NTA JEE Main 12th April 2019 Shift 1

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? R = 8.3 J/mol K

A submarine A travelling at 18 km hr$$^{-1}$$ is being chased along the line of its velocity by another submarine B travelling at 27 km hr$$^{-1}$$. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency v. The value of v is close to (Speed of sound in water 1500 m s$$^{-1}$$)

A progressive wave travelling along the positive x-direction is represented by $$y(x, t) = A\sin(kx - \omega t + \phi)$$. Its snapshot at t = 0 is given in the figure.

For this wave, the phase $$\phi$$ is:

Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre a dipole $$\vec{p}$$ is placed as shown then:

A Point dipole $$\vec{p} = -p_0\hat{x}$$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Taken V = 0 at infinity)

Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K$$_1$$, K$$_2$$ and K$$_3$$. The first capacitor is filled as shown in figure I, and the second one is filled as shown in figure II.

If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (E$$_1$$ refers to capacitor I and E$$_2$$ to capacitor II):

To verify Ohm's law, a student connects the voltmeter across the battery as shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained.

If V$$_0$$ is almost zero, identify the correct statement:

A galvanometer of resistance 100 Ω has 50 divisions on its scale and has sensitivity of 20 μA/division. It is to be converted to voltmeter with three ranges, of 0 - 2 V, 0 - 10 V and 0 - 20 V. The appropriate circuit to do so is:

The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is:

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45° and 40 times per minute where the dip is 30°. If B$$_1$$ and B$$_2$$ are the net magnetic fields due to the earth at the two places respectively, then the ratio B$$_1$$/B$$_2$$ is approximately equal to