NTA JEE Main 12th April 2019 Shift 2

A Carnot engine has an efficiency of $$\frac{1}{6}$$. When the temperature of the sink is reduced by 62°C, its efficiency is doubled. The temperatures of the source and the sink are, respectively,

A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?

The number density of molecules of a gas depends on their distance r from the origin as, $$n(r) = n_0 e^{-\alpha r^4}$$. Then the numer of molecules is proportional to:

A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as $$10^{-12}$$ W/m$$^2$$]

Two sources of sound S$$_1$$ and S$$_2$$ produce sound waves of same frequency 660 Hz. A listener is moving from source S$$_1$$ towards S$$_2$$ with a constant speed u$$_0$$ m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u$$_0$$ equals:

Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $$\rho(r) = kr$$, where r is the distance from the centre. Two charges A and B, of -Q each, are placed on diametrically opposite points, at equal distance, a, from the centre. If A and B do not experience any force, then:

In the given circuit, the charge on 4 μF capacitor will be:

A moving coil galvanometer, having a resistance G, produces full scale deflection when a current I$$_G$$ flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to I$$_0$$ (I$$_0$$ > I$$_g$$) by connecting a shunt resistance R$$_A$$ to it and (ii) into a voltmeter of range 0 to V (V = GI$$_0$$) by connecting a series resistance R$$_V$$ to it. Then,

An electron, moving along the x-axis with an initial energy of 100 eV, enters a region of magnetic field $$\vec{B} = (1.5 \times 10^{-3}$$ T)$$\hat{k}$$ at S (see figure). The field extends between x = 0 and x = 2 cm. The electron is detected at the point Q on a screen placed 8 cm away from the point S. The distance d between P and Q (on the screen) is:
(electron’s charge $$1.6 ×10^{−19} C$$, mass of electron $$=9.1×10^{−31} kg$$)

Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5 A. (See figure) ($$\mu_0 = 4\pi \times 10^{-7}$$ NA$$^{-2}$$)