# Questions by Lakshman Patel RJIT

1 vote
1
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
2
Twelve $1\;\Omega$ resistances are used as edges to from a cube. The resistance between two diagonally opposite corners of the cube is $\frac{5}{6}\;\Omega$ $\frac{1}{6}\;\Omega$ $\frac{6}{5}\;\Omega$ $\frac{3}{2}\;\Omega$
3
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
1 vote
4
A sequential circuit using D flip-flop and logic gates is shown in Figure, where $X$ and $Y$ are the inputs and $Z$ is the output. The circuit is $\text{S-R}$ Flip-flop with inputs $X = R$ and $Y=S$ $\text{S-R}$ Flip-flop with inputs $X = S$ and $Y=R$ $\text{J-K}$ Flip-flop with inputs $X = J$ and $Y=K$ $\text{J-K}$ Flip-flop with inputs $X = K$ and $Y=J$
5
A $4$ bit ripple counter and a $4$ bit synchronous counter are made using flip-flops having a propagation delay of $10$ ns each. If the worst case delay in the ripple counter and the synchronous counter be $R$ and $S$ respectively, then $R = 10$ ns, $S = 40$ ns $R = 40$ ns, $S = 10$ ns $R = 10$ ns, $S = 30$ ns $R = 30$ ns, $S = 10$ ns
6
In MOSFET fabrication, the channel; length is defined during the process of Isolation oxide growth Channel stop implantation Poly-silicon gate patterning Lithography step leading to the contact pad
7
Twelve $1\;\Omega$ resistances are used as edges to from a cube. The resistance between two diagonally opposite corners of the cube is $\frac{5}{6}\;\Omega$ $\frac{1}{6}\;\Omega$ $\frac{6}{5}\;\Omega$ $\frac{3}{2}\;\Omega$
8
An ideal op-amp is an ideal voltage controlled current source voltage controlled voltage source current controlled current source current controlled voltage source
9
The final value theorem is used to find the Steady state value of the system output Initial value of the system output Transient behavior of the system output None of these
10
For the discrete signal $x[n] = a^{n}u[n],a>0$ the $z$-transform is $\frac{(z+a)}{z}$ $\frac{(z-a)}{z}$ $\frac{z}{(z-a)}$ $\frac{z}{(z+a)}$
11
For a periodic signal $v(t) = 30\sin 100t + 10\cos 300t + 6\sin(500t + \frac{\pi}{4}),$ the fundamental frequency in rad/s $100$ $300$ $500$ None of these
12
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
13
If the number of bits per sample in a PCM system is increased from a $n$ to $n+1,$ the improvement in signal to quantization nose ratio will be $3\;dB$ $6\;dB$ $2n\;dB$ $n\;dB$
14
A carrier $Ac\cos(\omega c)t$ is frequency modulated by a signal $Em\cos(\omega m)t.$ The modulation index is $mf.$ The expression for the resulting FM signal is $Ac\cos [\omega ct + mf\sin(\omega m)t]$ $Ac\cos [\omega ct + mf\cos(\omega m)t]$ $Ac\cos [\omega ct + \pi mf\sin \omega m t]$ $Ac\cos [\omega ct + 2\pi mf Em \cos(\omega m)t/\omega m]$
15
A sequential circuit using D flip-flop and logic gates is shown in Figure, where $X$ and $Y$ are the inputs and $Z$ is the output. The circuit is $\text{S-R}$ Flip-flop with inputs $X = R$ and $Y=S$ $\text{S-R}$ Flip-flop with inputs $X = S$ and $Y=R$ $\text{J-K}$ Flip-flop with inputs $X = J$ and $Y=K$ $\text{J-K}$ Flip-flop with inputs $X = K$ and $Y=J$
16
A $4$ bit ripple counter and a $4$ bit synchronous counter are made using flip-flops having a propagation delay of $10$ ns each. If the worst case delay in the ripple counter and the synchronous counter be $R$ and $S$ respectively, then $R = 10$ ns, $S = 40$ ns $R = 40$ ns, $S = 10$ ns $R = 10$ ns, $S = 30$ ns $R = 30$ ns, $S = 10$ ns
17
In MOSFET fabrication, the channel; length is defined during the process of Isolation oxide growth Channel stop implantation Poly-silicon gate patterning Lithography step leading to the contact pad
The open-loop transfer function of a feedback control system is $G(s)\cdot H(s) = 1/(s+1)^{3}.$ The gain margin of the system is $2$ $4$ $8$ $16$
Solve the recurrence relation for the number of rounds in the tournament described in question $14.$
How many rounds are in the elimination tournament described in question $14$ when there are $32$ teams?