NTA JEE Main 30th January 2023 Shift 2

A body of mass $$2$$ kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power $$P$$. Its displacement in $$4$$ s is $$\frac{1}{3}\alpha^2\sqrt{P}$$ m. The value of $$\alpha$$ will be ______.

A uniform disc of mass $$0.5$$ kg and radius $$r$$ is projected with a velocity $$18$$ m s$$^{-1}$$ at $$t = 0$$ s on a rough horizontal surface. It starts off with a purely sliding motion at $$t = 0$$ s. After $$2$$ s it acquires a purely rolling motion. The total kinetic energy of the disc after $$2$$ s will be ______ J.
(given, coefficient of friction is $$0.3$$ and $$g = 10$$ m s$$^{-2}$$).

A faulty thermometer reads $$5°$$C in melting ice and $$95°$$C in steam. The correct temperature on absolute scale will be ______ K when the faulty thermometer reads $$41°$$C.

The velocity of a particle executing SHM varies with displacement $$(x)$$ as $$4v^2 = 50 - x^2$$. The time period of oscillations is $$\frac{x}{7}$$ s. The value of $$x$$ is ______. [Take $$\pi = \frac{22}{7}$$]

As shown in figure, a cuboid lies in a region with electric field $$E = 2x^2\hat{i} - 4y\hat{j} + 6\hat{k}$$ N C$$^{-1}$$. The magnitude of charge within the cuboid is $$n\varepsilon_0$$ C. The value of $$n$$ is ______ (if dimension of cuboid is $$1 \times 2 \times 3$$ m$$^3$$)

The equivalent resistance between $$A$$ and $$B$$ is ______ $$\Omega$$.

If the potential difference between $$B$$ and $$D$$ is zero, the value of $$x$$ is $$\frac{1}{n}$$ $$\Omega$$. The value of $$n$$ is ______.

In an ac generator, a rectangular coil of $$100$$ turns each having area $$14 \times 10^{-2}$$ m$$^2$$ is rotated at $$360$$ rev min$$^{-1}$$ about an axis perpendicular to a uniform magnetic field of magnitude $$3.0$$ T. The maximum value of the emf produced will be ______ V. [Take $$\pi = \frac{22}{7}$$]

In a Young's double slit experiment, the intensities at two points, for the path difference $$\frac{\lambda}{4}$$ and $$\frac{\lambda}{3}$$ ($$\lambda$$ being the wavelength of light used) are $$I_1$$ and $$I_2$$ respectively. If $$I_0$$ denotes the intensity produced by each one of the individual slits, then $$\frac{I_1+I_2}{I_0} =$$ ______.

A radioactive nucleus decays by two different process. The half life of the first process is $$5$$ minutes and that of the second process is $$30$$ s. The effective half-life of the nucleus is calculated to be $$\frac{\alpha}{11}$$ s. The value of $$\alpha$$ is ______.