5.PRACTICE TEST-3 (Paper-1)

PRACTICE TEST THRE PAPER – 1 INSTRUCTIONS PART - I (PHYSICS) SECTION - I Straight Objective Type This section contains 7 multiple choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. The potential energy (in S units) of a particle of mass 2 kg in a conservative field is U = 6x – 8y. If the initial velocity of the particle is → = – 1.5 ˆi + 2 ˆj then the total distance travelled by the particle in first two seconds is (A) 10 m (B) 12 m (C) 15 m (D) 18 m 2. A thin rod of length 4 l, mass 4m is bent at the points as shown in the fig. What is the moment of inertia of the rod about the axis passing point O and perpendicular to the plane of the paper. m𝑙2 (A) 3 10m𝑙2 (B) 3 (C) (C) m𝑙2 12 (D) (D) m𝑙2 24 3. Which of the following travelling wave will produce standing wave, with node at x = 0, when superimposed on y = A sin (t  k x) (A) A sin (t + k x) (B) A sin (t + k x + ) (C) A cos (t + k x) (D) A cos (t + k x + ) 4. In an adiabatic expansion the product of pressure and volume : (A) decreases (B) increases (C) remains constant (D) first increases, then decreases. 5. A solid spherical black body of radius r and uniform mass distribution is in free space. It emits power ‘P’ and its rate of colling is R then (A) R P  r2 (B) R P  r (C) R P  1/r2 (D) R P  1/r 6. In the figure shown, initially the spring of negligible mass is in undeformed state and the block has zero velocity E is a uniform electric field. Then : (i) The maximum speed of the block will be (ii) The maximum speed of the block will be (iii) The maximum compression of the spring will be QE K (iv) The maximum compression of the spring will be 2QE K (A) only (i) and (iii) are correct (B) only (i) and (iv) are correct (C) only (ii) and (iii) are correct (D) only (ii) and (iv) are correct 7. ' n' identical light bulbs, each designed to draw P power from a certain voltage supply are joined in series and that combination is connected across that supply. The power consumed by one bulb will be- (A) n P (B) P (C) P/n (D) P/n2 SECTION- II Multiple Correct Answers Type This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE may be correct. 8. Which of the following statements are true for a moving body ? (A) if its speed changes, its velocity must change and it must have some acceleration (B) if its velocity changes, its speed must change and it must have some acceleration (C) if its velocity changes, its speed may or may not change, and it must have some acceleration (D) if its speed changes but direction of motion does not change, its velocity may remain constant. 9. In the figure shown all the surface are smooth. All the blocks A, B and C are y movable, x-axis is horizontal and y-axis vertical as shown. Just after the system is A  released from the position as shown. B x (A) Acceleration of 'A' relative to ground is in negative y-direction C (B) Acceleration of 'A' relative to B is in positive x-direction (C) The horizontal acceleration of 'B' relative to ground is in negative x-direction.  Horizontal Surface (D) The acceleration of 'B' relative to ground directed along the inclined surface of 'C' is greater than g sin . 10. Two concentric rings of radii R1 = m and R2= 4m are placed in y-z +Q -q plane with their centres at origin. They have uniform charge –q and R1 +Q = 2 2 q on the inner and outer rings respectively. Consider the x electrostatic potential to be zero at infinity. Then (A) The electric potential is zero at origin. (B) The electric field intensity is zero at r = 2 m. R2 (C) A positive charged particle disturbed from origin along the x-axis will restore back to origin. (D) Where potential is maximum on the x-axis, field intensity is zero. 11. In the circuit shown, resistance R = 100 , inductance L = 2 H and  capacitance C = 8 F  are connected in series with an ac source of 200volt and frequency ‘f’. If the readings of the hot wire voltmeters V1 and V2 are same then : (A) f = 125 Hz (B) f = 250  Hz (C) current through R is 2A (D) V1 = V2 = 1000 volt SECTION - III Comprehension Type This section contains 2 paragraphs. Based upon one of the paragraphs 3 multiple choice questions and based on the other paragraph 2 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph for Question Nos. 12 to 13 Raindrops are falling with a velocity 10 m/s making an angle of 450 with the vertical. The drops appear to be falling vertically to a man running with constant velocity. The velocity of rain drops change such that the rain drops now appear to be falling vertically with running with same velocity. times the velocity it appeared earlier to the same person 12. The magnitude of velocity of man with respect to ground is (A) 10 m/s (B) 10 m/s (C) 20 m/s (D) 10 m/s 13. The angle (in degrees) between the initial and the final velocity vectors of the raindrops with respect to the ground is (A) 8 (B) 15 (C) 22.5 (D) 37 Paragraph for Question Nos. 14 to 16 Resistance value of an unknown resistor is calculated using the formula R  V where V and I be the I readings of the voltmeter and the ammeter respectively. Consider the circuits below. The internal resistances of the voltmeter and the ammeter (Rv and RG respectively) are finite and non zero. Let RA and RB be the calculated values in the two cases A and B respectively. 14. The relation between RA and the actual value R is (A) R > RA (B) R < RA (C) R = RA (D) dependent upon E and r. 15. The relation between RB and the actual value R is : (A) R < RB (B) R > RB (C) R = RB (D) dependent upon E and r. 16. If the resistance of voltmeter is Rv = 1 k  and that of ammeter is R = 1 , the magnitude of the percentage error in the measurement of R (the value of R is nearly 10 ) is : (A) zero in both cases (B) non zero but equal in both cases (C) more in circuit A (D) more in circuit B SECTION - IV (Total Marks : 28) (Integer Answers Type) This section contains 7 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the ORS. 17. A planet is made of two materials of density  and  as shown in figure. 1 The acceleration due to gravity at surface of planet is same as a depth ‘R’. The ratio of 2 of x. x is 3 . Find the value 18. A concave mirror of radius of curvature 10 cm is filled with water upto a very small thickness ( = 4 ). 3 Paraxial converging rays are incident of the system, whose intersection is 15 cm behind the mirror. At how much distance from the mirror, final image will be formed. Write the answer in cm. 19. A block of mass m is slided up along a fixed incline plane with a speed of 10 m/sec. The inclination angle of the incline is 37º and the coefficient of friction s = k = 0.8. Find the distance travelled by the block in 2 seconds. (sin 37º = 3/5 and g = 10 m/sec2). Write your answer in meters and in nearest single digit 20. Two parallel infinitely long wires carrying currents in opposite directions so that repulsive force per unit length on wires is 0.1 N. The separation between the wires is 2m. If the mimimum magnetic field is k × 10–4 T exactly midway between the wires and in the plane of the wires. Then the value of k is : 21. A particle moves in a straight line such that it moves in the same direction but its speed decreases uniformly with time to zero in time interval T = 10s. It travels a total distance 'S' = 12.5 m. Find the velocity (in m/s) at any intermediate time t = 6.s. 22. A particle is projected from a horizontal plane at an angle 60º with horizontal and with a speed of projection 10 m/s. Find minimum radius of curvature (in meters) during its flight. 23. The chain of length L is released from rest on a smooth incline with x = 0 as shown in the figure. 4 Determine velocity v of the chain when a half of the length has fallen. (Take L = 25 m) in m/s. (Neglect edge effect of inclined). ANSWER KEY TO PRACTICE TEST-THREE PAPER-1 1. (C) 2. (B) 3. (B) 4. (A) 5. (B) 6. (B) 7. (D) 8. (A,C) 9. (A,B,C,D) 10. (B,C,D) 11. (A,C,D) 12. (D) 13. (B) 14. (A) 15. (A) 16. (D) 17. 7 18. 3 19. 4 20. 4 21. 1 22. 5 23. 1