1.

A convex lens of glass is immersed in water compared to its power in air, its power in water will

• increase
• decrease
• not change
• decrease for red light increase for violet light

2.

Find the vector and the cartesian equations of the lines that pass through the origin and(5,-2,3).

3.

Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 &  3\\ 5 & 7 \end{bmatrix}\)

4.

A circular disc is rotating about its own axis. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. The initial angular momentum of disc is

• $0.1\,kgm^2s^{-1}$
• $0.04\,kgm^2s^{-1}$
• $0.025\,kgm^2s^{-1}$
• $0.01\,kgm^2s^{-1}$

5.

If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

6.

Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4  \end{bmatrix}\)