List of practice Questions

All values of \( (8i)^{\frac{1}{3}} \) are:
A Carnot engine has the same efficiency between 800 K and 500 K, and \( x>600 \) K and 600 K. The value of \( x \) is:
If both the roots of the equation \( x^2 - 6ax + 2 - 2a + 9a^2 = 0 \) exceed 3, then:
When the temperature of a gas is raised from 27°C to 90°C, the increase in the rms velocity of the gas molecules is:

If the frequency of a wave is increased by 25%, then the change in its wavelength is (medium not changed):

The angle between the electric dipole moment of a dipole and the electric field strength due to it on the equatorial line is:

Two condensers \( C_1 \) & \( C_2 \) in a circuit are joined as shown in the figure. The potential of point A is \( V_1 \) and that of point B is \( V_2 \). The potential at point D will be:

If the \(2^{\text{nd}}\), \(3^{\text{rd}}\), and \(4^{\text{th}}\) terms in the expansion of \( (x + a)^n \) are 96, 216, and 216 respectively, and \( n \) is a positive integer, then \( a + x \) is:
In a hydrogen atom, an electron is making \( 6.6 \times 10^5 \) revolutions around the nucleus of radius \( 0.47 \) Å. The magnetic field induction produced at the center of the orbit is nearly:
Any magnetic material loses its magnetic property when it is:
A resistance of \( 20 \Omega \) is connected to a source of an alternating potential \( V = 200 \sin(10\pi t) \). If \( t \) is the time taken by the current to change from the peak value to the rms value, then \( t \) is (in seconds):
The average value of electric energy density in an electromagnetic wave is: [where \( E_0 \) is the peak value]
In Morgan's linkage experiments on Drosophila recombinants percentage for white eye and yellow body is:
An electron of mass \( m \) with initial velocity \( \vec{v} = v_0 \hat{i} \) (\( v_0>0 \)) enters in an electric field \( \vec{E} = -E_0 \hat{i} \) (\( E_0 \) is constant \(>0 \)) at \( t = 0 \). If \( \lambda \) is its de-Broglie wavelength initially, then the de-Broglie wavelength after time \( t \) is:
A \( \mu \)-meson of charge \( e \), mass \( 208 \, m_e \) moves in a circular orbit around a heavy nucleus having charge \( +3e \). The quantum state \( n \) for which the radius of the orbit is the same as that of the first Bohr orbit for the hydrogen atom is (approximately):
A nucleus with atomic mass number \( A \) produces another nucleus by losing 2 alpha particles. The volume of the new nucleus is 60 times that of the alpha particle. The atomic mass number \( A \) of the original nucleus is:
A full-wave rectifier circuit is operating from 50 Hz mains, the fundamental frequency in the ripple output will be:
A PN junction diode is used as:
A carrier is simultaneously modulated by two sine waves with modulation indices of 0.3 and 0.4; then the total modulation index is:

The angular momentum of an electron in a stationary state of \(Li^{2+}\) (\(Z=3\)) is \( \frac{3h}{\pi} \). The radius and energy of that stationary state are respectively.

Identify the pair of elements in which the number of electrons in the (n-1) shell is the same:
The correct order of bond angles of the molecules \( SiCl_4 \), \( SO_3 \), \( NH_3 \), \( HgCl_2 \) is:

Match the following: 

If \( |x| < 1 \), then the number of terms in the expansion of \( \left[ \frac{1}{2} (1.2 + 2.3x + 3.4x^2 + \dots) \right]^{-25} \) is:
If \( |x| < 1 \), the coefficient of \( x^2 \) in the power series expansion of \( \frac{x^4}{(x+1)(x-2)} \) is: