NTA JEE Main 17th March 2021 Shift 1

Two blocks ($$m = 0.5$$ kg and $$M = 4.5$$ kg) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $$\frac{3}{7}$$. Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is $$N$$. (Round off to the Nearest Integer) [Take $$g$$ as 9.8 m s$$^{-2}$$]

The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is ________. (Assuming the acceleration to be uniform).

The following bodies, (1) a ring, (2) a disc, (3) a solid cylinder, (4) a solid sphere, of same mass $$m$$ and radius $$R$$ are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ________. [Mark the body as per their respective numbering given in the question]

The radius in kilometer to which the present radius of earth ($$R = 6400$$ km) to be compressed so that the escape velocity is increased 10 times is ________.

Consider two identical springs each of spring constant $$k$$ and negligible mass compared to the mass $$M$$ as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is $$\frac{T_b}{T_a} = \sqrt{x}$$, where value of $$x$$ is ________. (Round off to the Nearest Integer)

Four identical rectangular plates with length, $$l = 2$$ cm and breadth, $$b = \frac{3}{2}$$ cm are arranged as shown in figure. The equivalent capacitance between $$A$$ and $$C$$ is $$\frac{x\varepsilon_0}{d}$$. The value of $$x$$ is ________. (Round off to the Nearest Integer)

A parallel plate capacitor whose capacitance $$C$$ is 14 pF is charged by a battery to a potential difference $$V = 12$$ V between its plates. The charging battery is now disconnected and a porcelain plate with $$k = 7$$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of ________ pJ. (Assume no friction)

The equivalent resistance of series combination of two resistors is $$s$$. When they are connected in parallel, the equivalent resistance is $$p$$. If $$s = np$$, then the minimum value for $$n$$ is ________. (Round off to the Nearest Integer)

If $$2.5 \times 10^{-6}$$ N average force is exerted by a light wave on a non-reflecting surface of 30 cm$$^2$$ area during 40 min of time span, the energy flux of light just before it falls on the surface is ________ W cm$$^{-2}$$. (Round off to the Nearest Integer) (Assume complete absorption and normal incidence conditions are there)

For VHF signal broadcasting, ________ km$$^2$$ of maximum service area will be covered by an antenna tower of height 30 m, if the receiving antenna is placed at ground. Let radius of the earth be 6400 km. (Round off to the Nearest Integer) (Take $$\pi$$ as 3.14)