NTA JEE Main 27th August 2021 Shift 1

The resultant of these forces $$\vec{OP}, \vec{OQ}, \vec{OR}, \vec{OS}$$ and $$\vec{OT}$$ is approximately ______ N.
[Take $$\sqrt{3} = 1.7, \sqrt{2} = 1.4$$. Given $$\hat{i}$$ and $$\hat{j}$$ unit vectors along $$x, y$$ axis]

If $$E$$ and $$H$$ represents the intensity of electric field and magnetizing field respectively, then the unit of $$\frac{E}{H}$$ will be:

Which of the following is not a dimensionless quantity?

A huge circular arc of length 4.4 ly subtends an angle 4s at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second?
Given : 1 ly = $$9.46 \times 10^{15}$$ m
1 AU = $$1.5 \times 10^{11}$$ m

Moment of inertia of a square plate of side $$l$$ about the axis passing through one of the corner and perpendicular to the plane of square plate is given by:

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius $$2.0 \times 10^{-5}$$ m and density $$1.2 \times 10^3$$ kg m$$^{-3}$$? Take viscosity of liquid = $$1.8 \times 10^{-5}$$ N s m$$^{-2}$$. (Neglect buoyancy due to air).

An ideal gas is expanding such that $$PT^3$$ = constant. The coefficient of volume expansion of the gas is:

A balloon carries a total load of 185 kg at normal pressure and temperature of 27°C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is -7°C. Assuming the volume constant?

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.

The potential energy $$U(x)$$ versus time $$(t)$$ plot of the particle is correctly shown in figure:

A uniformly charged disc of radius $$R$$ having surface charge density $$\sigma$$ is placed in the $$xy$$ plane with its center at the origin. Find the electric field intensity along the $$z$$-axis at a distance $$Z$$ from origin: