Tiêu đề K-2513 (Physical Science) (Paper-III) 16 page.pdf ✅

Total Number of Pages : 16 Paper III 2 K-2513 PHYSICAL SCIENCE Paper – III Note : This paper contains seventy-five (75) objective type questions. Each question carries two (2) marks. All questions are compulsory. 1. If μ A and Bγ are components of contravariant and covariant vectors, what is the nature of the quantity μ A Br ? (A) Zero (B) An invariant (C) A contravariant tensor (D) A mixed tensor of rank 2 2. For the Ricci tensor, Rμr what is the quantity gμr in the summation convention ? (A) A vector (B) Scalar (C) A pseudoscalar (D) Scalar curvature 3. The value of ∫ + 1 01 x dx by Simpon’s rule is (A) 0.96315 (B) 0.63915 (C) 0.69315 (D) 0.69351 4. The order of error in the Simpson’s rule for numerical integration with a step size h is (A) h (B) h2 (C) h3 (D) h4 5. G is a finite group of order n, a ∈G and order of a is m, if G is cyclic then (A) m = n = 0 (B) m = n (C) m > n (D) m < n 6. The set of all non-singular square matrices of same order with respect to matrix multiplication is (A) Quasi-group (B) Monoid (C) Group (D) Abelian group

Total Number of Pages : 16 Paper III 4 K-2513 13. The canonical transformation corresponding to the generating function = ∑ i F qi pi (A) Identify transformation (B) Reflection transformation (C) Exchange transformation (D) Reflection exchange transformation 14. Which one of the following is not the generating function of the canonical transformation Q 1 P = and q = PQ2 (A) Q q (B) 2 qP (C) P P (D) P Q 15. Which of the following statements is false ? (A) The Poisson bracket of momentum conjugate to a cyclic co-ordinate with Hamiltonian vanishes (B) Lagrangian bracket is invariant under canonical transformations (C) Poisson bracket changes sign under commutation of concerned dynamical variables (D) Lagrangian bracket is commutative with respect to concerned dynamical variables 16. If (X, H) = 0 and (Y, H) = 0, the value of (H (X, Y)) is (A) 0 (B) 1 (C) –1 (D) 2 17. The value of (q p ) dt d i j is (A) Always zero (B) Always one (C) Zero when i ≠ j (D) Zero when i = j 18. If the Hamiltonian of a system is V(q) 2m p H 2 ⎟ + ⎠ ⎞ ⎜ ⎝ ⎛ = , the value of (p, (p, H)) is (A) Zero (B) One (C) 2 2 q v ∂ ∂ (D) q v ∂ ∂