NTA JEE Main 27th July 2021 Shift 2

A physical quantity $$y$$ is represented by the formula $$y = m^2 r^{-4} g^x l^{-\frac{3}{2}}$$. If the percentage errors found in $$y$$, $$m$$, $$r$$, $$l$$ and $$g$$ are 18, 1, 0.5, 4 and $$p$$ respectively, then find the value of $$x$$ and $$p$$.

Match List I with List II.
    List-I                                                             List-II
a. Capacitance, C                                  i.   $$M^1 L^1 T^{-3} A^{-1}$$
b. Permittivity of free space, $$\varepsilon_0$$          ii.  $$M^{-1} L^{-3} T^4 A^2$$
c. Permeability of free space, $$\mu_0$$       iii. $$M^{-1} L^{-2} T^4 A^2$$
d. Electric field, E                                  iv. $$M^1 L^1 T^{-2} A^{-2}$$
Choose the correct answer from the options given below:

A particle of mass $$M$$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $$F = F_0\left[1 - \left(\frac{t-T}{T}\right)^2\right]$$ where $$F_0$$ and $$T$$ are constants. The force acts only for the time interval $$2T$$. The velocity $$v$$ of the particle after time $$2T$$ is:

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that $$E_{mech} = 8$$ J, the incorrect statement for this system is:

An automobile of mass $$m$$ accelerates starting from the origin and initially at rest, while the engine supplies constant power $$P$$. The position is given as a function of time by:

Two identical particles of mass 1 kg each go round a circle of radius $$R$$, under the action of their mutual gravitational attraction. The angular speed of each particle is:

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of $$9.0 \times 10^3$$ km. Find the mass of Mars.
$$\left\{\text{Given } \frac{4\pi^2}{G} = 6 \times 10^{11} \text{ N}^{-1} \text{ m}^{-2} \text{ kg}^2\right\}$$

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyancy may be neglected, then the terminal speed attained by the raindrop is: [Density of water $$f_w = 1000$$ kg m$$^{-3}$$ and Density of air $$f_a = 1.2$$ kg m$$^{-3}$$, g = 10 m/s$$^2$$, Coefficient of viscosity of air = $$1.8 \times 10^{-5}$$ N s m$$^{-2}$$]

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27°C to 37°C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J mol$$^{-1}$$ K$$^{-1}$$]

Two Carnot engines $$A$$ and $$B$$ operate in series such that engine A absorbs heat at $$T_1$$ and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine $$A$$ and rejects heat to the sink at $$T_3$$. When workdone in both the cases is equal, to value of T is: