VITEEE PYQs for LCR Circuit with Solutions: Practice VITEEE Previous Year Questions

1.

The pressure inside a tyre is 4 times that of the atmosphere. If the tyre bursts suddenly at temperature \( 300K \), what will be the new temperature?

• \( 300(4)^{7/2} \)
  
• \( 300(4)^{2/7} \)
  
• \( 300(2)^{7/2} \)
  
• \( 300(4)^{-27} \)
  

2.

Which of the following figure represents the variation of \( \ln \left( \frac{R}{R_0} \right) \) with \( \ln A \) (If \( R \) is the radius of a nucleus and \( A \) is its mass number)?

3.

A ball of radius \( r \) and density \( \rho \) falls freely under gravity through a distance \( h \) before entering water. The velocity of the ball does not change even on entering water. If the viscosity of water is \( \eta \), the value of \( h \) is given by:
\includegraphics[width=0.5\linewidth]{28.png}

• \( \frac{2}{9} \frac{r^2 (1 - \rho)}{\eta g} \)
  
• \( \frac{2}{81} \frac{r^2 (\rho - 1)}{\eta g} \)
  
• \( \frac{2}{81} \frac{r^4 (\rho - 1)}{\eta^2 g} \)
  
• \( \frac{2}{9} \frac{r^4 (\rho - 1)}{\eta^2 g} \)
  

4.

The magnetic field of a plane electromagnetic wave is given by: \[ \vec{B} = 2 \times 10^{-8} \sin \left(0.5 \times 10^3 x + 1.5 \times 10^{11} t \right) \hat{j} \, {T}. \] {The amplitude of the electric field would be:}

• \( 6 \, {V/m} \, {along x-axis} \)
  
• \( 3 \, {V/m} \, {along z-axis} \)
  
• \( 6 \, {V/m} \, {along z-axis} \)
  
• \( 2 \times 10^{-8} \, {V/m} \, {along z-axis} \)

5.

The self-induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10A to 25 A in 1s, the change in the energy of the inductance is:

• 740J
  
• 437.5J
  
• 540J
  
• 637.5J

6.

A vertical electric field of magnitude \( 4.9 \times 10^5 \, {N/C} \) just prevents a water droplet of a mass \( 0.1 \, {g} \) from falling. The value of charge on the droplet will be: (Given \( g = 9.8 \, {m/s}^2 \))

• \( 1.6 \times 10^{-9} \, {C} \)
  
• \( 2.0 \times 10^{-9} \, {C} \)
  
• \( 3.2 \times 10^{-9} \, {C} \)
  
• \( 0.5 \times 10^{-9} \, {C} \)

7.

The current in an $L-R$ circuit builds up to $\left(3 / 4^{\text {th }}\right)$ of its steady state value in $4$ seconds. The time constant of this circuit is

• $\frac{1}{\ln 2} \sec$
• $\frac{2}{\ln 2} \sec$
• $\frac{3}{\ln 2} \sec$
• $\frac{4}{\ln 2} \sec$

8.

The ozone layer in the atmosphere absorbs:

• Only the radio waves
  
• Only the visible light
  
• Only the \( \gamma \)-rays
  
• X-rays and ultraviolet rays
  

9.

A particle is moving with a velocity \( \vec{v} = K (y \hat{i} + x \hat{j} )\), where \( K \) is a constant. The general equation for its path is:

• \( y = x^2 + {constant} \)
  
• \( y^2 = x + {constant} \)
  
• \( y^2 = x^2 + {constant} \)
  
• \( xy = {constant} \)

10.

Water falls from a \( 40 \) m high dam at the rate of \( 9 \times 10^4 \) kg per hour. Fifty percent of gravitational potential energy can be converted into electrical energy. The number of \( 100W \) lamps that can be lit is:

• \( 25 \)
  
• \( 50 \)
  
• \( 100 \)
  
• \( 18 \)
  

11.

The equation of a wave on a string of linear mass density \( 0.04 \) kg/m is given by:
\[ y = 0.02 \sin 2\pi \left( \frac{t}{0.04} - \frac{x}{0.50} \right) \] The tension in the string is:

• \( 4.0 N \)
  
• \( 12.5 N \)
  
• \( 0.5 N \)
  
• \( 6.25 N \)
  

12.

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be:
 

• −450J
  
• 450J
  
• 900J
  
• 1350J

13.

A sinusoidal voltage of amplitude 25 V and frequency 50 Hz is applied to a half-wave rectifier using a P-N junction diode. No filter is used, and the load resistor is \( 1000\Omega \). The forward resistance \( R_f \) of the ideal diode is \( 10\Omega \). The percentage rectifier efficiency is:

• \( 40\% \)
  
• \( 20\% \)
  
• \( 30\% \)
  
• \( 15\% \)