List of practice Questions

For a straight wire carrying steady current in the vertically upward direction as shown below
Four closed surfaces and corresponding charge distributions are shown below. The respective electric fluxes through the surfaces \( S_1, S_2, S_3, S_4 \) are \( \Phi_1, \Phi_2, \Phi_3, \Phi_4 \). Then, which of the following is correct?
Two very long, straight, and insulated wires are kept at a 90° angle from each other in the x-y plane as shown in the figure. These wires carry equal currents of magnitude \( I \), whose directions are shown in the figure. The net magnetic field at point P will be:
At temperature \( T \), the probability of ideal gas molecules with mass \( m \) having speed \( v \) is given by \( P(v) \). Two quantities \( I_1 \) and \( I_2 \) are defined in terms of \( P(v) \) as follows:
\[ I_1 = \int_0^\infty P(v) v^3 \, dv \quad \text{and} \quad I_2 = \int_0^\infty P(v) v \, dv \] Which of the following relationship is true?
Consider a viscous fluid having uniform density \( \rho \) and coefficient of viscosity \( \eta \). Two solid spheres with radius \( R_1 \) and \( R_2 \) fall into this liquid and acquire terminal velocities of \( V \) and \( 8V \) respectively. If the densities of the two spheres are \( 2\rho \) and \( 3\rho \) respectively, then \( R_1 \) is equal to \( R_2 \)?
In a Doppler effect experiment, initially an observer and the source are moving towards each other with equal speeds. The observed frequency in this case is found to be \( f_0 \). The observed frequency once they cross each other is found to be \( f' \). If \( f \) is the frequency at the source, \( f' \) is equal to:
1 gm of ice at 0°C is mixed with 1 gm of water at 100°C. At thermal equilibrium, the temperature of the mixture will be:
Consider two radioactive materials A and B. When A decays into 6.25 percent of its original amount, B decays into 25 percent of its original amount. The ratio of their decay constants \( \lambda_A \) and \( \lambda_B \) is:
In the uranium radioactive series the initial nucleus is \(^{238}U\) and the final nucleus is \(^{206}Pb\). When the uranium nucleus decays to lead, the number of \(\alpha\)-particles and \(\beta\)-particles emitted respectively are:
The ratio of specific heats \( \frac{C_P}{C_V} \) in terms of degrees of freedom (n) is given by:
A transverse wave is described by the equation \( y = A \sin \left( 2 \pi \left( \frac{r}{\lambda} - \frac{t}{T} \right) \right) \). The maximum particle velocity is equal to four times the wave velocity if:
A pulse of light of duration 50 ns is absorbed completely by a small object initially at rest. Power of the pulse is 60 mW and speed of light is \( 3 \times 10^8 \) m/s. The final momentum of the object is:
A series R-C combination is connected to an AC voltage of angular frequency \( \omega = 1000 \) rad/s. If the impedance of the RC circuit is \( R/\sqrt{2} \), the time constant (in milliseconds) of the circuit is:
A block of mass 300 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force \( F = \sqrt{a} \, N \) as shown in the figure. The value of \( a \) is (Take \( g = 10 \, \text{m/s}^2 \)):
A piece of copper and another of germanium are cooled from room temperature to 100K. The resistance of
Convert the sentence into INDIRECT SPEECH: She said, "I will visit my grandmother tomorrow."
The natural logarithm of the activity \( R \) of a radioactive sample varies with time \( t \) as shown. At \( t = 0 \), there are \( N_0 \) undecayed nuclei. Then \( N_0 \) is equal to \([\text{Take} \ e^{7.5}] \)
natural logarithm
The minimum excitation energy of an electron revolving in the first orbit of hydrogen is:
The electric current flowing through a given conductor varies with time as shown in the graph below. The number of free electrons which flow through a given cross-section of the conductor in the time interval \( 0 \leq t \leq 20 \, \text{s} \) is
electric current flowing through a given conductor
Function of oligodendrocytes is:
Let \( e_1 \) be the eccentricity of the hyperbola $$ \frac{x^2}{16} - \frac{y^2}{9} = 1 $$ and \( e_2 \) be the eccentricity of the ellipse $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b, $$ which passes through the foci of the hyperbola. If \( e_1 e_2 = 1 \), then the length of the chord of the ellipse parallel to the x-axis and passing through (0, 2) is: 
The sum of the coefficients of \( x^{2/3} \) and \( x^{-2/5} \) in the binomial expansion of $$ \left( x^{2/3} + \frac{1}{2} x^{-2/5} \right)^9 $$ is: 
The area (in square units) of the region enclosed by the ellipse $$ x^2 + 3y^2 = 18 $$ in the first quadrant below the line \( y = x \) is: 
If \( A = (1,2,3), B = (3,4,7) \) and \( C = (-3,-2,-5) \) are three points then the ratio in which the point C divides AB externally is
Consider the relations $R_1$ and $R_2$ defined as \[a R_1 b \iff a^2 + b^2 = 1 \quad \text{for all } a, b \in \mathbb{R},\]and \[(a, b) R_2 (c, d) \iff a + d = b + c \quad \text{for all } (a, b), (c, d) \in \mathbb{N} \times \mathbb{N}.\]Then: