12. Which of the following transformation matrix corresponds to rotation by an angle®, any one
of the Euler angles?

—cos® sin® 0 cos® -sin® 0
(A) sin® cos® 0 (8) sin® 0086 0
0 0 1 0 0 1
1 0 0 1 0 0
(0) 0 008% शाक ൯) [0 0080 81೧0
0 -sin® 0080 0 sin® -cos®

13. Logistic map is defined by the equation X,,,,=A X,(1-X,), where A is the control

parameter and X, and X,,,, are values of some variable X after n“" and n+1" iterations

respectively. The range of X and A 8೩7೮ 05೫51806 0% 4% 4 respectively. Then the
equilibrium points of the system, for A =1.25 are:

(A) 0.5, which is a stable equilibrium point only

(B) 0, a stable point and 1, an unstable equilibrium point

(C) 0.2, an unstable equilibrium point and 0, a stable equilibrium point

(D) 0, anunstable stable equilibrium point and 0.2 a stable equilibrium point

14. If S represents Hamilton’s characteristics function, the Hamilton Jacobi equation for a free
particle of mass m is:

۶ٰ۹ ۴

० रै) ‏ك‎ ന്‌ു:
15. Which of the following is not a Hermitian operator?

ல ims ൪ (೧ മും

کو رم 5 ‎oe‏ )©

16. If o,,o0,and o, are Pauli’s spin matrices, ௪, 0, + 20,0, is equal to:
(A) ൨൭. (B) 0
© io, 0 ೩

A 5 084/2023
[7.7.0.]