NTA JEE Main 15th April 2018 Shift 1

The relative error in the determination of the surface area of a sphere is $$\alpha$$. Then the relative error in the determination of its volume is:

An automobile, travelling at 40 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is (assume no skidding):

The velocity-time graphs of a car and a scooter are shown in the figure. (i) the difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively.

A given object takes n times more time to slide down a 45$$^\circ$$ rough inclined plane as it takes to slide down a perfectly smooth 45$$^\circ$$ incline. The coefficient of kinetic friction between the object and the incline is:

A uniform rod AB is suspended from a point X, at a variable distance x from A, as shown. To make the rod horizontal, a mass m is suspended from its end A. A set of (m, x) values is recorded. The appropriate variable that give a straight line, when plotted, are:

A force of 40 N acts on a point B at the end of an L-shaped object, as shown in the figure. The angle $$\theta$$ that will produce maximum moment of the force about point A is given by:

A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $$\frac{R}{2}$$, and the other mass, in a circular orbit of radius $$\frac{3R}{2}$$. The difference between the final and initial total energies is:

Take the mean distance of the moon and the sun from the earth to be $$0.4 \times 10^6$$ km and $$150 \times 10^6$$ km respectively. Their masses are $$8 \times 10^{22}$$ kg and $$2 \times 10^{30}$$ kg respectively. The radius of the earth is 6400 km. Let $$\Delta F_1$$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $$\Delta F_2$$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to $$\frac{\Delta F_1}{\Delta F_2}$$ is:

A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $$\rho_1$$ and $$\rho_2$$ ($$\rho_1 > \rho_2$$) fill half the circle. The angle $$\theta$$ between the radius vector passing through the common interface and the vertical is:

A Carnot's engine works as a refrigerator between 250 K and 300 K. It receives 500 cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is: