NTA JEE Main 8th April 2019 Shift 1

Ship A is sailing towards north-east with velocity $$\vec{v} = 30\hat{i} + 50\hat{j}$$ km h$$^{-1}$$ where $$\hat{i}$$ points east and $$\hat{j}$$, north. The ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards the west at 10 km h$$^{-1}$$. A will be at the minimum distance from B in:

In SI units, the dimensions of $$\sqrt{\frac{\varepsilon_0}{\mu_0}}$$ is:

A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled 3 m is:

If $$10^{22}$$ gas molecules each of mass $$10^{-26}$$ kg collides with a surface (perpendicular to it) elastically per second over an area 1 m$$^{2}$$ with a speed $$10^{4}$$ m/s, the pressure exerted by the gas molecules will be of the order of:

Four particles A, B, C and D with masses $$m_A = m$$, $$m_B = 2m$$, $$m_C = 3m$$ and $$m_D = 4m$$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is:

A thin circular plate of mass $$M$$ and radius $$R$$ has its density varying as $$\rho(r) = \rho_0 r$$ with $$\rho_0$$ as constant and $$r$$ is the distance from its centre. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is $$I = aMR^{2}$$. The value of the coefficient $$a$$ is:

Four identical particles of mass M are located at the corners of a square of side 'a'. What should be their speed if each of them revolves under the influence of other's gravitational field in a circular orbit circumscribing the square?

A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms$$^{-1}$$. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to:

A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1$$\pi$$ m s$$^{-2}$$, what will be the tensile stress that would be developed in the wire?

Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of: (density of water = 100 kg/m$$^{3}$$, coefficient of viscosity of water = 1 mPa s)