Question 1 
In the following graph, the number of trees (P) and the number of cutset (Q)
are
P = 2,Q = 2  
P = 2,Q = 6  
P = 4,Q = 6  
P = 4,Q = 10 
Question 1 Explanation:
Different trees (P) are shown below
Different cutsets (Q) are shown below:
Different cutsets (Q) are shown below:
Question 2 
Consider the network graph shown in the figure. Which one of the following is
NOT a 'tree' of this graph ?
a  
b  
c  
d 
Question 2 Explanation:
It is forming a closed loop. So it can't be a tree.
Question 3 
The differential equation for the current i(t) in the circuit of the figure is
2\frac{d^{2}i}{dt^{2}}+2\frac{di}{dt}+i(t)=\sin t
 
\frac{d^{2}i}{dt^{2}}+2\frac{di}{dt}+2i(t)=\cos t
 
2\frac{d^{2}i}{dt^{2}}+2\frac{di}{dt}+i(t)=\cos t  
\frac{d^{2}i}{dt^{2}}+2\frac{di}{dt}+2i(t)=\sin t

Question 3 Explanation:
Applying KVL,
\sin t=i(t) \times 2+L \frac{d i(t)}{d t}+\frac{1}{c} \int i(t) d t
\sin t=2 i(t)+2 \frac{d i(t)}{d t}+\int i(t) d t
Differentiating with respect to t
\cos (t)=\frac{2 d i(t)}{d t}+\frac{2 d^{2} i(t)}{d t^{2}}+i(t)
\sin t=i(t) \times 2+L \frac{d i(t)}{d t}+\frac{1}{c} \int i(t) d t
\sin t=2 i(t)+2 \frac{d i(t)}{d t}+\int i(t) d t
Differentiating with respect to t
\cos (t)=\frac{2 d i(t)}{d t}+\frac{2 d^{2} i(t)}{d t^{2}}+i(t)
There are 3 questions to complete.