Title K-2517 (Physical Science).pdf ✅

Total Number of Pages : 8 Paper II 2 K-2517 1. The absolute value of the integral Ο × ∫ r dr around an equilateral triangle of side ‘a’ with the origin at its center is (A) a2 (B) 2a2 (C) 2 a 2 3 (D) 2 πa 2. If F [f(x)] = ( ) ∫ ∞ −∞ − π f x e dx 2 1 ikx , then F2 [f(x)] is equal to (A) f(x) (B) –f(x) (C) f(–x) (D) () ( ) 2 f x + f − x 3. The Fourier transform of dx df is related to the Fourier transform () () ∫ ∞ −∞ h k = e f x ikx dx of the function f(x) by (A) ( ) dk dh k (B) ( ) ∫ h k dk (C) –ik h(k) (D) ik h(k) 4. The value of the integral Ο∫ C 2 z dz, where C is a unit circle, is (A) 3 1 (B) zero (C) 2πi (D) 3 z3 PHYSICAL SCIENCES Paper – II Note : This paper contains fifty (50) objective type questions. Each question carries two (2) marks. All questions are compulsory. 5. The value of the integral ∫ Ο π − C 2 z 1 dz i 1 where the contour C is a circle of radius a ≠ 1, with origin as centre is given by (A) 1, independent of a (B) 1, if a > 1 (C) 1, if a < 1 and 0, if a > 1 (D) 0, independent of a 6. Consider the matrix ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ − − − = 2 1 3 5 2 6 1 1 3 A . The product of the eigen values of the matrix is (A) 1 (B) zero (C) –1 (D) –6 7. The average value of a function f(x) = sin x in the interval 0 ≤ x ≤ π is (A) 2 1 (B) π 2 (C) π 1 (D) π 4 8. Eigen values of real 3 × 3 matrix (A) must have at least one of the eigen values real (B) must be all real (C) must have at least two real eigen values (D) must have all three eigen values imaginary