NTA JEE Main 10th April 2016 Online

A thin 1 m long rod has a radius of 5 mm. A force of $$50\pi \times 10^3$$ N is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false?

$$A$$, $$B$$, $$C$$, and $$D$$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $$AD = C\ln(BD)$$ holds true. Then which of the combination is not a meaningful quantity?

A particle of mass $$m$$ is acted upon by a force $$F$$ given by the empirical law $$F = \frac{R}{t^2}v(t)$$. If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot

Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to:
(Take the radius of the drum to be 1.25 m and its axle to be horizontal):

The velocity-time graph of a particle of mass 10 kg is shown in the figure. The net work done on the particle in the first two seconds of the motion is

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by $$n^2Rt^2$$, where $$n$$ is a constant. The power delivered to the particle by the force acting on it, is:

In the figure shown $$ABC$$ is a uniform wire. If the center of mass of the wire lies vertically below point $$A$$, then $$\frac{BC}{AB}$$ is close to

An astronaut of mass $$m$$ is working on a satellite orbiting the earth at a distance $$h$$ from the earth's surface. The radius of the earth is $$R$$, while its mass is $$M$$. The gravitational pull $$F_G$$ on the astronaut is

A bottle has an opening of radius a and length b. A cork of length b and radius $$(a + \Delta a)$$ where $$(\Delta a \ll a)$$, is compressed to fit into the opening completely (see figure). If the bulk modulus of the cork is B and the coefficient of friction between the bottle and the cork is $$\mu$$, then the force needed to push the cork into the bottle is

A Carnot freezer takes heat from water at $$0°C$$ inside it and rejects it to the room at a temperature of $$27°C$$. The latent heat of ice is $$336 \times 10^3$$ J kg$$^{-1}$$. If 5 kg of water at $$0°C$$ is converted into ice at $$0°C$$ by the freezer, then the energy consumed by the freezer is close to: