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1.

A message signal is used to modulate a carrier signal of frequency  5 MHz and peak voltage of 40 V . In the process, two side-bands are produced separated by 40 kHz. If the modulation  index is 0.75, then the peak voltage  and frequency of the messages  signal, respectively are

A) 60 V, 10 kHz

B) 60 V, 20 kHz

C) 30 V, 10 kHz

D) 30V, 20 kHz

2.

A person applies a sine wave and square wave to an AND gate as shown in the figure (i) and (ii) . Assuming that both the voltages are applied in phase , the person observers the output  at E and F on (i) and (ii) , respectively. [Assume minimum voltage of 5V is equivalent to logic (i)]

A) Sqaure wave at 50 Hz and square wave at 100 Hz

B) Sine wave at 50 Hz and square wave at 100 Hz

C) No output and sine wave at 100 Hz

D) No output and pulsed wave at 100 Hz

3.

Consider a toroid with rectangular cross-section, of inner radius a,  outer radius b  and height h, carrying n number of turns. Then  the self-inductance of the toroidal  coil when  current I passing through the toroid is

A) $\frac{\mu_{0}n^{2}h}{2 \pi}ln\left(\frac{b}{a}\right)$

B) $\frac{\mu_{0}n^{}h}{2 \pi}ln\left(\frac{b}{a}\right)$

C) $\frac{\mu_{0}n^{2}h}{2 \pi}ln\left(\frac{a}{b}\right)$

D) $\frac{\mu_{0}n^{}h}{2 \pi}ln\left(\frac{a}{b}\right)$

4.

Two  particles carrying equal charges move parallel  to each other  with the speed 150 km/s. If $F_{1}$ and $F_{2}$  are magnetic  and electric  forces between  two charged  particles  then

$\frac{|F_{1}|}{|F_{2}|}$ is    $\left( Let \mu_{0}\epsilon_{0}=\frac{1}{9 \times 10^{16}} s^{2}/m^{2}\right)$

A) $1.0 \times 10^{-6}$

B) $1.5 \times 10^{-7}$

C) $3.0 \times 10^{-6}$

D) $2.5 \times 10^{-7}$

5.

Four identical metal plates are located in the air at equal distance d from each other . The area of each plate in S. If the outermost plates are connected by a  conducting  wire as shown in the figure the  capacitance between points A and B will be

A) $\frac{\epsilon_{0}S}{d}$

B) $\frac{3}{2}\frac{\epsilon_{0}S}{d}$

C) $\frac{1}{2}\frac{\epsilon_{0}S}{d}$

D) $\frac{2}{3}\frac{\epsilon_{0}S}{d}$

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