4.PRACTICE TEST-2 (Paper-2)

PRACTICE TEST TWO 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. Two men P & Q are standing at corners A & B of square ABCD of side 8 m. They start moving along the track with constant speed 2 m/s and 10 m/s respectively. The time when they will meet for the first time, is equal to (A) 2 sec (B) 3 sec (C) 1 sec (D) 6 sec 2. Given mA = 20 kg, mB = 10 kg, mC = 20 kg. Between A and B  = 0.3, between B and C  = 0.3 and between C and ground  = 0.1. The least horizontal force F to start the 2 3 motion of any part of the system of three blocks resting upon one another as shown in figure is (g = 10 m/s2) (A) 60 N (B) 90 N (C) 80 N (D) 50 N 3. 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 is : (A) 22.5 J (B) 10 J (C) 0 (D) None of these 4. There are two thin spheres A and B of the same material and same thickness. They emit like black bodies. Radius of A is double that of B. A and B have same temperature T. When A and B are kept in a room of temperature T0 (< T), the ratio of their rates of cooling (rate of fall of temperature) is: [ assume negligible heat exchange between A and B ] (A) 2 : 1 (B) 1 : 1 (C) 4 : 1 (D) 8 : 1 5. If a tuning fork of frequency (f0) 340Hz tolerance ±1% is used in resonance column method [v = 2f0 (𝑙2 – 𝑙1)], the first and the second resonance are measured at 𝑙1 = 24.0 cm and 𝑙2 = 74.0 cm. The max. permissible error in speed of sound is : (f0) 340Hz and tolerance  1% column method [v = 2f0 (𝑙2 – 𝑙1)], 𝑙1 = 24.0 cm 𝑙2 = 74.0 cm permissible (A) 1.2 % (B) 1.8 % (C) 1% (D) 0.8 % 6. Figure shows two large cylindrical shells having uniform linear charge densities +  and – . Radius of inner cylinder is ‘a’ and that of outer cylinder is ‘b’. A charged particle of mass m, charge q revolves in a circle of radius r. Then its speed ‘v’ is : (Neglect gravity and assume the radii of both the cylinders to be very small in comparison to their length.) (A) (B) (C) (D) 7. A battery of internal resistance 2  is connected to a variable resistor whose value can vary from 4  to 10 . The resistance is initially set at 4  If the resistance is now increased then (A) power consumed by it will decrease (B) power consumed by it will increase (C) power consumed by it may increase or may decrease (D) power consumed will first increase then decrease. 8. A square ABCD of side 1mm is kept at distance 15 cm infront of the concave mirror as shown in the figure. The focal length of the mirror is 10 cm. The length of the perimeter of its image will be : (A) 8 mm (B) 2 mm (C) 12 mm (D) 6 mm SECTION- II Multiple Correct Answers Type This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is/are correct. 9. A circular conducting loop of radius R and carrying current I0(direction not shown) is bent in two equal halves, one lying in x–y plane and other in x–z plane. Centre is at the origin. Loop is immersed in uniform external → 0 0 ˆ ˆ magnetic field B  2R ( i  k) . If portion in x–y plane experiences a net force in positive y–direction due to external field then : R2  ˆ ˆ (A) Magnetic dipole moment of the loop is 2 0 (k  j) 002 ˆ (B) Net magnetic force due to external field on the portion lying in x–z plane is   j 002R ˆ ˆ ˆ (C) Net torque experience by the loop is (i  j  k) 4 (D) Net magnetic field at the origin is 00 (ˆj  kˆ) 4R 10. A person in a car moving with constant velocity of 15 m/s in positive x–direction throws a ball parallel to positive y–direction with respect to himself. At that time the car is 90m away from the origin. The ball hits the target kept along y–axis at 120 m from the origin. If the car reaches the origin at the same time when ball hits the target then for the given condition (here XY plane is horizontal): (g = 10 m/s2) (A) Possible velocity of projection of ball with respect to ground is ( 15ˆi  20ˆj  30kˆ )m/s (B) Possible velocity of projection of ball with respect to ground is ( 18ˆi  24ˆj  25kˆ )m/s (C) There are two possible velocity of projection (D) There is only one possible velocity of projection 11. A uniform solid metallic cylinder is placed in frictionless bearings and set to rotate about its cylindrical axis with some angular velocity. Now it is heated uniformly without mechanical contact. Consider the thermal expansion of the body. Select the correct statement(s) : (A) Its angular momentum will not change (B) Its K.E. of rotation decreases (C) Its angular velocity increases (D) Fractional change in K.E. = fractional change in angular velocity 12. A student working with sodium light (590 nm) in YDSE puts a thin transparent sheet ( = 1.5) before one of the slits and it appears to him as if position of fringes were remain unchanged. Possible thickness of the sheet is/ are : (A) 1.18 m (B) 2.36 m (C) 3.54 m (D) 4.72 m SECTION - III (Total Marks : 24) (Integer Answer Type) This section contains 6 questions. Answer each of the questions in a single-digit integer, ranging from 0 to 9. 13. A compound rod, 2m long is constructed of a solid steel core, 1cm in diameter surrounded by copper casing whose outside diameter is 2cm. The outer surface of rod is thermally insulated. One end is maintained at 100ºC and other at 0ºC. What fraction (in %) of heat current is carried by steel core. (Ksteel = 12 cal/m-K, Kcopper = 92 cal/m-K). 14. The resistance of uniform wire AB is 9. Find the resistance of part BC for which galvanometer G will show zero deflection. 15. A small wooden rod of length 5mm is fixed at the bottom of the container filled with 4 water ( = 3 ). It is making an angle 37º with vertical. If an observer (in air)  observes the rod paraxially, and the rod is appeareing at an angle x vertical then the find the value of x. radian with 17. Light of intensity = 3W/m2 is incident on a perfectly absorbing metal surface of area 1 m2 making an angle of 600 with the normal.If the force exerted by the photons on the surface is p x10-9 (in Newton) find the value of p. 18. A heavy particle is projected from a point at the foot of a fixed plane inclined at an angle 45° to the horizontal in the vertical plane containing the line of greatest slope through the point. If  ( > 45°) is the inclination to the horizontal of the initial direction of projection, for what value of tan will the particle strike at the top of the plane when it is also at max height from ground. SECTION - IV (Total Marks : 16) (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. In column-I condition on velocity, force and acceleration of a particle is given. Resultant motion is described in column-II. → = initial velocity, F = resultant force and → = instantaneous velocity. Column-I Column-III (A) → F  0 and F = constant (p) path will be circular path (B) → F  0 and F = constant (q) speed will increase (C) → F  0 all the time and | F | = constant (r) path will be straight line and the particle always remains in one plane. → ˆ ˆ → ˆ ˆ (D) u  2 i  3 j and acceleration at all time a  6 i  9 j (s) path will be parabolic (t) Speed will remain constant. 20. In each situation of column-I, some charge distributions are given with all details explained. In column -II The electrostatic potential energy and its nature is given situation in column -II. Then match situation in column-I with the corresponding results in column-II. Column-I Column-II (A) A thin shell of radius a and having a charge – Q uniformly distributed (p) over its surface as shown (B) A thin shell of radius 5a and having 2 1 8 0 3 Q2 a in magnitude Q2 a charge – Q uniformly distributed (q) over its surface and a point charge – Q placed at its centre as shown. (C) A solid sphere of radius a and having a charge – Q uniformly distributed (r) throughout its volume as shown. (D) A solid sphere of radius a and having a charge – Q uniformly distributed 20 0 a 2 Q2 5 0 a in magnitude in magnitude throughout its volume. The solid sphere (s) Negative in sign is surrounded by a concentric thin uniformly charged spherical shell of radius 2a and carrying charge –Q as shown (t) Positive in sign PAPER-2 1. (B) 2. (D) 3. (B) 4. (B) 5. (A) 6. (A) 7. (A) 8. (C) 9. (B,C) 10. (A,D) 11. (A,B,D) 12. (A,B,C,D) 13. 4 14. 3 15. 4 16. 4 17. 5 18. 2 19. (A - r) ; (B - q,s) ; (C - p,t) ; (D - q,r) 20. (A - p,s) ; (B - q,s) ; (C - q,s) ; (D - s)