JEE Main 11th January 2019 Shift 2

A particle moves from the point $$(2.0\hat{i} + 4.0\hat{j})$$ m, at $$t = 0$$, with an initial velocity $$(5.0\hat{i} + 4.0\hat{j})$$ ms$$^{-1}$$. It is acted upon by a constant force which produces a constant acceleration $$(4.0\hat{i} + 4.0\hat{j})$$ ms$$^{-2}$$. What is the distance of the particle from the origin at time 2 s?

If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be:

A particle of mass m is moving in a straight line with momentum p. Starting at time $$t = 0$$, a force $$F = kt$$ acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is

The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5 m, the angle between the force and the position vector is (in radians):

A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string)

A circular disc $$D_1$$ of mass M and radius R has two identical discs $$D_2$$ and $$D_3$$ of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO', passing through the centre of $$D_1$$, as shown in the figure, will be

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be:

Two rods A and B of identical dimensions are at temperature $$30°C$$. If A is heated upto $$180°C$$ and B upto $$T°C$$, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is

A thermometer graduated according to a linear scale reads a value $$x_0$$ when in contact with boiling water, and $$x_0/3$$ when in contact with ice. What is the temperature of an object in °C, if this thermometer in the contact with the object reads $$x_0/2$$?

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is increased by $$\Delta T$$. The amount of heat absorbed by gas is (R is gas constant):