10.

11.

12.

13.

14.

15.

The Lagrangian of a system is given by
L= ப்‌ + न ^ + y? + 2%y cos ಉ + mgy sin ०. Which among the following
represent the components of momenta of the system ?

(A) + = m(x + y cos 0) (8) p,=m(y +x cos a)

(ಲ) p,=Mx+m(x + y cos a) (D) Py =My + m(y + त cos ०)
Which among the following helps in converting the Lagrangian equations into a
Hamiltonian ?

(^) Lorentz transform (B) Legendre transform
(6) Fourier transform (D) Laplace transform

Which among the following correctly represent the Hamiltonian of a simple pendulum ?
2

= 70 _ _॥ ⋅
A) H= - 0 B H= —mg/sin@
(A) ome ` ण्ट (B) Ime me
_ = _Po ⋅
≼∁⋝↕−⊢↴−⊣∏≣∣∁∘⊱⊝ ≼⊡⋝↕−⊢⋝−⊣∏⊰⊱⋯⊝
മമ്പ്‌ 20,0

Which among the following is expressed by saying that the Hamiltonian phase flow
preserves volume ?
(4) Fermat’s principle ‏رق‎ Hamilton’s principle
(C) Euler - Lagrange theorem (>) Liouville’s theorem

If Q is the angular velocity of a particle of mass m that moves with velocity v in a non-
inertial frame, the magnitude of the Coriolis force acting on the body is given by

(A) mQ xr (B) 2mQxv

(0 mQx(Qxx) (0) mQx(Qxv)

2 3
The eigen values of the matrix ۴ 1 sare:

(A) -1,1 (B) 1,1
(ಲ) -1,5 (0) 1-5
Which among the following is NOT a correct representation of complex functions ?
‏على €+ على‎ ez
(^) cos(z) = ‏ل‎ (8) ಗ ಜ್ಜ
2 21
€+€ > ‏تج تع‎

(೮) ००॥(2) =

(2) ಆಖ) =

Which among the following equations relate the Cartesian to the cylindrical unit vectors ?
(७) ۶ =cosdi + sind}; 6 =—sindi + 0050]; 2-2
(8)
(0)

(೧) t= 00501 + sino} 495 581 + 0056) ; 2 = 00802

۶ = 00301 — ஸ்ட்‌]; ¢ = sini — ००४९); 2 = ००४९2

= 00561 + ऽक ; $ =—sindi + 0050; 2 = ௦0562

019/2021 = ` 4 A