NTA JEE Main 10th January 2019 Shift 2 - Physics

The diameter and height of a cylinder are measured by a meter scale to be $$12.6 \pm 0.1$$ cm and $$34.2 \pm 0.1$$ cm, respectively. What will be the value of its volume in appropriate significant figures?

Two vectors $$\vec{A}$$ and $$\vec{B}$$ have equal magnitudes. The magnitude of $$(\vec{A} + \vec{B})$$ is '$$n$$' times the magnitude of $$(\vec{A} - \vec{B})$$. The angle between $$\vec{A}$$ and $$\vec{B}$$ is:

Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle $$\theta$$ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle $$\theta$$ is:

A particle starts from the origin at time $$t = 0$$ and moves along the positive $$x$$-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time $$t = 5s$$?

A particle which is experiencing a force, given by $$\vec{F} = 3\hat{i} - 12\hat{j}$$, undergoes a displacement of $$\vec{d} = 4\hat{i}$$. If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement?

Two identical spherical balls of mass $$M$$ and radius $$R$$ each are stuck on two ends of a rod of length $$2R$$ and mass $$M$$ (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is:

A rigid massless rod of length $$3l$$ has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis. When released from the initial horizontal position, its instantaneous angular acceleration will be:

Two stars of masses $$3 \times 10^{31}$$ kg each, and at distance $$2 \times 10^{11}$$ m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is: (Take Gravitational constant $$G = 6.67 \times 10^{-11}$$ N m$$^2$$ kg$$^{-2}$$)

Half mole of an ideal monoatomic gas is heated at a constant pressure of 1 atm from 20$$^{\circ}$$C to 90$$^{\circ}$$C. Work done by the gas is (Gas constant, $$R = 8.21$$ J mol$$^{-1}$$ K$$^{-1}$$)

An unknown metal of mass 192 g heated to a temperature of 100$$^{\circ}$$C was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4$$^{\circ}$$C. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5$$^{\circ}$$C. (Specific heat of brass is 394 J kg$$^{-1}$$K$$^{-1}$$)

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:

A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is:

At some location the horizontal component of earth's magnetic field is $$18 \times 10^{-6}$$ T. At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes 45$$^{\circ}$$ angles with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is:

The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10A to 25A in 1s, the change in the energy of the inductance is:

The electric field of a plane polarized electromagnetic wave in free space at time $$t = 0$$ is given by the expression $$\vec{E}(x, y) = 10\hat{j}\cos(6x + 8z)$$. The magnetic field $$\vec{B}(x, z, t)$$ is given by ($$c$$ is the velocity of light.)

The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of the cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.

Consider a Young's double slit experiment as shown in figure. What should be the slit separation $$d$$ in terms of wavelength $$\lambda$$ such that the first minima occurs directly in front of the slit ($$S_1$$)?

A metal plate of area $$1 \times 10^{-4}$$ m$$^2$$ is illuminated by a radiation of intensity 16 m W/m$$^2$$. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be: [$$1eV = 1.6 \times 10^{-19}$$ J]

Consider the nuclear fission, $$Ne^{20} \rightarrow 2He^4 + C^{12}$$. Given that the binding energy/nucleon of $$Ne^{20}$$, $$He^4$$ and $$C^{12}$$ are 8.03 MeV, 7.86 MeV, respectively. Identify the correct statement:

For the circuit shown below, the current through the Zener diode is:

The modulation frequency of an AM radio station is 250 kHz, which is 10% of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot?