NTA JEE Main 24th June 2022 Shift 1 - Physics

Identify the pair of physical quantities which have different dimensions:

A projectile is projected with velocity of $$25$$ m s$$^{-1}$$ at an angle $$\theta$$ with the horizontal. After $$t$$ seconds its inclination with horizontal becomes zero. If $$R$$ represents horizontal range of the projectile, the value of $$\theta$$ will be : [use $$g = 10$$ m s$$^{-2}$$]

A boy ties a stone of mass $$100$$ g to the end of a $$2$$ m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of $$80$$ N. If the maximum speed with which the stone can revolve is $$\frac{K}{\pi}$$ rev min$$^{-1}$$. The value of $$K$$ is : (Assume the string is massless and un-stretchable)

A block of mass $$10$$ kg starts sliding on a surface with an initial velocity of $$9.8$$ ms$$^{-1}$$. The coefficient of friction between the surface and block is $$0.5$$. The distance covered by the block before coming to rest is : [use $$g = 9.8$$ ms$$^{-2}$$]

A particle experiences a variable force $$\vec{F} = \left(4x\hat{i} + 3y^2\hat{j}\right)$$ in a horizontal $$x - y$$ plane. Assume distance in meters and force in Newton. If the particle moves from point $$(1, 2)$$ to point $$(2, 3)$$ in the $$x - y$$ plane, then Kinetic Energy changes by :

The approximate height from the surface of earth at which the weight of the body becomes $$\frac{1}{3}$$ of its weight on the surface of earth is :
[Radius of earth $$R = 6400$$ km and $$\sqrt{3} = 1.732$$]

The bulk modulus of a liquid is $$3 \times 10^{10}$$ Nm$$^{-2}$$. The pressure required to reduce the volume of liquid by $$2\%$$ is :

Two metallic blocks $$M_1$$ and $$M_2$$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $$M_2$$ is $$K$$ then the thermal conductivity of $$M_1$$ will be : [Assume steady state heat conduction]

A Carnot engine whose heat sinks at $$27°$$C, has an efficiency of $$25\%$$. By how many degrees should the temperature of the source be changed to increase the efficiency by $$100\%$$ of the original efficiency?

The equations of two waves are given by :
$$y_1 = 5 \sin 2\pi(x - vt)$$ cm
$$y_2 = 3 \sin 2\pi(x - vt + 1.5)$$ cm
These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

A vertical electric field of magnitude $$4.9 \times 10^{5}$$ N C$$^{-1}$$ just prevents a water droplet of a mass $$0.1$$ g from falling. The value of charge on the droplet will be : (Given $$g = 9.8$$ m s$$^{-2}$$)

A parallel plate capacitor is formed by two plates each of area $$30\pi$$ cm$$^2$$ separated by $$1$$ mm. A material of dielectric strength $$3.6 \times 10^{7}$$ V m$$^{-1}$$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $$7 \times 10^{-6}$$ C, the value of dielectric constant of the material is :
[Use $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}$$ N m$$^2$$ C$$^{-2}$$]

Two identical cells each of emf $$1.5$$ V are connected in parallel across a parallel combination of two resistors each of resistance $$20$$ $$\Omega$$. A voltmeter connected in the circuit measures $$1.2$$ V. The internal resistance of each cell is :

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.
Reason (R) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.

The magnetic field at the centre of a circular coil of radius $$r$$, due to current $$I$$ flowing through it, is $$B$$. The magnetic field at a point along the axis at a distance $$\frac{r}{2}$$ from the centre is :

A resistance of $$40$$ $$\Omega$$ is connected to a source of alternating current rated $$220$$ V, $$50$$ Hz. Find the time taken by the current to change from its maximum value to the rms value :

A plane electromagnetic wave travels in a medium of relative permeability $$1.61$$ and relative permittivity $$6.44$$. If magnitude of magnetic intensity is $$4.5 \times 10^{-2}$$ A m$$^{-1}$$ at a point, what will be the approximate magnitude of electric field intensity at that point?
(Given : Permeability of free space $$\mu_0 = 4\pi \times 10^{-7}$$ N A$$^{-2}$$, speed of light in vacuum $$c = 3 \times 10^{8}$$ m s$$^{-1}$$)

Choose the correct option from the following options given below :

Nucleus $$A$$ is having mass number $$220$$ and its binding energy per nucleon is $$5.6$$ MeV. It splits in two fragments $$B$$ and $$C$$ of mass numbers $$105$$ and $$115$$. The binding energy of nucleons in $$B$$ and $$C$$ is $$6.4$$ MeV per nucleon. The energy $$Q$$ released per fission will be:

A baseband signal of $$3.5$$ MHz frequency is modulated with a carrier signal of $$3.5$$ GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal?

From the top of a tower, a ball is thrown vertically upward which reaches the ground in $$6$$ s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in $$1.5$$ s. A third ball released, from the rest from the same location, will reach the ground in ______ s.

A ball of mass $$100$$ g is dropped from a height $$h = 10$$ cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $$\frac{h}{2}$$. The spring constant is ______ N m$$^{-1}$$
(Use $$g = 10$$ m s$$^{-2}$$)

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass $$10$$ g are put one on the top of the other at the $$10.0$$ cm mark the scale is found to be balanced at $$40.0$$ cm mark. The mass of the metre scale is found to be $$x \times 10^{-2}$$ kg. The value of $$x$$ is ______.

$$0.056$$ kg of Nitrogen is enclosed in a vessel at a temperature of $$127°$$C. The amount of heat required to double the speed of its molecules is ______ kcal.
(Take $$R = 2$$ cal mole$$^{-1}$$ K$$^{-1}$$)

In a potentiometer arrangement, a cell gives a balancing point at $$75$$ cm length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is $$3 : 2$$, the difference in the balancing length of the potentiometer wire in above two cases will be ______ cm.

As shown in the figure an inductor of inductance $$200$$ mH is connected to an AC source of emf $$220$$ V and frequency $$50$$ Hz. The instantaneous voltage of the source is $$0$$ V when the peak value of current is $$\frac{\sqrt{a}}{\pi}$$ A. The value of $$a$$ is ______.

Two identical thin biconvex lenses of focal length $$15$$ cm and refractive index $$1.5$$ are in contact with each other. The space between the lenses is filled with a liquid of refractive index $$1.25$$. The focal length of the combination is ______ cm.

Sodium light of wavelengths $$650$$ nm and $$655$$ nm is used to study diffraction at a single slit of aperture $$0.5$$ mm. The distance between the slit and the screen is $$2.0$$ m. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is ______ $$\times 10^{-5}$$ m.

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is $$v_1$$. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes $$v_2$$. If $$v_2 = xv_1$$, the value of $$x$$ will be ______.

A transistor is used in common-emitter mode in an amplifier circuit. When a signal of $$10$$ mV is added to the base-emitter voltage, the base current changes by $$10\mu$$A and the collector current changes by $$1.5$$ mA. The load resistance is $$5$$ k$$\Omega$$. The voltage gain of the transistor will be ______.