List of practice Questions

If three elements A, B, C crystallise in a cubic lattice with B at cube centres, C at edge centres and A at corners, the formula of the compound is
An LPG (Liquefied Petroleum Gas) cylinder weighs 15.0 kg when empty. When full, it weighs 30.0 kg and shows a pressure of 3.0 atm. In the course of usage at $27^\circ$C, the mass of the full cylinder is reduced to 24.2 kg. The volume of the used gas in the normal usage condition (1 atm and $27^\circ$C) is (assume LPG to be normal butane and it behaves ideally):
The molar conductances of Ba(OH)$_2$, BaCl$_2$ and NH$_4$Cl at infinite dilution are 523.28, 280.0 and 129.8 S cm$^2$ mol$^{-1$ respectively. The molar conductance of NH$_4$OH at infinite dilution will be:}
A wave disturbance in a medium is described by \[ y(x,t)=0.02\cos\left(50\pi t + \frac{\pi}{2}\right)\cos(10\pi x), \] where \( x,y \) are in meters and \( t \) in seconds. Which statements are correct?
If the dimensions of length are expressed as \( G^x c^y \hbar^z \), where \( G \), \( c \) and \( \hbar \) are gravitational constant, speed of light and Planck’s constant respectively, then
Let \( \bar{v}, v_{rms}, v_p \) denote the mean speed, root mean square speed and most probable speed of molecules of mass \( m \) in an ideal monoatomic gas at temperature \( T \). Which statements are correct?
Two spheres \( S_1 \) and \( S_2 \) of masses \( m_1 \) and \( m_2 \) collide. Initially \( S_1 \) is at rest and \( S_2 \) moves with velocity \( v \) along x-axis. After collision \( S_2 \) has velocity \( \frac{v}{2} \) in a direction perpendicular to the original direction. The motion of \( S_1 \) after collision is
Equal volumes of two solutions A and B of a strong acid having pH = 6.0 and pH = 4.0 respectively are mixed together. The pH of the new solution will be in the range
\(10^{20}\) photons of wavelength \(660\,\text{nm}\) are emitted per second from a lamp. The wattage of the lamp is (Planck’s constant \(h=6.6\times10^{-34}\,\text{Js}\))
The apparent coefficient of expansion of a liquid when heated in a copper vessel is \( C \) and in a silver vessel is \( S \). If \( A \) is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is
The equation of a stationary wave along a stretched string is \[ y = 5\sin\left(\frac{\pi x}{3}\right)\cos(40\pi t), \] where \( x,y \) are in cm and \( t \) in seconds. The separation between two adjacent nodes is
Let the binding energy per nucleon of nucleus be denoted by \( E_{bn} \) and radius of the nucleus by \( r \). If mass numbers of nuclei A and B are 64 and 125 respectively, then
The minimum force required to start pushing a body up a rough plane is \( F_1 \) while the minimum force needed to prevent it from sliding down is \( F_2 \). The plane makes an angle \( \theta \) with horizontal such that \( \tan\theta = 2\mu \). The ratio \( F_1/F_2 \) is
A ball falls from a height \( h \) upon a fixed horizontal floor. The coefficient of restitution is \( e \). The total distance covered by the ball before coming to rest (neglect air resistance) is
A radioactive nucleus decays as follows: \[ X \xrightarrow{\alpha} X_1 \xrightarrow{\beta^-} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4 \] If the mass number and atomic number of \( X_4 \) are 172 and 69 respectively, then the atomic number and mass number of \( X \) are
A particle of charge \( q \) and mass \( m \) moves in a circular orbit of radius \( r \) with angular speed \( \omega \). The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on
The variation of displacement with time of a simple harmonic motion is \[ y = 2\sin\left(\frac{\pi t}{2}+\phi\right)\text{ cm}. \] The maximum acceleration of the particle is
An electron in Hydrogen atom jumps from the second Bohr orbit to the ground state and emits a photon. This photon strikes a material. If the work function of the material is 4.2 eV, then the stopping potential is
A simple pendulum is taken at a place where its distance from the earth’s surface is equal to the radius of the earth. Calculate the time period of small oscillations if the length is 4.0 m. (Take \( g=\pi^2\,\text{m/s}^2 \) at surface.)
The minimum wavelength of Lyman series lines is \( P \), then the maximum wavelength of these lines is
The resistance \( R=\frac{V}{I} \) where \( V=(25\pm0.4)\,\text{V \) and \( I=(200\pm3)\,\text{A} \). The percentage error in \( R \) is}
The de-Broglie wavelength of a moving bus with speed \( v \) is \( \lambda \). Some passengers left the bus at a stoppage. Now when the bus moves with twice of its initial speed, its kinetic energy is found to be twice its initial value. What is the de-Broglie wavelength of the bus now?
Ruma reached the metro station and found that the escalator was not working. She walked up the stationary escalator with velocity \( v_1 \) in time \( t_1 \). On another day if she remains stationary on the escalator moving with velocity \( v_2 \), then the escalator takes her up in time \( t_2 \). The time taken by her to walk up with velocity \( v_1 \) on the moving escalator will be
A single slit diffraction pattern is obtained using a beam of red light. If red light is replaced by blue light then
A quantity \( X \) is given by \[ X=\varepsilon_0 L \frac{\Delta V}{\Delta t}, \] where \( \varepsilon_0 \) is permittivity of free space, \( L \) is length, \( \Delta V \) is potential difference and \( \Delta t \) is time interval. The dimension of \( X \) is same as that of