NTA JEE Main 29th June 2022 Shift 1

As per the given figure, two plates $$A$$ and $$B$$ of thermal conductivity $$K$$ and $$2K$$ are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm$$^2$$ for each plate. The equivalent thermal conductivity of the compound plate is $$\left(1 + \frac{5}{\alpha}\right)K$$, then the value of $$\alpha$$ will be ______.

300 calories of heat is given to a heat engine, and it rejects 225 calories of heat. If source temperature is 227°C, then the temperature of sink will be ______ °C.

A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air Jet when it is at 5 cm from its mean position. The new amplitude of vibration is $$\sqrt{x}$$ cm. The value of $$x$$ is ______.

Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be ______ min.

The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is 31.4 cm. The diameter of wire is measured as 2.4 cm. The resistivity of the given wire is measured as $$x \times 10^{-3}$$ $$\Omega$$ cm. The value of $$x$$ is ______. [Take $$\pi = 3.14$$]

For the network shown below, the value of $$V_B - V_A$$ is ______ V.

The intensity of the light from a bulb incident on a surface is 0.22 W m$$^{-2}$$. The amplitude of the magnetic field in this light-wave is ______ $$\times 10^{-9}$$ T.
(Given: Permittivity of vacuum $$\epsilon_0 = 8.85 \times 10^{-12}$$ C$$^2$$ N$$^{-1}$$ m$$^{-2}$$, speed of light in vacuum $$c = 3 \times 10^8$$ m s$$^{-1}$$)

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which beam of light can converge is ______ mm.

$$\sqrt{d_1}$$ and $$\sqrt{d_2}$$ are the impact parameters corresponding to scattering angles 60° and 90° respectively, when an $$\alpha$$ particle is approaching a gold nucleus. For $$d_1 = xd_2$$, the value of $$x$$ will be ______.

A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by 100 $$\mu$$A, it brings a change of 10 mA in collector current. If the load resistance is 2 k$$\Omega$$ and input resistance is 1 k$$\Omega$$. The value of power gain is $$x \times 10^4$$. The value of $$x$$ is ______.