Title K-2517 (Physical Science).pdf ✅

Paper III 4 K-2517 Total Number of Pages : 16 8. In the modified Euler’s method, solution to the differential equation f(x,y) dx dy = is obtained by using the algorithm (A) (r 1) (r) n1 n n n n1 n1 h y y f(x ,y ) f(x , y ) 2 + + ++ =+ + ⎡ ⎤ ⎣ ⎦ (B) y y h [ ] f(x ,y ) f(x , y ) (r) n n n n 1 n 1 (r 1) n 1 + + + + = + + (C) (r 1) (r) n1 n n n n1 n1 h y y f(x ,y ) 2f(x , y ) 2 + + ++ =+ + ⎡ ⎤ ⎣ ⎦ (D) (r 1) (r) n1 n n n n1 n1 h y y 2f(x ,y ) f(x , y ) 2 + + ++ =+ + ⎡ ⎤ ⎣ ⎦ Where (r 1) yn 1 + + is the (r + 1)th approximation to the value of y at xn + 1. 9. If the line element of a space is given as ds2 = 2dq2 + 4dq1dq2 + 3 2 dq2 , the metric tensor is given by (A) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 4 3 2 4 (B) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 2 3 2 2 (C) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 2 3 2 2 (D) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 4 3 2 4 10. The phase space of a simple harmonic oscillator with mass ‘m’ and force constant ‘k’ with energy ‘E’ is given by the curve (A) 2 P 1 2 kx E 2m 2 − = (B) 2 P 1 2 kx E 2m 2 + = (C) 2 P k 2 x E 2m 2 + = (D) 2 P 1 2 2 kx E 2m 2 + = 11. Assuming the fundamental Poisson bracket [q, p] = 1, evaluate the Poisson bracket [p2, q2]. (A) 0 (B) 2pq (C) 4pq (D) – 4pq 12. The transformation from (qi , pi ) to (Qi , IP i ) is canonical when the following condition is satisfied. (A) ∑( ) + i Pi dQi pi dqi I is an exact differential (B) ∑( ) − i Pi dQi pi dqi I is an exact differential (C) ∑( ) − i Pi dqi pi dQi I is an exact differential (D) ∑( ) − i Pi dpi Qi dqi I is an exact differential