NTA JEE Main 8th April 2017 Online

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure ($$C_p$$) and at constant volume ($$C_V$$) is:

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s$$^{-1}$$. At, $$t = 0$$ the displacement is 5 m. What is the maximum acceleration? The initial phase is $$\frac{\pi}{4}$$.

A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to a 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is:

Two wires $$W_1$$ and $$W_2$$ have the same radius $$r$$ and respective densities $$\rho_1$$ and $$\rho_2$$, such that $$\rho_2 = 4\rho_1$$. They are joined together at the point $$O$$, as shown in the figure. The combination is used as a sonometer wire and kept under tension $$T$$. The point $$O$$ is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in $$W_1$$ to $$W_2$$ is:

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $$P$$, in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60° with the direction of the field?

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 $$\mu$$C charge, its radius will be: $$\left[\text{Take } : \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}\right]$$

A 9 V battery with an internal resistance of 0.5 $$\Omega$$ is connected across an infinite network, as shown in the figure. All ammeters $$A_1$$, $$A_2$$, $$A_3$$ and voltmeter $$V$$ are ideal. Choose the correct statement.

A potentiometer $$PQ$$ is set up to compare two resistances, as shown in the figure. The ammeter $$A$$ in the circuit reads 1.0 A when the two-way key $$K_3$$ is open. The balance point is at a length $$l_1$$ cm from $$P$$ when the two-way key $$K_3$$ is plugged in between 2 and 1, while the balance point is at a length $$l_2$$ cm from $$P$$ when the key $$K_3$$ is plugged in between 3 and 1. The ratio of two resistances $$\frac{R_1}{R_2}$$, is found to be:

A magnetic dipole in a uniform magnetic field has: (Take zero potential energy when magnetic dipole is perpendicular to magnetic field)

In a certain region static electric and magnetic fields exist. The magnetic field is given by $$\vec{B} = B_0(\hat{i} + 2\hat{j} - 4\hat{k})$$. If a test charge moving with a velocity $$\vec{v} = v_0(3\hat{i} - \hat{j} + 2\hat{k})$$ experiences no force in that region, then the electric field in the region, in SI units, is: