NTA JEE Main 8 April 2018 Offline

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere $$\left(\frac{dr}{r}\right)$$, is:

Two moles of an ideal monoatomic gas occupies a volume V at 27$$^\circ$$C. The gas expands adiabatically to a volume 2V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $$10^{12}$$ s$$^{-1}$$. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 g mol$$^{-1}$$ and Avogadro number = $$6.02 \times 10^{23}$$)

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $$2.7 \times 10^3$$ kg m$$^{-3}$$ and its Young's modulus is $$9.27 \times 10^{10}$$ Pa. What will be the fundamental frequency of the longitudinal vibrations?

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $$+\sigma$$, $$-\sigma$$ and $$+\sigma$$ respectively. The potential of shell B is:

A parallel plate capacitor of capacitance 90 pF is connected to a battery of EMF 20 V. If a dielectric material of dielectric constant $$K = \frac{5}{3}$$ is inserted between the plates, the magnitude of the induced charge will be:

Two batteries with e.m.f. 12 V and 13 V are connected in parallel across a load resistor of 10 $$\Omega$$. The internal resistance of the two batteries are 1 $$\Omega$$ and 2 $$\Omega$$ respectively. The voltage across the load lies between,

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k$$\Omega$$. How much was the resistance on the left slot before interchanging the resistances?

In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of 5 $$\Omega$$, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is $$B_1$$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $$B_2$$. The ratio $$\frac{B_1}{B_2}$$ is: