NTA JEE Main 26th August 2021 Shift 1

The magnitude of vectors $$\overrightarrow{OA}$$, $$\overrightarrow{OB}$$ and $$\overrightarrow{OC}$$ in the given figure are equal. The direction of $$\overrightarrow{OA} + \overrightarrow{OB} - \overrightarrow{OC}$$ with x-axis will be:

If $$E$$, $$L$$, $$M$$ and $$G$$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of $$P$$ in the formula $$P = EL^2M^{-5}G^{-2}$$ are:

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 m s$$^{-2}$$. The gases come out at a relative speed of 500 m s$$^{-1}$$, with respect to the rocket: [Use $$g = 10$$ m s$$^{-2}$$]

Inside a uniform spherical shell:
(a) The gravitational field is zero.
(b) The gravitational potential is zero.
(c) The gravitational field is the same everywhere.
(d) The gravitation potential is the same everywhere.
(e) All the above.
Choose the most appropriate answer from the options given below:

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube.
[Take surface tension of water $$T = 7.3 \times 10^{-2}$$ N m$$^{-1}$$, angle of contact = 0, $$g = 10$$ m s$$^{-2}$$ and density of water = $$1.0 \times 10^3$$ kg m$$^{-3}$$]

An electric appliance supplies 6000 J min$$^{-1}$$, heat to the system. If the system delivers a power of 90 W. How long it would take to increase the internal energy by $$2.5 \times 10^3$$ J?

The R.M.S. speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are $$v_H$$, $$v_O$$ and $$v_C$$ respectively, then:

A solid metal sphere of radius $$R$$ having charge $$q$$ is enclosed inside the concentric spherical shell of inner radius $$a$$ and outer radius $$b$$ as shown in the figure. The approximate variation electric field $$\vec{E}$$, as a function of distance $$r$$, from centre $$O$$, is given by:

The material filled between the plates of a parallel plate capacitor has resistivity 200 $$\Omega$$ m. The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permittivity of material is 50)

In the given figure, the emf of the cell is 2.2 V and if internal resistance is 0.6 $$\Omega$$. Calculate the power dissipated in the whole circuit: