Correct Answer:- Option-C

5002 ‏رہ ری‎ हि 5
Question19:-The value of a so that the vector (2x 7 3202 Oy -22 y "(7162 dk
‏ا‎
‎B:-4
‎6-5
‎D:--7
‎Correct Answer:- Option-D
Question20:-For a system in which the Lagrangian is not an explicit function of time, the Hamiltonian is
A:-constant
B:-infinity
C:-zero
D:-none of these
Correct Answer:- Option-A
Question21:-For a system of two coupled oscillators, the total number of normal modes is
‏ا‎
‎8:-2
‎C:-3
‎D:-4
‎Correct Answer:- Option-B
Question22:-In the short wavelength limit, the schrédinger equation reduces to
A:-Lagrange's equation
B:-Euler-Lagrange equation
C:-Hamilton's equations
D:-Hamilton-Jocobi equation
Correct Answer:- Option-D
Question23:-What is the dimension of the fractal-Cantor set ?
A:-0.52
B:-0.63
C:-0.74
D:-0.85
Correct Answer:- Option-B

Question24:-If [F, H] represents the Poisson bracket between an arbitrary function F and the Hamiltonian of a system H, the
equation of motion will be

A:- (dF)Adt) = ([F, H]
(dF)/(dt)’ =[H, F]

C:-\(dF)/(dt) =(delF)/(delt) + [F, H]”

D:-* (dF)/(dt) =(delF)/(delt) + [H, F]°

Correct Answer:- Option-C
Question25:-The maximum number of rotational degrees of freedom possible for a rigid body is

ا

8:-2

C:-6

D:-3

Correct Answer:- Option-D
Question26:-If *a_(0)° donates the Bohr radius, the most probable distance of the electron from the nucleus in a Hydrogen
atom in its ground state is

൧: (a_(0))/(2)°

B:-\a_(0)°

@-28 0)`

0:- (32 (0))/(2)`

Correct Answer:- Option-B
Question27:-The normalized wave functions ` [051 (1) 210 ‘Psi_(2)° correspond to the ground state and the first excited
state of a particle in a potential. An operator A acts on the wave functions as A’ psi_(1)=Psi_(2)° and
A’Psi_(2)° = *Psi_(1)°. The expectation value of A for the state ‘psi’ = "(3061 (1) + 4psi_(2))/(6)° is

A:-0.67

B:-0.33

C:-0.44

D:-0.82

Correct Answer:- Option-A

is solenoidal is