t sec; heater was switched off, and final temperature is  . If there is no heat loss to surroundings Heat supplied by the heater = Heat absorbed by the liquid + heat absorbed by the calorimeter (V)t = (m – m ) S ( –  ) + m S ( –  ) The specific heat of the liquid S = (V) t f  0  m1SC 𝑙 (m2  m1 )  calorimeter Figure 1  time (t) Figure 2 Temperature vs time graph assuming no heat losses to surrounding. Radiation correction : There can be heat loss to environment. To compensate this loss, a correction is introduced. Let the heater was on for t sec, and then it is switched off. Now the temperature of the mixture falls due to heat loss to environment. The temperature of the mixture is measured at t/2 sec. after switching off. Let the fall in temperature during this time is  Now the corrected final temperature is taken as  =  +  11. In this experiment voltage across the heater is 100.0 V and current is 10.0A, and heater was switched on for t = 700.0 sec. Initially all elements were at room temperature  = 10.0°C and final temperature was measured as  = 73.0°C. Mass of empty calorimeter was 1.0 kg and the combined mass of calorimeter + liquid is 3.0 kg . The specific heat capacity of the calorimeter Sc = 3.0 × 103 J/kg°C. The fall in temperature 350 second after switching off the heater was 7.0°C. Find the specific heat capacity of the unknown liquid in proper significant figures. (A) 3.5 × 103 J/kg°C (B) 3.50 × 103 J/kg°C (C) 4.0 × 103 J/kg°C (D) 3.500 × 103 J/kg°C 12. If mass and specific heat capacity of calorimeter is negligible, what would be maximum permissible error in S𝑙. Use the data mentioned below. m1  0, Sc  0, m2 = 1.00 kg, V = 10.0 V,  = 10.0 A, t = 1.00 × 10 sec., 0 = 15°C, Corrected f = 65°C (A) 4% (B) 5% (C) 8% (D) 12% Paragraph for Question Nos. 13 to 14 A block of mass 15 kg is placed over a frictionless horizontal surface. Another block of mass 10 kg is placed over it, that is connected with a light string passing over two pulleys fastened to the 15 kg block. A force F = 80 N is applied horizontally to the free end of the string. Friction coefficient between two blocks is 0.6. The portion of the string between 10 kg block and the upper pulley is horizontal. Pulley, string & connecting rods are massless. (Take g = 10 m/s2) 13. The magnitude of accelerations of the 10 kg,15 kg block are : (A) 3.2 m/s2 , 3.2 m/s2 (B) 2.0 m/s2 , 4.2 m/s2 (C) 1.6 m/s2 ,16/3 m/s2 (D) 0.8 m/s2 , 2.0 m/s2 14. If applied force F = 120 N, then magnitude of acceleration of 15 kg block will be : (A) 8 m/s2 (B) 4 m/s2 (C) 3.2 m/s2 (D) 4.8 m/s2 Paragraph for Question Nos. 15 to 16 A horizontal uniform rod of mass 'm' has its left end hinged to the fixed incline plane, while its right end rests on the top of a uniform cylinder of mass 'm' which in turn is at rest on the fixed inclined plane as shown. The coefficient of friction between the cylinder and rod, and between the cylinder and inclined plane, is sufficient to keep the cylinder at rest. 15. The magnitude of normal reaction exerted by the rod on the cylinder is (A) mg 4 mg (B) 3 (C) mg 2 2mg (D) 3 16. The ratio of magnitude of frictional force on the cylinder due to the rod and the magnitude of frictional force on the cylinder due to the inclined plane is: (A) 1 : 1 (B) 2 : (C) 2 : 1 (D) 1 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. Two blocks A and B of mass m and 2m respectively are connected by a massless spring of spring constant K. This system lies over a smooth horizontal surface. At t = 0 the block A has velocity u towards right as shown while the speed of block B is zero, and the length of spring is equal to its natural length at that instant. In each situation of List I, certain statements are given and corresponding results are given in List II. Match the statements in List  corresponding results in List  and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the OMR. List - I List - II P. The velocity of block A 1. can never be zero Q. The velocity of block B 2. may be zero at certain instants of time R. The kinetic energy of system of two blocks 3. is minimum at maximum compression of spring S. The potential energy of spring 4. is maximum at maximum extension of spring Codes: P Q R S (A) 1 3 2 4 (B) 2 1 4 2 (C) 1 2 3 4 (D) 1 2 4 3 18. Consider a system of particles (it may be rigid or non rigid). In the List- some condition on force and torque is given. List- contains the effects on the system. (Letters have usual meaning) List - I List - II → P. Fres  0 → 1. Psystem will be constant → Q. res  0 2. Lsystem will be constant R. External force is absent 3. total work done by all forces will be zero S. No nonconservative force acts. 4. total mechanical energy will be constant. Codes : P Q R S (A) 1 2 3 4 (B) 1 2 2 4 (C) 4 2 1 3 (D) 1 3 3 4 19. A particle of mass m = 1 kg executes SHM about mean position O with angular frequency  = 1.0 rad/s and total energy 2J. x is positive if measured towards right from O. At t = 0, particle is at O and moves towards right. Match the condition in List-I with the position of the particle in List-II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the OMR. P Q R S (A) 3 4 1 2 (B) 4 3 2 1 (C) 1 2 1 3 (D) 2 1 4 3 20. An ideal monoatomic gas undergoes different types of processes which are described in List-I. Match the corresponding effects in List-II. The letters have usual meaning. List - I List - II P. P = 2V2 1. If volume increases then temperature will also increase. Q. PV2 = constant 2. If volume increases then temperature will decrease. R. C = CV + 2R 3. For expansion, heat will have to be supplied to the gas. S. C = CV – 2R Codes : 4. If temperature increases then work done by gas is positive. P Q R S (A) 2 1 3 4 (B) 4 3 1 2 (C) 3 4 2 1 (D) 4 2 1 3 A nswers 1. (A,B) 2. (B,C) 3. (A,B,C) 4. (A,B,C) 5. (B,C,D) 6. (A,B) 7. (B,C) 8. (B,D) 9. (A) 10. (B) 11. (A) 12. (C) 13. (A) 14. (B) 15. (C) 16. (A) 17. (C) 18. (B) 19. (A) 20. (D)