NTA JEE Main 10th January 2019 Shift 2

2 kg of a monoatomic gas is at a pressure of $$4 \times 10^4$$ N m$$^{-2}$$. The density of the gas is 8 kg m$$^{-3}$$. What is the order of energy of the gas due to its thermal motion?

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are $$T_h$$ and $$T_c$$ respectively, then:

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is:

A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $$\omega$$. If the radius of the bottle is 2.5 cm then $$\omega$$ is close to: (density of water $$= 10^3$$ kg/m$$^3$$)

A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be (Assume that the highest frequency a person can hear is 20,000 Hz).

Charges $$-q$$ and $$+q$$, located at A and B, respectively, constitute an electric dipole. Distance $$AB = 2a$$, $$O$$ is the mid point of the dipole and $$OP$$ is perpendicular to $$AB$$. A charge $$Q$$ is placed at P where $$OP = y$$ and $$y \gg 2a$$. The charge $$Q$$ experiences an electrostatic force $$F$$. If $$Q$$ is now moved along the equatorial line to P' such that $$OP' = \frac{y}{3}$$, the force on $$Q$$ will be close to ($$\frac{y}{3} \ll 2a$$):

Four equal point charges $$Q$$ each are placed in the $$xy$$ plane at $$(0, 2)$$, $$(4, 2)$$, $$(4, -2)$$ and $$(0, -2)$$. The work required to put a fifth charge $$Q$$ at the origin of the coordinate system will be:

A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is:

The actual value of resistance $$R$$, shown in the figure is 30$$\Omega$$. This is measured in an experiment as shown using the standard formula $$R = \frac{V}{I}$$, where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of $$R$$ is 5% less, then the internal resistance of the voltmeter is:

The Wheatstone bridge shown in the figure below, gets balanced when the carbon resistor used as $$R_1$$ has the colour code (orange, red, brown). The resistors $$R_2$$ and $$R_4$$ are 80 $$\Omega$$ and 40 $$\Omega$$, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as $$R_3$$, would be: