List of practice Questions

In a meter bridge, two balancing resistances are \( 30 \, \Omega \) and \( 20 \, \Omega \). If the galvanometer shows zero deflection for the jockey's contact point \( P \), then find the length \( A P \).

Choose correct option :
(A) Number of photons required for a light beam of 2000 pm wavelength and 1 Joule energy is \(1.01 \times 10^{16}\).
(B) Light with wavelength 300 nm has energy \(E_1\) and for wavelength 900 nm has energy \(E_2\), then \(E_1/E_2 = 1/3\).
(C) Frequency of light is \(4.5 \times 10^{16}\) Hz then its wavelength is \(6.7 \times 10^{-9}\) m.
(D) If electrons and protons are accelerated by same potential difference, then their de-Broglie wavelength are equal.

Internal energy of a gas is given as U = 3nRT. 1 mole of He gas takes 126 J of heat and its temperature rises by 4°C. Atmospheric pressure is \(P_0 = 10^5\) Pa and area of piston is 17 cm\(^2\). Find distance moved by piston.

Two spheres having equal mass \( m \), charge \( q \), and radius \( R \), are moving towards each other. Both have speed \( u \) at an instant when the distance between their centers is \( 4R \). Find the minimum value of \( u \) so that they touch each other.

A particle starts moving from time \(t=0\) and its coordinate is given as \[ x(t)=4t^3-3t. \] Consider the following statements:
[A.] The particle returns to its original position (origin) \(0.866\) units later.
[B.] The particle is \(1\) unit away from origin at its turning point.
[C.] Acceleration of the particle is non-negative.
[D.] The particle is \(0.5\) units away from origin at its turning point.
[E.] The particle never turns back as acceleration is non-negative.
Choose the correct answer from the options given below:

Tell about any four sweets prepared using Chenna.

A wave propagates whose electric field is given by \[ \vec{E} = 69 \sin(\omega t - kx)\,\hat{j}. \] Find the direction of the magnetic field.

There are two point charges, one at the vertex and the other at the face of a cube as shown. Find the electric flux through the cube.

The electric field of an electromagnetic wave travelling through a medium is given by \[ \vec{E}(x,t)=25\sin(2\times10^{15}t-10^{7}x)\,\hat{n}. \] Then the refractive index of the medium is ________. (All given measurements are in SI units)

A rod of mass \(m\) and length \(L\) is released on a rail placed in a uniform magnetic field \(B\) as shown. The circuit has resistance \(R\). What will be the terminal velocity of the rod? v

A planet 'A' having density \( \rho \) and radius \( R \) has escape velocity \( = 10 \, \text{km/sec} \). Find the escape velocity of a planet B having density and radius both 10% that of planet A.

For an object revolving around a planet of mass \( M \) and radius \( R_0 \) at a distance \( r \) from the center of the planet. If area velocity of the object is 10 km/sec. Now if the density of the planet increases by +10% and radius of the planet increases by +10%, then find the new area velocity at the same orbital radius.

A set of measurements of a certain parameter is: $20.00,\; 19.75,\; 18.25,\; 17.01$. Find the relative error for the set of measurements.

If resistance between \(A\) and \(C\) is increased by \(10%\) through heating, then calculate \(|V_A - V_B|\).

What will be the ratio of the wavelength of the 3rd line of the Paschen Series to the 2nd line of the Balmer series of H-atom?

A \(12\,\text{F}\) capacitor is connected to a \(5\,\text{V}\) battery and fully charged. After disconnecting the battery, it is connected in parallel to an uncharged \(6\,\text{F}\) capacitor. Find the final charge on the \(6\,\text{F}\) capacitor.

Match the following as per dimensional formula.

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is:
[A.] maximum at either end of the conductor
[B.] maximum at the axis of the conductor and minimum at the midpoint
[C.] minimum at the surface of the conductor
[D.] minimum at the axis of the conductor
[E.] same at all points in the cross-section of the conductor
Choose the correct answer from the options given below:

When the position vector \[ \vec r = x\hat{i}+y\hat{j}+z\hat{k} \] changes sign as \(\vec r \rightarrow -\vec r\), which one of the following vectors will {not flip under sign change?}

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I = 10 \sin (\omega t)$ A, where $\omega = 1000$ rad./s. A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed $v = 1$ cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is $\alpha / \sqrt{2} \mu A$. The value of $\alpha$ is ___. [Resistance of the loop = 10 $\Omega$]

A curve is given between the potential energy \(U\) of a particle and its position on the \(x\)-axis as shown. Given: \[ \tan\theta_1 = 1,\qquad \tan\theta_2 = 3,\qquad \tan\theta_3 = -\frac{1}{2} \] If \(F_{AB}\) is the force acting on the particle during motion from \(A\) to \(B\), similarly \(F_{BC}\), \(F_{CD}\) and \(F_{DE}\) are the forces during \(B\) to \(C\), \(C\) to \(D\) and \(D\) to \(E\) respectively, arrange the magnitudes of these forces in decreasing order.