NTA JEE Main 10th January 2019 Shift 2

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$$^{-1}$$)