1.

For what values of x,\(\begin{bmatrix} 1 & 2 & 1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 2 & 0\\ 2 & 0 & 1 \\1&0&2 \end{bmatrix}\)\(\begin{bmatrix} 0 \\2\\x\end{bmatrix}\)=O?

2.

A series LCR circuit with R = 20 W, L = 1.5 H and C = 35 μF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

3.

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

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

4.

Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 &  3\\ 2 & 7\end{bmatrix}\)

5.

Draw the structures of optical isomers of: 
(i) \([Cr(C_2O_4)_3]^{3–}\)
(ii) \([PtCl_2(en)_2]^{2+}\)
(iii) \([Cr(NH_3)2Cl_2(en)]^{+}\)

6.

Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N