List of practice Questions

Using the given P-V diagram, the work done by an ideal gas along the path ABCD is: \includegraphics[]{43.PNG}
The energy of a system is given as \( E(t) = \alpha e^{-\beta t \), where \( t \) is the time and \( \beta = 0.3 \, \text{s}^{-1} \). The errors in the measurement of \( \alpha \) and \( t \) are 1.2 percent and 1.6 percent, respectively. At \( t = 5 \) s, the maximum percentage error in the energy is:}
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The binding energy per nucleon is found to be practically independent of the atomic number \( A \), for nuclei with mass numbers between 30 and 170. Reason (R): Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below:
The width of one of the two slits in Young's double-slit experiment is \( d \) while that of the other slit is \( x d \). If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is 9 : 4, then what is the value of \( x \)? (Assume that the field strength varies according to the slit width.)
A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity):
A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius
Choose the correct nuclear process from the below options:
Given below are two statements: one is labelled as Assertion \(A\) and the other as Reason \(R\):
Assertion \(A\): A sound wave has higher speed in solids than in gases.
Reason \(R\): Gases have higher value of Bulk modulus than solids.
In a resistive circuit, the power dissipated by a resistor \( R \) when a current \( I \) flows through it is given by \( P = I^2 R \). What happens to the power when the current is doubled?
In the experiment for measurement of viscosity \( \eta \) of a given liquid with a ball having radius \( R \), consider following statements: A. Graph between terminal velocity \( V \) and \( R \) will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of \( \eta \) will change.
A Carnot engine (E) is working between two temperatures 473K and 273K. In a new system two engines - engine \(E_1\) works between 473K to 373K and engine \(E_2\) works between 373K to 273K. If \(\eta_{12}\), \(\eta_1\) and \(\eta_2\) are the efficiencies of the engines \(E\), \(E_1\) and \(E_2\), respectively, then:
For a particular ideal gas, which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?
The center of mass of a thin rectangular plate (fig - x) with sides of length \( a \) and \( b \), whose mass per unit area (\( \sigma \)) varies as \( \sigma = \sigma_0 \frac{x}{ab} \) (where \( \sigma_0 \) is a constant), would be
The center of mass of a thin rectangular plate
In a sound wave, the displacement of the air particles follows the equation \( y = A \cos(kx - \omega t) \). What is the wave velocity?
Consider the following statements: 
Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface of a liquid. As the temperature of liquid rises, the coefficient of viscosity increases. As the temperature of gas increases, the coefficient of viscosity increases. The onset of turbulence is determined by Reynolds number. In a steady flow, two streamlines never intersect.
Choose the correct answer from the options given below:
A hemispherical vessel is completely filled with a liquid of refractive index \( \mu \). A small coin is kept at the lowest point \( O \) of the vessel as shown in the figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point \( E \) (at the level of the vessel) is:
A hemispherical vessel is completely filled with a liquid of refractive index
A particle of mass \( m \) and charge \( q \) is fastened to one end \( A \) of a massless string having equilibrium length \( l \), whose other end is fixed at point \( O \). The whole system is placed on a frictionless horizontal plane and is initially at rest. If a uniform electric field is switched on along the direction as shown in the figure, then the speed of the particle when it crosses the x-axis is:
A particle of mass m and charge q
Which of the following circuits has the same output as that of the given circuit?
circuits has the same output as that of the given circuit
What is the time period of a simple pendulum of length \( L \) and acceleration due to gravity \( g \)?
Two capacitors \( C_1 \) and \( C_2 \) are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are \( U_1 \) and \( U_2 \), respectively. Which of the given statements is true?
Two capacitors C1 and C2 are connected in parallel to a battery
Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?
A block of mass \( m \) is moving with velocity \( v \) on a smooth horizontal surface. If a constant force \( F \) is applied to the block, what is the work done by this force after 5 seconds?
Find the equivalent resistance between two ends of the following circuit:
equivalent resistance between two ends

Due to presence of an em-wave whose electric component is given by \( E = 100 \sin(\omega t - kx) \, NC^{-1} \), a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as:

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:
A proton of mass 'mp' has same energy as that of a photon of wavelength 'λ'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.