2.PRACTICE TEST-1 (Paper-2)

INSTRUCTIONS PART - I (PHYSICS) SECTION - I Straight Objective Type This section contains 8 multiple choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. A small uniform tube is bent into a circular tube of radius R and kept in the vertical plane. Equal volumes of two liquids of densities  and  ( > ) fill half of the tube as shown. If  is the angle which the radius passing through the interface makes with the vertical then        (A)  = tan–1   (B)  = tan–1                 (C)  = tan–1   (D)  = tan–1           2. 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 maximum distance travelled by ball parallel to road : (A) 20.2 m (B) 12 m (C) 31.2 m (D) 62.4 m 3. The blocks A and B shown in the figure have masses MA = 5 kg and MB = 4 kg. The system is released from rest. The speed of B after A has travelled a distance 1 m along the incline is (A) (B) 3 4 g (C) (D) 2 4. Two particles A & B separated by a distance 2 R are moving counter clockwise along the same circular path of radius R each with uniform speed v. At time t = 0, A is given a tangential acceleration of magnitude 72v 2 a = 25R . 6R (A) the time lapse for the two bodies to collide is 5V 11 (B) the angle covered by A is 6 11V (C) angular velocity of A is 5R 289 v2 (D) radial acceleration of A is 5R 5. A gun which fires small balls of mass 20 gm is firing 20 balls per second on the smooth horizontal table surface ABCD. If the collision is perfectly elastic and balls are striking at the centre of table with a speed 5 m/sec at an angle of 60º with the vertical just before collision, then force exerted by one of the leg on ground is (assume total weight of the table is 0.2 kg and g = 10 m/s2) : (A) 0.5 N (B) 1 N (C) 0.25 N (D) 0.75 N 6. When a galvanometer is shunted with a 4 resistance, the deflection is reduced to one - fifth. If the galvanometer is further shunted with a 2 wire, the further reduction (find the ratio of decrease in current to the previous current) in the deflection will be (the main current remains the same). (A) (8/13) of the deflection when shunted with 4 only (B) (5/13) of the deflection when shunted with 4 only (C) (3/4) of the deflection when shunted with 4 only (D) (3/13) of the deflection when shunted with 4 only 7. In the figure shown the plates of a parallel plate capacitor have unequal charges. Its capacitance is 'C'. P is a point outside the capacitor and close to the plate of charge –Q. If distance between the plates is 'd' then select incorrect statement: (A) A point charge at point 'P' will experience electric force due to capacitor 3Q (B) The potential difference between the plates will be 2C (C) The energy stored in the electric field in the region between the plates is 9Q2 8C (D) The force on one plate due to the other plate is Q2 2 0 d2 8. An LCR series circuit with 100  resistance is connected to an AC source of 200 V and angular frequency 300 radians per second. When only the capacitance is removed, the current lags behind the voltage by 60°. When only the inductance is removed, the current leads the voltage by 60º. Then the current and power dissipated in LCR circuit are respectively (A) 1A, 200 watt. (B) 1A, 400 watt. (C) 2A, 200 watt. (D) 2A, 400 watt. SECTION - II Multiple Correct Answers(s) 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. The graph shows the variation of stopping potential VS with the frequency  of the incident light in a photoelectric experiment.From the graph it can be concluded that (e is electronic charge) (A) the work function of the metal is eb. (B) the work function of the metal is ea. eb (C) the value of Planck’s constant is equal to a ea (D) the value of Planck’s constant is equal to b 10. The figure shows a block of mass M=2m having a spherical smooth cavity of radius R placed on a smooth horizontal surface .There is a small ball of mass m moving at an instant vertically downward with a velocity v with respect to the block .At this instant : horizontal smooth surface (A) The normal reaction on the ball by the block is mv2 R 2 (B) The normal reaction on the ball by the block is 3 mv2 R v 2 (C) The acceleration of the block with respect to the ground is 3R v 2 (D) The acceleration of the block with respect to the ground is 2R 11. If  is the density of the material of a uniform rod and is  is the breaking stress , and the length of the rod is such that the rod is just about to break due to its own weight when suspended vertically from a fixed support, then  (A) length of the rod is g (B) stress at a cross section perpendicular to the rod, at one fourth the length of the rod above its lowest point  is 4 (C) stress at all horizontal sections of the rod is same (D) the rod is about to break from its mid point 12. Two capacitors C1 = 8 F and C2 = 4 F are connected in series between points A and B.An ideal cell of emf 12 V is connected between A and B for a long time.Now a slab of dielectric constant k = 2 is slowly and fully filled in the gap of capacitor C2 . (A) During the filling process the energy taken from the cell is 192 J (B) In the filling process the increase in electrostatic energy stored in the capacitors is 96 J (C) The work done by dielectric slab on the filling agent during the filling process is positive. (D) The work done by dielectric slab on the filling agent during the filling process is zero. SECTION - III (Integer Answer Type) This section contains 6 questions. Answer each of the questions in a single-digit integer, ranging from 0 to 9. 13. In a moving coil galvanometer, a coil of area  cm2 and 10 windings is used. Magnetic field strength applied on the coil is 1 tesla and torsional stiffness of the torsional spring is 6 × 10–5 N.m/rad. A needle is welded with the coil. Due to limited space, the coil (or needle) can rotate only by 90º, For marking, the 90º space is equally devided into 10 parts as shown. Find the least count of this galvanometer in mA. 14. A neutron strikes a hydrogen atom which is initially at rest and free to move.The initial speed of the neutron is u.After the collision both neutron and the H atom move making 300 angle with the initial velocity of the neutron.Also the H atom is found to get excited to first excited state.If the initial KE = p times first excitation energy of the H atom, find the value of p (assume mass of neutron = mass of H atom) 15. A small object stuck on the surface of a glass sphere (n = 1.5) is viewed from the diametrically opposite position. Find transverse magnification. 16. The two blocks shown are moving together and on the verge of relative sliding between them. If the coefficient of friction is  between them, then find 10 . 17. A string is wrapped around a cylinder of mass M = 1kg and radius R = 10m . The string is pulled vertically upward to prevent the center of mass from falling as the cylinder unwinds the string. The length of the string unwound when the cylinder has reached a speed  = 4rad/s is x m. Find ‘x’. (g = 10m/s2). The axis of the cylinder remains horizontal. 18. The linear charge density on the circumference of a ring of radius 'R' is  =  sin  where '' is defined as shown in f igure. Find the magnitude of electric dipole moment (in coulomb.m) of the ring if 1 0 =  coul/m and R = 1m. x SECTION - IV (Matrix - Match Type) This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II. The answers to these questions have to be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p, B-s, C-r, C-s and D-q, D-t then the answer should be written as : A  p,r ; B  p, s ; C  r, s ; D  q, t. 19. Column-I gives situations involving a charged particle which may be realised under the condition given in column-II. Match the situations in column-I with the condition in column-II. Column I Column II (A) Increase in speed of a charged particle (p) Electric field uniform in space and constant in time (B) Exert a force on an electron initially at rest (q) Magnetic field uniform in space and constant in time. (C) Move a charged particle in a circle with (r) Magnetic field uniform in space uniform speed but varying with time. (D) Accelerate a moving charged particle (s) Magnetic field non-uniform in space but constant with time (t) Electric field and magnetic field both in orthogonal direction having constant magnitude. 20. In the column-, the path of a projectile (initial velocity 10 m/s and angle of projection with horizontal 60° in all cases) is shown in different cases. Rangle 'R' is to be matched in each case from column-. Take g = 10 m/s2. Arrow on the trajectory indicates the direction of motion of projectile. Column-I Column-II (A) (p) R = 15 3 m 2 40 (B) (q) R = 3 m (C) (r) R = 10 m (D) (s) R = 5 3m 20 (t) R = 3 m PAPER-2 1. (A) 2. (D) 3. (C) 4. (B) 5. (B) 6. (A) 7. (D) 8. (D) 9. (A)(C) 10. (B)(C) 11. (A)(B) 12. (A)(B)(C) 13. 3 14. 3 15. 3 16. 3 17. 4 18. 1 19. (A - p,r,t); (B - p,r,t); (C - q,s ); (D - p,q,r,s,t) 20. (A - r) ; (B - p) ; (C - s) ; (D - q) 21. (B) 22. (B) 23. (B) 24. (C) 25. (A) 26. (B) 27. (B) 28. (C) 29. (A,B) 30. (A,B,D)