PRACTICE TEST-1 PAPER-1

PRACTICE TEST ONE PAPER-1 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. For each question in Section 1, you will be awarded 2 marks if you darken the bubble corresponding to the correct answer each zero mark if no bubbles are darkened. No negative marks will be awarded for incorrect answers in this section. 3. For each question in Section 2, you will be awarded 4 marks if you darken all the bubble(s) corresponding to only the correct answer(s) and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 4. For each question in Section 3, you will be awarded 4 marks if you darken the bubble corresponding to only the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. PART-I (PHYSICS) 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. 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 (B)  15 ˆi (C)  10 ˆi (D)  5ˆi 2. A transparent cylinder has its right half polished so as to act as a mirror. A paraxial light ray is incident from left, that is parallel to principal axis, exits parallel to the incident ray as shown. The refractive index n of the material of the cylinder is : (A) 1.2 (B) 1.5 (C) 1.8 (D) 2.0 3. 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 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 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 A , A = Area of rods y , y = 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 6. A light ray gets reflected from a pair of mutually  mirrors, not necessarily along axes. The intersection point of mirrors is at origin. The incident light is along y = x + 2. If the light ray strikes both mirrors in succession, then it may get reflected finally along the line : (A) y = 2x – 2 (B) y = – x + 2 (C) y = – x – 2 (D) y = x – 4 7. The graph shown gives the temperature along an x axis that extends directly through a wall consisting of three layers A, B and C. The air temperature on one side of the wall is 150°C and on the other side is 80°C. Thermal conduction through the wall is steady. Out of the three layers A, B and C, thermal conductivity is greatest of the layer (A) A (B) B (C) C (D) Thermal conductivity of A = Thermal conductivity of B. 8. When a metallic surface is illuminated with monochromatic light of wavelength , the stopping potential is 5 V . When the same surface is illuminated with light of wavelength 3, the stopping potential is V . 0 0 Then the work function of the metallic surface is : hc (A) 6  hc (B) 5  hc (C) 4  (D) (D) 2 hc 4  9. A Young’s double slit experiment is conducted in water ( ) as shown in the figure, and a glass plate of thickness t and refractive index  is placed in the path of S . The magnitude of the phase difference at O is : (Assume that ‘’ is the wavelength of light in air). O is symmetrical w.r.t. S and S . (A)  2 10. The ratio of r.m.s. speed to the r.ms. angular speed of a diatomic gas at certain temperature is: (assume m = mass of one molecule, M = molecular mass,  = moment of inertia of the molecules) (A) (B) (C) (D) 1 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. When two point charges qA and qB are placed at some separation on positive x-axis at points (xA, 0) and (xB, 0). Given that |qA| > |qB| and xB > xA. If null point is the point where net electric field due to both the charges is zero, then : (A) If both qA and qB are positiv e, null point lies at some point xA < x < xB (B) If qA is positive and qB is negative, null point lies at some point x < xA (C) If qA is positive and qB is negative, null point lies at some point x > xB (D) If qA is negative and qB is positive, null point lies at some point x > xB 12. 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 cm. (B) Transverse displacement of the particle at x = 0.04 m and t = 0.025 s is – 2 2 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 13. 'Identical dielectric slabs are inserted into two identical capacitors A and B. These capacitors and a battery are connected as shown in figure and steady state is achieved. Now the slab of capacitor B is pulled out with battery remaining connected : (A) During the process of removal positive charge flows from point a to point b. (B) Finally charge on capacitor B will be less than that on capacitor A. (C) During the process of removal, a positive work is done by the external force F, which appears completely as heat in the circuit. (D) During the process removal, internal energy of the battery increases. 14. Figure shows the path of an electron in a region of uniform magnetic field. The path consists of two straight sections, each between a pair of uniformly charged plates, and two half circles. The electric field exists only between the plates.   Pair-A   Pair-B (A) Plate I of pair A is at higher potential than plate-II of the same pair. (B) Plate I of pair B is at higher potential than plate II of the same pair. (C) Direction of the magnetic field is out of the page [ ]. (D) Direction of the magnetic field in to the page [ ]. 15. A light cylindrical tube ‘T’ of length 𝑙 and radius ‘r’ containing air is inverted in water (density d). One end of the tube is open and the other is closed. A block ‘B’ of density 2d is kept on the tube as shown in the figure. The tube stays in equilibrium in the position shown. (Assume the atmospheric pressure is to be P0.). Pick up the correct statement(s). r2𝑙 (A) the volume of block B is 3 2r 2𝑙 (B) the volume of block B is 3 h  𝑙  (C) the pressure of air trapped in the tube is P0 + d g    3  h  2𝑙  (D) the pressure of air trapped in the tube is P0 + d g    3  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) 75 16. A rigid structure consists of a thin ring of radius R = 290 m and a thin radial rod of equal mass and length 2R. The structure is pivoted around a horizontal axis xx’ in the plane of the ring, passing through its centre. The structure is released from rest and it rotates around the axis xx’ from the initial upright orientation. Find its angular speed in rad/s about the axis when it is inverted. Assume no frictional losses. X X' 17. 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  18. Two blocks A (3kg) and B (6kg) are connected by a spring of stiffness 512N/m and placed on a smooth horizontal surface. Initially the spring is in natural length. Velocity 1.8 m/s and 2.2 m/s are imparted to A and B in opposite direction. The maximum extension of the spring will be 5 cm. Find . 19. In the figure the variation of components of acceleration of a particle of mass 1 kg is shown w.r.t. time. The initial velocity of the particle is →  (3 ˆi  4ˆj) m/s. The total work done by the resultant force on the particle in time interval from t = 0 to t = 4 seconds in joules is : 20. A radioactive nucleus can decay by either emitting an  particle or by emitting a  particle. Probability of  decay is 75% while that of  decay is 25%. The decayconstant of  decay is  and that of  1 decay is  .  2 is A nswers 1. (D) 2. (D) 3. (B) 4. (C) 5. (B) 6. (D) 7. (A) 8. (A) 9. (C) 10. (C) 11. (A,C,D) 12. (D) 13. (A,D) 14. (A,B,C) 15. (A,C) 16. 8 17. 3. 18.  = 5 19. 10 20. 3