NTA JEE Mains 30th Jan 2024 Shift 2

A vector has magnitude same as that of $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and is parallel to $$\vec{B} = 4\hat{i} + 3\hat{j}$$. The $$x$$ and $$y$$ components of this vector in first quadrant are $$x$$ and 3 respectively where $$x$$ = ____.

Two discs of moment of inertia $$I_1 = 4$$ kg m$$^2$$ and $$I_2 = 2$$ kg m$$^2$$ about their central axes & normal to their planes, rotating with angular speeds 10 rad s$$^{-1}$$ & 4 rad s$$^{-1}$$ respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is _________ J.

A big drop is formed by coalescing 1000 small identical drops of water. If $$E_1$$ be the total surface energy of 1000 small drops of water and $$E_2$$ be the surface energy of single big drop of water, the $$E_1 : E_2$$ is $$x : 1$$, where $$x$$ = ________.

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m, then the time period of small oscillations will be _________ s. [take $$g = \pi^2$$ m s$$^{-2}$$]

A point source is emitting sound waves of intensity $$16 \times 10^{-8}$$ W m$$^{-2}$$ at the origin. The difference in intensity (magnitude only) at two points located at distances of 2 m and 4 m from the origin respectively will be ________ $$\times 10^{-8}$$ W m$$^{-2}$$.

Two identical charged spheres are suspended by strings of equal lengths. The string make an angle of $$37°$$ with each other. When suspended in a liquid of density $$0.7$$ g cm$$^{-3}$$, the angle remains same. If density of material of the sphere is $$1.4$$ g cm$$^{-3}$$, the dielectric constant of the liquid is _____ ($$\tan 37° = \frac{3}{4}$$)

Two resistance of $$100\Omega$$ and $$200\Omega$$ are connected in series with a battery of 4 V and negligible internal resistance. A voltmeter is used to measure voltage across $$100\Omega$$ resistance, which gives reading as 1 V. The resistance of voltmeter must be _______ $$\Omega$$.

The current of 5 A flows in a square loop of sides 1 m is placed in air. The magnetic field at the centre of the loop is $$X\sqrt{2} \times 10^{-7}$$ T. The value of X is _________.

A power transmission line feeds input power at 2.3 kV to a step down transformer with its primary winding having 3000 turns. The output power is delivered at 230 V by the transformer. The current in the primary of the transformer is 5 A and its efficiency is 90%. The winding of transformer is made of copper. The output current of transformer is ____ A.

In an experiment to measure the focal length $$(f)$$ of a convex lens, the magnitude of object distance $$(x)$$ and the image distance $$(y)$$ are measured with reference to the focal point of the lens. The $$y - x$$ plot is shown in figure. The focal length of the lens is ____ cm.