List of practice Questions

A plane glass mirror of thickness 3 cm of material of \( \mu = \frac{3}{2} \) is silvered on the black surface. When a point object is placed 9 cm from the front surface of the mirror, then the position of the brightest image from the front surface is:

An ideal gas is taken through the cycle \( A \to B \to C \to A \), as shown in the figure. If the net heat supplied to the gas in the cycle is 5 J, the work done by the gas in the process \( C \to A \) is 

A series L-C-R circuit is connected to an AC source of 220V and 50 Hz shown in figure. If the readings of the three voltmeters \( V_1, V_2, \) and \( V_3 \) are 65V, 415V, and 204V respectively, the value of inductance and capacitance will be 

The displacement \( x \) of a particle in a straight line motion is given by \( x = 1 - t - t^2 \). The correct representation of the motion is
Which of the following diagram represents the variation of the electric field with distance \( r \) from the centre of a uniformly charged non-conducting sphere of radius \( R \)?

From the following \( p-V \) diagram, an ideal gas undergoing a change of state from A to B. Four different processes I, II, III, and IV as shown in the figure may lead to the same change of state. 


A regular hexagon of side \( m \), which is a wire of length 24 m, is coiled on that hexagon. If current in hexagon is \( I \), then the magnetic moment is 

Which of the following gate gives the similar output as the output of the circuit diagram shown in the figure? 

Ultraviolet light of wavelength 99 nm falls on a metal plate of work function 1.0 eV. If the mass of the electron is \( 9.1 \times 10^{-31} \) kg, the wavelength of the fastest photoelectron emitted is:
In Young's double slit experiment, the fringe width is found to be 0.4 mm. If the whole apparatus is immersed in a liquid of refractive index \( \frac{4}{3} \) without changing the geometrical arrangement, the new fringe width will be:

In the network shown in figure, the equivalent capacitance between points P and Q is 

If \( \lim_{x \to 0} \frac{(1 + a^3)^x + 8e^{1/x}}{1 + (1 - b^3)^x e^{1/x}} = 2 \), then:
The approximate value of \( (0.007)^{1/3} \) is:
Let \( f(x) = a - (x-3)^{8/9} \), then the maxima of \( f(x) \) is:

If the derivative of the function \( f(x) = \begin{cases} b x^2 + ax + 4; & x \geq -1 \\ a x^2 + b; & x < -1 \end{cases} \) is everywhere continuous, then
 

If \( \lim_{x \to \infty} \left( 1 + \frac{a}{x} + \frac{b}{x^2} \right)^{2x} = e^2 \), then:
If for any \( 2 \times 2 \) square matrix \( A \), \( A(\text{adj} A) = \begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix} \), then find the value of \( \det(A) \).
If \( A = \begin{bmatrix} 2 - k & 2 \\ 1 & 3 - k \end{bmatrix} \) is a singular matrix, then the value of \( 5k - k^2 \) is:
If \( A = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix} \), then \( |A| \cdot \text{adj}(A) \) is equal to:
If \( A = \{3, 5, 7\} \) and \( B = \{1, 2, 3, 5\} \), then \( A \times B \cap B \times A \) is equal to:
The argument of \( \dfrac{1 - i\sqrt{3}}{1 + i\sqrt{3}} \) is:

Which of the following are not path functions? 
I. H - T S 
II. W 
III. q 
IV. q + W 
 

A newly prepared radioactive nuclide has a decay constant of 6.93 s\(^{-1}\). What is the half-life of the nuclide?
\( (i + \sqrt{3})^{100} + (i - \sqrt{3})^{100} + 2^{100} \) is equal to:
The total number of terms in the expansion of \( (x + y)^{100} + (x - y)^{100} \):