NTA JEE Main 12th April 2014 Online

Hot water cools from 60°C to 50°C in the first 10 minutes and to 42°C in the next 10 minutes. The temperature of the surroundings is:

A Carnot engine absorbs 1000 J of heat energy from a reservoir at 127°C and rejects 600 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be:

At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 ms$$^{-1}$$. The gas is:

Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants?

A source of sound A emitting waves of frequency 1800 Hz is falling towards ground with a terminal speed v. The observer B on the ground directly beneath the source receives waves of frequency 2150 Hz. The source A receives waves, reflected from ground of frequency nearly: (Speed of sound = 343 m/s)

A spherically symmetric charge distribution is characterised by the following charge density variations: $$\rho(r) = \rho_o\left(1 - \frac{r}{R}\right)$$ for $$r < R$$, $$\rho(r) = 0$$ for $$r \geq R$$. Where r is the distance from the centre of the charge distribution and $$\rho_o$$ is a constant. The electric field at an internal point ($$r < R$$) is:

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation: $$K(x) = K_o + \lambda x$$ ($$\lambda$$ = a constant). The capacitance C, of the capacitor, would be related to its vacuum capacitance C$$_o$$ for the relation:

The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors 3$$\Omega$$, 9$$\Omega$$ and 9$$\Omega$$ and a capacitor of 5.0 $$\mu$$F. How much is the current I in the circuit in steady state?

In the experiment of calibration of voltmeter, a standard cell of e.m.f. 1.1 volt is balanced against 440 cm of potential wire. The potential difference across the ends of resistance is found to balance against 220 cm of the wire. The corresponding reading of voltmeter is 0.5 volt. The error in the reading of volmeter will be:

A positive charge 'q' of mass 'm' is moving along the +x axis. We wish to apply a uniform magnetic field B for time $$\Delta t$$ so that the charge reverses its direction crossing the y axis at a distance d. Then: