JEE Main 2021 Physics Paper: 27 Aug, Shift 1

The alternating current is given by $i = \left\{\sqrt{42} \sin\left(\frac{2\pi}{T} t\right) + 10\right\} A$

The r.m.s. value of of this current is ................. A.

Calculate the amount of charge on capacitor of 4$\mu$F. The internal resistance of battery is 1$\Omega$:

A huge circular arc of length 4.4 ly subtends an angle of 4″ (4 seconds of arc) at the centre of the circle. How long it would take for a body to complete 4 revolutions if its speed is 8 AU per second? Given: 1 ly = 9.46 $\times$ 1015 m

1 AU = 1.5 $\times$ 1011 m

Five identical cells each of internal resistance 1$\Omega$ and emf 5V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same?

First, a set of n equal resistors of 10 $\Omega$ each are connected in series to a battery of emf 20V and internal resistance 10$\Omega$. A current I is observed to flow. Then, the n resistors are connected in parallel to the same battery. It is observed that the current is increased 20 times, then the value of n is ................

In a photoelectric experiment, increasing the intensity of incident light:

A bar magnet is passing through a conducting loop of radius R with velocity $v$. The radius of the bar magnet is such that it just passes through the loop. The induced e.m.f. in the loop can be represented by the approximate curve:

Electric field in a plane electromagnetic wave is given by E = 50 sin(500x $-$ 10 $\times$ 1010 t) V/m The velocity of electromagnetic wave in this medium is:

(Given C = speed of light in vacuum)

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 :-

A body of mass (2M) splits into four masses (m, M $-$ m, m, M $-$ m}, which are rearranged to form a square as shown in the figure. The ratio of $\frac{M}{m}$ for which, the gravitational potential energy of the system becomes maximum is x: 1. The value of x is .............

A rod CD of thermal resistance 10.0 KW${}^{-1}$ is joined at the middle of an identical rod AB as shown in figure. The end A, B and D are maintained at 200$^\circ$C, 100$^\circ$C and 125$^\circ$C respectively. The heat current in CD is P watt. The value of P is ..................

If the velocity of a body related to displacement x is given by $v = \sqrt{5000 + 24x}$ m/s, then the acceleration of the body is .................... m/s2.

A uniform conducting wire of length 24a and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source V0. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is 1: $\sqrt{y}$ where y is ..................

Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then:

There are 1010 radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? $\left(\sqrt{2} = 1.414\right)$

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:

Find the distance of the image from object O, formed by the combination of lenses in the figure:

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is d1 from C and the distance of the image formed is d2 from C, the radius of curvature of this mirror is:

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:

For a transistor in CE mode to be used as an amplifier, it must be operated in:

A circuit is arranged as shown in figure. The output voltage V0 is equal to ................... V.

A balloon carries a total load of 185 kg at normal pressure and temperature of 27$^\circ$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 $-7^\circ$C. Assuming the volume constant?

An ideal gas is expanding such that PT3 = constant. The coefficient of volume expansion of the gas is:

If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be:

Which of the following is not a dimensionless quantity?

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

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 $\times$ 103 kgm$-$ 3? Take viscosity of liquid = 1.8 $\times$ 10$-$5 Nsm${}^{-2}$. (Neglect buoyancy due to air).

Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air is 340 m/s, the actual frequency of the whistle sound produced is .................. Hz.

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45${}^\circ$ and 60${}^\circ$ with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is $\frac{1}{\sqrt{x}}$. The value of x is .....................