1.PRACTICE TEST-1 (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. A ball is dropped from the top of a building. The ball takes 0.5 s to fall past the 3 m length of a window some distance from the top of the building. If the speed of the ball at the top and at the bottom of the window are vT and v respectively, then (g = 9.8 m/sec2) (A) v + v = 12 ms–1 (B) v – v = 4.9 m s–1 vB (C) vBvT = 1 ms–1 (D) T = 1 ms–1 2. In the figure shown the acceleration of A is, a = 15ˆi 15ˆj then the acceleration of B is: (A remains in contact with B) (A) 6ˆi (C)  10 ˆi (B)  15 ˆi (D)  5ˆi 3. A 1.5 kg box is initially at rest on a horizontal surface when at t = 0 a horizontal force →  (1.8t)ˆi N (where t is in seconds) is applied to the box. The acceleration of the box as a function of time t is given by : → for 0  t  2.85 → a  (1.2t  2.4)i m/s2 for t > 2.85 The coefficient of kinetic friction between the box and the surface is : (A) 0.12 (B) 0.24 (C) 0.36 (D) 0.48 4. A collar ‘B’ of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5 m. The spring lying in the plane of the circular track and having spring constant 200 N/m is undeformed when the collar is at ‘A’. If the collar B starts from rest, the normal reaction exerted by the track on the collar when it passes through ‘A’ is : (A) 360 N (B) 720 N (C) 1440 N (D) 2880 N 5. Two vibrating strings of same length, same cross section area and stretched to same tension is made of materials with densities  & 2 . Each string is fixed at both ends. If v represents the fundamental mode of vibration of the one made with density  and v for another, then v /v is: (A) 1 (B) 2 2 (C) (D) 6. Two elastic rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature (  ,  = linear expansion co-efficient A1, A2 = Area of rods y1, y2 = Young modulus ) (A) A1 A2 = 1 y1 2 y2 (B) A1 A2 = L1 1 y1 L2 2 y2 (C) A1 A2 = L2 2 y2 L1 1 y1 (D) A1 A2 = 2 y2 1 y1 7. Two blocks ‘A’ and ‘B’ each of mass ‘m’ are placed on a smooth horizontal surface. Two horizontal force F and 2F are applied on both the blocks ‘A’ and ‘B’ respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is : (A) F (B) F/2 F (C) (D) 3F 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. 9. For a certain transverse standing wave on a long string, an antinode is formed at x = 0 and next to it, a node is formed at x = 0.10 m. the position y(t) of the string particle at x = 0 is shown in figure. 4 y(cm) t(s) -4 (A) Transv erse displacement of the particle at x = 0.05m and t = 0.05 s is – 2 (B) Transverse displacement of the particle at x = 0.04 m and t = 0.025 s is – 2 cm. cm. (C) Speed of the travelling waves that interfere to produce this standing wave is 2 m/s. 1 (D) The transverse velocity of the string particle at x = 15 m and t = 0.1 s is 20  cm/s P2 10. During an experiment, an ideal gas is found to obey a condition  = constant [ = density of the gas]. The  gas is initially at temperature T, pressure P and density . The gas expands such that density changes to 2 (A) The pressure of the gas changes to P. (B) The temperature of the gas changes to T. (C) The graph of the above process on the P-T diagram is parabola. (D) The graph of the above process on the P-T diagram is hyperbola. 11. From a cylinder of radius R, a cylinder of radius R/2 is removed, as shown. Current flowing in the remaining cylinder is . Magnetic field strength is : (A) zero at point A (B) zero at point B (C) 0 I at point A (D) 3R 0 I at point B 3R 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 14 A block of mass 1 kg is placed on a rough horizontal surface. A spring is attached to the block whose other end is joined to a rigid wall,as shown in the figure. A horizontal force is applied on the block so that mg it remains at rest while the spring is elongated by x. x  k . Let Fmax and Fmin be the maximum and minimum values of force F for which the block remains in equilibrium. For a particular x, Fmax– Fmin = 2 N. Also shown is the variation of Fmax+ Fmin versus x, the elongation of the spring. Fma+x Fmin 5N 0.1m x 12. The coefficient of friction between the block and the horizontal surface is : (A) 0.1 (B) 0.2 (C) 0.3 (D) 0.4 13. The spring constant of the spring is: (A) 25 N/m (B) 20 N/m (C) 2.5 N/m (D) 50 N/m 14. The value of Fmin , if x = 3 cm is :(A) 0 (B) 0.2N (C) 5N (D) 1N Paragraph for Question Nos. 15 to 16 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. 15. The equation of the wave is 16. (A) y = 0.1 sin (4t –1)+ 8(x – 2)) (C) y = 0.1 sin (4t –1)–8(x – 2)) The speed of particle at x = 2 m and t = 1sec is (B) y = 0.1 sin (t–1)– (x – 2)) (D) none of these (A) 0.2 m/s (B) 0.6 m/s (C) 0.4 m/s (D) 0 SECTION - IV (Integer Answers Type) This section contains 7 questions. Answer each of the questions in a single-digit integer, ranging from 0 to 9. 17. A glass bulb contains air and mercury. If the volume of air in bulb is to remain constant at all temperature, then x fraction of bulb must be occupied by mercury is 20 . Find out value of ‘x’. (Coefficient of linear expansion of glass = 9 × 10–6 K–1, coefficient of expansion of mercury is 1.8 × 10–4 K–1) 18. Figure shows the part of a hemisphere of radius (R) = 2m and surface charge density() = 2 C/m2. Calculate the electric potential (in volt) at centre O. 19. Plane surface of a thin planoconvex lens reflects 50% of light, while the curved surface is completely transparent, if final image of 'O' after refraction through lens coinsides with the image formed due to partial reflection from plane surface. If distance (in m) between 'O' and lens is x then find x/4. 2 20. A current carrying ring, carrying a constant current  Amp., radius 1m, mass 2 3 kg and having 10 windings is free to rotate about its tangential vertical axis. A uniform magnetic field of 1 tesla is applied perpendicular to its plane. How much minimum angular velocity (in rad/sec.) should be given to the ring in the direction shown, so that it can rotate 270º in that direction. Write your answer in nearest single digit in rad/sec. 21. A rod of mass m = 2 Kg and length 𝑙 = 10 cm moves such that its ends touch two fixed conducting parallel rails.A resistance R = 4 is connected between the rails as shown. If the rod is given an initial velocity 3m/sec and released, find the total amount of heat developed in the resistor in Joule. (friction is absent every where) 22. Photons having energy equivalent to  line of lyman series can eject electrons from a metal. These electrons can excite H atoms upto n=2 level .If the maximum work function of the metal in eV , is , find the integer next to  23. If the electric field in a region is given as E = y2 ˆi + 2xy ˆj and the potential is assumed 4 Volts at the origin, find the potential, in Volts, at the point (2,1,9). All values are in SI units. ANSWER KEY TO PRACTICE TEST-ONE PAPER-1 1. (A) 2. (D) 3. (B) 4. (C) 5. (C) 6. (D) 7. (D) 8. (B,D) 9. (A,C,D) 10. (B,D) 11. (C,D) 12. (A) 13. (A) 14. (A) 15. (A) 16. (C) 17. 3 18. 1 19. 3 20. 9 21. 9 22. 3 23. 2