NTA JEE Main 15th April 2018 Shift 2

Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K. If the efficiencies of the two engines A and B are represented by $$\eta_A$$ and $$\eta_B$$ respectively, then what is the value of $$\frac{\eta_A}{\eta_B}$$?

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms$$^{-1}$$ is: [k$$_B$$ = 1.4 $$\times$$ 10$$^{-23}$$ J/K; m$$_{He}$$ = 7 $$\times$$ 10$$^{-27}$$ kg]

Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures. $$x(t) = A\sin(at + \delta)$$, $$y(t) = B\sin(bt)$$. Identify the correct match below.

5 beats/second are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be:

A solid ball of radius R has a charge density $$\rho$$ given by $$\rho = \rho_0\left(1 - \frac{r}{R}\right)$$ for $$0 \leq r \leq R$$. The electric field outside the ball is:

A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is $$\rho$$, how long will the charges take to travel a distance d?

A parallel plate capacitor with area 200 cm$$^2$$ and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is $$25 \times 10^{-6}$$ N, the value of V is approximately: $$\left(\varepsilon_0 = 8.85 \times 10^{-12} \frac{C^2}{N \cdot m^2}\right)$$

A capacitor C$$_1$$ is charged up to a voltage V = 60 V by connecting it to battery B through switch (1). Now C$$_1$$ is disconnected from battery and connected to a circuit consisting of two uncharged capacitors C$$_2$$ = 3.0$$\mu$$F and C$$_3$$ = 6.0$$\mu$$F through a switch (2) as shown in the figure. The sum of final charges on C$$_2$$ and C$$_3$$ is:

A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be:

A current of 1 A is flowing on the sides of an equilateral triangle of side $$4.5 \times 10^{-2}$$ m. The magnetic field at the centre of the triangle will be: