Title 25 Physical Science Paper-II.pdf ✅

7. The value of the contour integral ∫ z (z + 3) dx 2 , where c denotes the unit circle z = 1 traced in the contour clockwise direction is (A) 0 (B) 2π i (C) 2 πi/3 (D) – 2 πi/9 8. Identify the correct statement for the following vectors : a = 6 i ˆ – 9 j ˆ , and b = –2 i ˆ + 3 j ˆ . (A) The vectors a and b are linearly independent (B) The vectors a and b are linearly dependent (C) The vectors a and b are orthogonal (D) The vectors a and b are normalized 9. Constraints that can be expressed in terms of an equation relating to co-ordinates of system and time. (A) Holonomic (B) Non-Holonomic (C) Scleronomous (D) Rheonomous 10. The Lagrangian is a function of (A) qk, pk (B) qk, q- k (C) qk, p- k (D) pk, p- k 11. For repulsive inverse square forces, the shape of the orbit is (A) Hyperbolic (B) Elliptical (C) Circular (D) Parabolic 12. Kepler’s second law states that (A) Areal velocity in is zero (B) Areal velocity is constant (C) Angular momentum is not constant (D) Linear velocity is constant 13. In the Hamiltonian formalism (A) H = ∑ k pkq- k – L (B) H = ∑k pk qk – L (C) L = ∑k pkq- k + H (D) L = ∑k pk qk + H 14. Hamilton’s principal function S and Hamilton’s characteristic function W for conservative system are related as (A) S = W (B) S = Et (C) S = W + Et (D) S = W – Et 15. The Lagrangian for a particle of charge ‘e’ in an electromagnetic field is given by (A) A.V c e T − eφ + (B) A.V c e T + eφ + (C) A.V c e T + eφ − (D) A.V c e T − eφ − 16. The length of space vehicle is 100 m on the ground. When it is in flight, its length as observed on the ground is 99 m the speed of the vehicle in the space is (A) 42.32 × 108 ms–1 (B) 42.32 × 106 ms–1 (C) 42.32 × 1010 ms–1 (D) 42.32 × 1012 ms–1 Total Number of Pages : 8 K-2514 3 Paper II