NTA JEE Main 25th January 2023 Shift 1

If $$\vec{P} = 3\hat{i} + \sqrt{3}\hat{j} + 2\hat{k}$$ and $$\vec{Q} = 4\hat{i} + \sqrt{3}\hat{j} + 2.5\hat{k}$$, then, the unit vector in the direction of $$\vec{P} \times \vec{Q}$$ is $$\frac{1}{x}(\sqrt{3}\hat{i} + \hat{j} - 2\sqrt{3}\hat{k})$$. The value of $$x$$ is

An object of mass $$m$$ initially at rest on a smooth horizontal plane starts moving under the action of force $$F = 2$$ N. In the process of its linear motion, the angle $$\theta$$ (as shown in figure) between the direction of force and horizontal varies as $$\theta = kx$$, where $$k$$ is a constant and $$x$$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $$E = \frac{n}{k}\sin\theta$$. The value of $$n$$ is _____.

$$I_{CM}$$ is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of the disc. $$I_{AB}$$ is its moment of inertia about an axis AB perpendicular to the plane and parallel to the axis CM at a distance $$\frac{2}{3}R$$ from the center, where R is the radius of the disc. The ratio of $$I_{AB}$$ and $$I_{CM}$$ is $$x : 9$$. The value of $$x$$ is _____.

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45° with the load axis. The length of the wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $$x \times 10^4$$ N m$$^{-2}$$. The value of $$x$$ is _____.

The distance between two consecutive points with phase difference of 60° in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is travelling is _____ km s$$^{-1}$$.

A uniform electric field of 10 N C$$^{-1}$$ is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($$\theta$$) of deviation of the path of electron as it comes out of the field is _____ (in degree).

In the given circuit, the equivalent resistance between the terminal A and B is _____ $$\Omega$$

An LCR series circuit of capacitance 62.5 nF and resistance of 50 $$\Omega$$, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is _____ mH. (Take $$\pi^2 = 10$$)

A ray of light is incident from air on a glass plate having thickness $$\sqrt{3}$$ cm and refractive index $$\sqrt{2}$$. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is _____ $$\times 10^{-2}$$ cm. (given sin 15° = 0.26)

The wavelength of the radiation emitted is $$\lambda_0$$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be $$\frac{20}{x}\lambda_0$$. The value of $$x$$ is _____.