6-Combined Test -1 - Paper - 2

COMBINED TEST - 1 (CT-1) PAPER-2 Duration : 3 Hours Max. Marks : 180 GENERAL INSTRUCTIONS 1. The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections and total number of questions are 60. 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 particle is subjected to two simple harmonic motions along x and y axis according to, x = 3 sin 100 t, y = 4 sin 100 t. (A) The path of the particle will be ellipse and it is moving in clockwise direction. (B) Motion of particle will be on a straight line. (C) Motion will be a simple harmonic motion with amplitude 5.  (D) Phase difference between two motions is 2 . 2. A thin uniform rigid rod of mass m and length 𝑙 is in mechanical equilibrium under the constraints of horizontal and vertical rough surfaces. Then select correct option(s): (A) The net torque of normal reactions about O is equal to mg (B) The net torque of friction about O is zero. 𝑙 cos. 2 (C) The net torque of normal reactions is numerically equal to net torque of frictional forces about the CM of road. (D) none of these 3. An ideal spring is permanently connected between two blocks of masses m and M. The (blocks + spring) system can move over a frictionless horizontal table along a straight line along the length of the spring as shown in figure. The blocks are brought nearer to compress the spring and then released. In the subsequent motion. (A) Initially they move in opposite direction with speeds inversly proportional to the their masses. (B) The ratio of their speeds remains constant in subsequent motion (C) Linear momentum and energy of the system remain conserved. (D) The two blocks will oscillate about their centre of mass which will remain stationary with respect to ground frame. 4. A monoatomic ideal gas undergoes a cyclic process ABCDEA as shown in the P-V diagram. (BC is isothermal and P3V1 < P1V3). Then which of the following curve(s) is/are correctly converted : (A) (B) (C) (D) 5. Find the thickness of the cubical object using the defective vernier calliper main scale has mm marks and 10 divisions of vernier scale coincide with 9 divisions of main scale. (A) 13.8 mm (B) 13.5 mm (C) 14.1 mm (D) 13.0 mm 6. A particle moving with kinetic energy = 3 J makes an elastic head-on collision with a stationary particle which has twice its mass. During the impact : (A) the minimum kinetic energy of the system is 1 J (B) the maximum elastic potential energy of the system is 2 J (C) momentum and total energy are conserved at every instant (D) the ratio of kinetic energy to potential energy of the system first decreases and then increases. 7. A ball of mass 1.6 kg is projected with a velocity of 20 m/s at an angle of 37º above the horizontal. After 1.2 sec., gravitational field vanishes and a force of constant magnitude is applied after that, force being always perpendicular to the direction of motion till it strikes the ground. When it strikes the ground it is moving vertically. Choose the correct option (g = 10 m/s2) : (A) Initially path is parabolic and later on it becomes hyperbolic 512 (B) The radius of the circle will be 7.2 m and constant magnitude of force applied is 9 N (C) The speed during circular motion will be 16 m/s (D) The time it takes to strike the ground is less than that it would have taken in projectile motion 8. A mass of 0.2kg is attached to the lower end of a massless spring of force-constant 200 N/m, the upper end of which is fixed to a rigid support. Which of the following statements is/are true? (A) In equilibrium, the spring will be stretched by 1cm. (B) If the mass is raised till the spring is unstretched state and then released, it will go down by 2cm before moving upwards. (C) The frequency of oscillation will be nearly 5 Hz. (D) If the system is taken to the moon, the frequency of oscillation will be the same as on the earth. 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 small mass slides down a fixed inclined plane of inclination  with the horizontal. The co-efficient of friction is  = 0 x where x is the distance through which the mass slides down and 0 is a constant. 9. The distance covered by the mass before it stops is: 2 4 1 1 (A)  tan  (B)  tan  (C) 2  tan  (D)  tan  0 0 0 0 10. The heat produced during the half journey of the particle is: (A) mg cos  2 0 tan2  (B) mg cos  4 0 tan2  (C) mg cos  8 0 tan2  (D) none of these Paragraph for Question Nos. 11 to 12 Two closed identical conducting containers are found in the laboratory of an old scientist. For the verification of the gas some experiments are performed on the two boxes and the results are noted. Experiment 1. When the two containers are weighed WA = 225 g , WB = 160 g and mass of evacuated container WC = 100 g. Experiment 2. When the two containers are given same amount of heat same temperature rise is recorded. The pressure change found are PA = 2.5 atm. PB = 1.5 atm. Required data for unknown gas : 11. Identify the gas filled in the container A and B. (A) N2, Ne (B) He, H2 (C) O2 , Ar (D) Ar, O2 12. Total number of molecules in ‘A’ (here NA = Avagadro number) (A) 125 N 64 (B) 3.125 NA (C) 125 N 28 (D) 31.25 NA Paragraph for Question Nos. 13 to 14 A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A particle of string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, /4 meter and 4 rad/sec respectively. 13. The equation of the wave is (A) y = 0.1 sin (4t –2) + 8(x + 1)) (B) y = 0.1 sin 4t–1) – 8(x – 2)) 1   1   (C) y = 0.1 sin (4t – ) + 8(x – 2)) (D) y = 0.1sin  4t –   8(x  1) 2 2     14. The speed of particle at x = 2 m and t = 1sec is (A) 0.2 m/s (B) 0.6 m/s (C) 0.4 m/s (D) 0 Paragraph for Question Nos. 15 to 16 An elastic string of unit cross–sectional area and natural length (a + b) where a > b and modules of elasticity Y has a particle of mass m attached to it at a distance a from one end , which is fixed to a point A of a smooth horizontal plane. The other end of the string is fixed to a point B so that string is just unstretched. If particle is held at B ( by stretching the length a of the string ) and then released, 15. The time period of the oscillation will be : (A) 2  (B) 2 (  b) (C)  (D) (  b ) 16. The separation between two extreme positions will be :  a  b   a  b  (A) a + b (B) 2 a (C)   b (D)   a        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. Regarding speed of sound in gas, match the statements in List-I with the results in List-II List - I List- II P. Temperature of gas is made 4 times and 1. speed becomes 2 times the initial value pressure 2 times Q. Only pressure is made 4 times without 2. speed becomes 2 times the initial value change in temperature R. Only temperature is changed to 4 times 3. speed remains unchanged S. Only Molecular mass of the gas is made 4 times 4. speed becomes half the initial value Codes : P Q R S (A) 2 3 2 4 (B) 2 2 3 4 (C) 2 1 3 4 (D) 1 2 3 4 18. The ring shown in figure is performing pure rolling on a rigid surface. Radius of ring is 'R' and angular velocity  of ring is ''. There are four points marked on the ring as shown. After time t =  . Match the columns. A List- I P. Displacement of A List - II 1. ( + 2) R Q. Displacement of B 2. R 2  4 R. Displacement of C S. Displacement of D 3. ( – 2) R 4. 4R Codes : P Q R S (A) 1 3 1 2 (B) 2 3 2 1 (C) 1 4 3 1 (D) 2 2 3 3 19. If man hold the rod with force F then match the following for reading shown by weighing machine (W.M.) (All forces are in Newton) Force F (in N) reading of weighing machine (applied by Ram on (in newton) rod to lift himself) List –I List – II P. 0 1. 500 Q. 100 2. 1200 R. 500 3. 700 S. 700 4. 1100 P Q R S (A) 1 3 2 4 (B) 2 1 4 3 (C) 2 3 4 1 (D) 2 4 3 1 20. Let V and E denote the gravitational potential and gravitational field respectively at a point due to certain uniform mass distribution described in four different situations of List-I. Assume the gravitational potential at infinity to be zero.The value of E and V are given in List-II. Match the statement in List-I with results in List-II. List-I List -II P. At centre of thin spherical shell 1. E = 0, V = 0 R. At centre of solid sphere 2. E  0, V  0 R A solid sphere has a non-concentric spherical cavity. At the centre of the spherical cavity 3. E = 0,V  0 S. At centre of line joining two point masses of equal magnitude 4. E  0, V = 0 P Q R S (A) 3 2 2 3 (B) 3 3 2 3 (C) 1 1 2 4 (D) 1 2 4 3 A nswers 1. (B,C) 2. (A,B,C) 3. (A,B,C,D) 4. (A,B) 5. (B) 6. (A,B,C,(D) 7. (B,C,D) 8. (A,B,C,D) 9. (A) 10. (A) 11. (C) 12. (B,D) 13. (A) 14. (C) 15. (D) 16. (C) 17. (A) 18. (B) 19. (D) 20. (B)