PART A Straight Objective Type This section contains 30 multiple choice questions. Each question has 4 choices (1), (), (3) and (4) for its answer, out of which ONLY ONE is correct. 1. The apparent depth of object O from AB is :- A B 1 =1.4 4cm 1 =1.5 5cm (1) 4.9 cm () 5.43 cm (3) 6.19 cm (4) 5.99 cm O. A convex lens forms inverted image of a real object on a fixed screen. The size of image is 1 cm. When lens is displaced 0 cm along principle axis it again forms a real image of size 3 cm on the screen. Choose the correct option. (Assume image formation only by paraxial rays) (1) Focal length of the lens is 40 3 cm () Focal length of the lens is 80 3 cm (3) Size of object is 8 cm (4) Size of object is 9 cm P05ERMCT351118C0-1
3. In given figure, a smooth square platform ABCD is moving towards right with a uniform speed 10 3 m/s. At what angle must a particle be projected from B with speed 0 m/s so that it strikes the point A? (1) 60º () cos 1 (3) 30º (4) sin 1 3 3 4. The reflecting surface of a plane mirror is vertical. A particle is projected in the vertical plane which is also perpendicular to the mirror. The initial velocity of the particle is 10 m/s and the angle of projection is 60º. The point of projection is at a distance 5 m from the mirror. The particle moves towards the mirror, just before the particle touches the mirror the velocity of approach of the particle and its image (in m/s) is (1) 10 () 5 (3) 10 3 (4) 5 3 P05ERMCT351118C0-
5. A ray of light enters at grazing angle of incidence into an assembly of three isosceles right-angled prisms having refractive indices 1 =, = x and 3 = 3. If finally emergent light ray also emerges at grazing angle then calculate x : µ µ 1 µ 3 (1) () 3 (3) 7 (4) 10 6. All surface are smooth and both A and B are released from rest, then velocity of B when A hits the ground is: A m h m B (1) gh cos () gh tan (3) gh cos (4) gh tan P05ERMCT351118C0-3
7. Two bodies A and B are moving with same constant speed v in clockwise direction in a horizontal circle of radius R and are initially diagonally opposite. The particle B now achieves a tangential acceleration a m/s. Then: (1) they collide after time () they collide after time (3) they collide after time (4) none of these R a R a 6R a 8. A ray is incident on combination two right angular prisms placed in air of refractive indices as shown in the figure. The angle of incidence is 45. The total angle of deviation is. 45 30 30 3 60 60 (1) 45 () 30 (3) 60 (4) 75 P05ERMCT351118C0-4
9. Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is first connected at point A and zero deflection is observed at length PJ = 10 cm. In second case it is connect at point C and zero deflection is observed at a length 30 cm from P. Then the unknown resistance X is P J G Q R A X C (1) R () R (3) R 3 (4) 3R 10. The equivalent resistance between A and B in the arrangement of resistances as shown, is : (1) 4r () 3r (3).5r (4) r P05ERMCT351118C0-5
11. A parallel plate capacitor is charged to a potential V, then battery is disconnected. Separation between the plates is d and plate dimension is (L L). A dielectric of dielectric constant K which L has thickness slightly less than d and dimension L is inserted between the plate. New potential difference between the plates will be : K 1 (1) () V V (3) K 1 V (4) K V 1. A position dependent force F = 7 x 3x newton acts on a small body of mass kg and displaces it from x = 0 to x = 5m. The work done in joules is (1) 70 () 70 (3) 35 (4) 135 P05ERMCT351118C0-6
13. Three charged capacitors C 1,C and C 3 of capacitance 3F, 6F and 6F respectively and having charge 30C each are connected with a resistor of resistance R = 10 through a switch S as shown. The switch S is closed at t = 0. Choose the correct options : (1) The initial current in the circuit will be A () Total heat dissipated in the resistor will be 75 J (3) As all the capacitors are in series the final charge will be same on each capacitor (4) The final charge on C 1 and C will be equal and amount of charge that flows in the circuit till steady state is 5C 14. A non conducting semicircular disc (as shown in figure) has a uniform surface charge density. The ratio of electric field to electric potential at the centre of the disc will be : (1) 1 n b / a (b a) () (3) 1 n (b / a) (b a) (4) (b a) n(b / a) P05ERMCT351118C0-7
15. Two concentric spherical shells of radius r and r are such that their surface charge densities are 1 and respectively. Then the potential difference between a point at the center and another point at a distance 5r from the center is: r (1) [ 1 3 ] 5 0 r () [ 1 4 ] 3 0 r (3) ( 1 ) 0 (4) Zero 16. Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (assume x > > a) (1) 0 Qa () x 0 3 (3) Qa 0 x 3 3Qa (4) 3 x 0 P05ERMCT351118C0-8
17. The moment of inertia of a uniform ring of mass M and radius r about a tangent lying in its own plane is (1) Mr () 3 Mr (3) Mr (4) 1 Mr 18. India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the radius of Earth's orbit is a e = 1.5 10 11 m, that of Mar's orbit a m =.5 10 11 m, taken Kepler's laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to (The time period of revolution of earth around sun is 1 year) Mars orbit O M Sun E Earth orbit (1) () (3) 14 3 15 3 13 3 / 3 / 3 / years years years (4) 3 years P05ERMCT351118C0-9
19. A planet is revolving in an elliptical orbit around sun, fixed at the focus of ellipse. The minimum and maximum distance of planet from sun are r 1 and r respectively. The minimum distance of planet from centre of ellipse is : r r (1) 1 r1 r () r r 1 (3) rr 1 r r (4) 1 0. There is a solid sphere of radius R having uniformly distributed charge throughout it. What is the relation between electric field E and distance r from the centre (r < R)? (1) E r () E r 1 (3) E r (4) E r 1. An uncharged metal sphere is placed between two equal and oppositely charged metal plates. The nature of lines of force will be :- (1) (3) () (4) P05ERMCT351118C0-10
. Seven identical disc are arranged in a hexagonal, planar pattern so as to touch each neighbor, as shown in the figure. Each disc has mass m and radius r. What is the moment of inertia of the system of seven disks about an axis passing through the centre of central disk and normal to plane of all disks? (1) 7 mr () 13 mr (3) 9 mr (4) 55 mr 3. System is at limiting equilibrium. Rod and wedge contact is smooth, remaining contacts are rough. If coefficient of friction values between 4m, ground and m, ground are 1 and. Find the value of 1:. 45 (1) : 5 () : 1 (3) 1 : (4) 5 : P05ERMCT351118C0-11
4. A uniform semi circular ring of radius R = 5m and mass m is free to rotate in vertical plane about fixed horizontal axis passing through A as shown in the figure. The angular acceleration of ring immediately after it is released from rest from the position shown is g A (1) 1 rad/sec () rad/sec (3) 3 rad/sec (4) 4 rad/sec 5. In the figure shown, a small ball of mass 'm' can move without sliding in a fixed semicircular track of radius R in vertical plane. It is released from the top. The resultant force on the ball at the lowest point of the track is (1) 10mg 7 () 17 mg 7 (3) 3 mg 7 (4) zero P05ERMCT351118C0-1
6. The electric field of long uniformly charged wire varies with respect to perpendicular distance (r) from wire. Which of the following graph is correct :- E E (1) O E 1/r () O E 1/r (3) O 1/r (4) O 1/r P05ERMCT351118C0-13
7. The particle of mass 1 kg is acted upon by a force F F ˆi F ˆj for time t = 4 sec starting from t = 0. Find the velocity of the particle at t = 4 sec., if its initial velocity is u ˆ i ˆ j and the variation of applied force with time is as shown in the graphs : F X (N) x y 5 0 4 T (sec) 5 F Y (N) 5 0 4 T (sec) (1) v ˆ i ˆ j () v ˆ i 11j ˆ (3) v 10ˆj (4) v ˆ i 10j ˆ P05ERMCT351118C0-14
8. A particle of mass m 0, travelling at speed v 0, strikes a stationary particle of mass m 0. As a result, v0 the particle of mass m 0 is deflected through 45º and has a final speed of. Then the speed of the particle of mass m 0 after this collision is : v0 (1) v0 () (3) v 0 v0 (4) 9. In the figure shown a particle P strikes the inclined smooth plane horizontally and rebounds vertically. If the angle is 60º, then the co-efficient of restitution is : (1) 1 3 () 1 3 (3) 1 (4) 1 P05ERMCT351118C0-15
30. Two metal spheres of same mass are suspended from a common point by a light insulating string. The length of each string is same. The spheres are given electric charges q on one end and 4q on the other. Which of the following diagrams best shows the resulting positions of spheres? (1) () q 4q q 4q (3) (4) 1 q q 4q 4q P05ERMCT351118C0-16