List of practice Questions

In the below diagram inductance \(L_1 = L_2 = L_3 = L\). Find the ratio of total energy stored in all inductors to energy stored in inductor \(L_2\). 

In a vernier caliper, 1 main scale division equals \(1\,\text{mm}\) and \(9\) MSD are divided into \(10\) equal parts by the vernier scale. When nothing was present in the jaws, zero of the vernier scale lies to the right of zero of the main scale and the \(7^{th}\) division of vernier scale coincides with one of the main scale divisions. Find zero error in the vernier caliper.

Upper wire has cross-section area \(0.008\,\text{cm}^2\) and lower wire has area \(0.004\,\text{cm}^2\). Find the maximum mass of the pan that can be connected without breaking any wire. Given breaking stress of wire is \(\sigma = 8\times10^8\,\text{N/m}^2\). 


 

For the circuit shown below, find current across \(AB\) \((I_{AB})\). 

Correct option for the circuit shown is: 

Find time taken by the block to slide a distance \(8.8\,\text{m}\) with respect to the wedge (in seconds). All surfaces are smooth. 

Displacement current inside a capacitor of capacitance \(6\,\mu F\) is \(4\,A\). Find the rate of change of voltage across the capacitor.
Moment of inertia of a rod about an axis passing through a point at distance \(\ell/4\) from the center and perpendicular to the rod is: (The uniform rod has mass \(m\) and length \(\ell\)).
In an AC circuit having \(R\) and \(C\), angular frequency \(\omega\) has peak current \(I\). If angular frequency becomes \(\omega/4\), the peak current becomes \(I/3\). Find the ratio of resistance and reactance at frequency \(\omega\).
In a compound microscope objective and eyepiece are both biconvex lenses of focal length \(f_0\). If objective lens is cut into two halves such that a plano–convex lens is made and now it is used as objective to get same magnification, by how many times should the tube length be changed?
Identify correct statements (1) Zeroth law of thermodynamics gives concept of temperature. (2) In isothermal expansion \(\Delta Q \neq \Delta W\). (3) First law of thermodynamics gives concept of internal energy. (4) Product of intensive and extensive properties is extensive. (5) Ratio of extensive property and mass is extensive.
In a region where electric field exists as \[ \vec{E} = -E_0 \hat{i} \] Initially at \(t=0\), velocity of particle of mass \(m\) is \(4v_0 \hat{i\). If de-Broglie wavelength \(\lambda_0 = \dfrac{h}{4mv_0}\), find wavelength \(\lambda\) at time \(t\).}
A charged particle is moving in a magnetic field \[ \vec B = (3\hat i + 2\hat j)\ \text{T} \] with acceleration \[ \vec a = 4\hat i - \frac{x}{2}\hat j\ \text{m/s}^2 \] Find \(x\).
In YDSE, \(\beta = 2.4\) mm where \(\beta\) is fringe width. If the setup is dipped in a medium of refractive index \(\mu = 1.2\), find the new fringe width (in mm).
For ideal gas: \(n\): number of moles, \(C_v\): molar specific heat at constant volume, \(\gamma\): adiabatic exponent of gas, \(T_f\): final temperature, \(T_i\): initial temperature, \(R\): gas constant. Assertion : \[ nC_v(T_f-T_i)=\frac{nR}{\gamma-1}(T_f-T_i) \] Reason : \[ \gamma = 1 + \frac{2}{f} \]
A travelling wave on a string is given by \[ y = 3\sin\left(100t + 0.018x + \frac{\pi}{6}\right) \] Find the minimum distance (in m) between two crests.
In hydrogen atom an electron jumps from state \(i\) to \(f\). Radius of path of electron in state \(i\) and \(f\) are \(r_i\) and \(r_f\) respectively such that \[ \frac{r_i}{r_f}=\frac{4}{1} \] If Rydberg constant \(R = 1.0976\times10^7\ \text{m^{-1}\), find wavelength of emitted photon (in \(\text{\AA}\)). (\(r_i\) and \(r_f\) are minimum possible radius.)}
If a metal rod has length \(\ell\) and area of cross-section \(A\), its Young's modulus is \(Y\). What will happen to \(Y\) if length is doubled and area is halved?
If \[ (2\alpha+1,\; \alpha^2-3\alpha,\; \frac{\alpha-1}{2}) \] is the image of the point \[ (\alpha,\; 2\alpha,\; 1) \] in the line \[ \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}, \] then find the possible values of \(\alpha\).
For a given reversible reaction at \(300\,K\): \[ 2\text{N}_2\text{O}_5(g) \rightleftharpoons 4\text{NO}_2(g) + \text{O}_2(g) \] If \( \text{N}_2\text{O}_5 \) is 50% dissociated at 5 bar and 300 K at equilibrium, then find \( \Delta G^\circ \) for the reaction? [Given: \( \log 2 = 0.3,\ \log 7 = 0.84 \)]

For the reaction: \[ R \rightarrow P \] The variation of concentration of reactant \([R]\) with time is shown below. Statements: I. Curve 1 will be observed when order of reaction is 1. II. If curve 2 & curve 3 are observed for \(1^{st}\) order then rate constant for \(3^{rd}\) curve will be greater than rate constant for \(2^{nd}\) curve. III. Decomposition of HI on gold surface represent curve (1). Select the option representing correct set of statements: 

Styrene undergoes the following sequence of reactions Molar mass of product (P) is:

For the first order reaction \[ A \rightarrow P \] Based on the given data, find the time \(x\) (in min):

Given:
\(t = 0 \, \text{min} \Rightarrow [A] = 0.625 \, M\)
\(t = x \, \text{min} \Rightarrow [A] = 0.0625 \, M\)
\(t = 20 \, \text{min} \Rightarrow [A] = 0.00625 \, M\)

Assume internuclear axis to be z-axis, the correct molecular orbital representation of \(\pi^*\) antibonding molecular orbital formed by overlapping between two \(p\) orbitals will be: 

Consider the following setup separated by a semi–permeable membrane (SPM): Left compartment (x): \(K_4[Fe(CN)_6]\) solution \(0.1\,M\), \(100\,ml\) Right compartment (y): \(FeCl_3\) solution \(0.1\,M\), \(100\,ml\) Which of the following is correct for the above figure?