ISRO Scientist or Engineer Electronics Dec 2017

Find the area of the region bounded by the curves $$y = x^{2}, y = \frac{1}{x}$$ and $$x = \frac{1}{2}$$ (see in graphical representive figure)

Find the Eigen values $$\lambda$$ in the system $$\begin{bmatrix}4 & 1 \\3 & 2 \end{bmatrix}$$ $$\begin{bmatrix} x \\ y \end{bmatrix}$$ =\lambda $$\begin{bmatrix} x \\ y \end{bmatrix}$$

Find the transient response of a pair of complex poles as given below

A random variable z , has a probability density function f(z) where $$f(Z) =e^{-z} O\leq Z < \infty$$ the probability of $$O \leq Z \leq 2$$ will be approximately

Evaluate $$\lim_{x \rightarrow 2} \frac{\sqrt{x^{2}+5-3}}{x^{2}-2x}$$

What is the R.M.S of following waveform if the average value is zero?

A radar system uses TWTA as high power RF source for transmitting 300W Peak Power. The efficiency of transmitter during pulse is 75% and the transmit duty is 25%. If the DC
power required during pulse off period is 20W. The average power dissipation in TWTA is

The ramp signal $$(V_{t} : 0 to 5V)$$ is compared with the Soft-Start Signal provided by N-channel MOSFET $$(Q_{1} )$$ for Amplifier $$( A_{1} )$$ output. If $$Q_{1}$$ having low threshold voltage of 0.7V and 1 negligible ON resistance. What is the duty of $$c_{1}$$ output signal of comparator $$(C _{1})$$ after $$100 \mu$$ Sec?

A High speed digital Subsystem requires three voltages $$V_{1} , V_{2}$$ and $$V_{3}$$ with 1 : 2 : 1 power 3 ratings respectively. The power supply is designed with the distribute power conversion scheme as shown in the following figure. What is the overall power conversion efficiency?

If the transformer and diodes in the following circuit are ideal, Find out the value of Capacitor (Co) provides 5% ripple voltage across $$R_{L}$$.
(Assume that $$\sin^{-1} (0.95) \sim \frac{2 \pi}{5}$$ in Radians $$\ln(0.95) = -0.051$$)