NTA JEE Main 15th April 2023 Shift 1

A block of mass $$10$$ kg is moving along $$x$$-axis under the action of force $$F = 5x$$ N. The work done by the force in moving the block from $$x = 2$$ m to $$4$$ m will be _____ J.

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively $$(k_{sph} : k_{cyl})$$ is $$2 : \sqrt{x}$$. The value of $$x$$ is _____.

There is an air bubble of radius $$1.0$$ mm in a liquid of surface tension $$0.075$$ N m$$^{-1}$$ and density $$1000$$ kg m$$^{-3}$$ at a depth of $$10$$ cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _____ Pa ($$g = 10$$ m s$$^{-2}$$).

The fundamental frequency of vibration of a string between two rigid support is $$50$$ Hz. The mass of the string is $$18$$ g and its linear mass density is $$20$$ g m$$^{-1}$$. The speed of the transverse waves so produced in the string is _____ m s$$^{-1}$$.

In the given figure the total charge stored in the combination of capacitors is $$100 \ \mu$$C. The value of 'x' is _____.

A network of four resistances is connected to $$9$$ V battery, as shown in figure. The magnitude of voltage difference between the points $$A$$ and $$B$$ is _____ V.

An electron in a hydrogen atom revolves around its nucleus with a speed of $$6.76 \times 10^6$$ m s$$^{-1}$$ in an orbit of radius $$0.52$$ A. The magnetic field produced at the nucleus of the hydrogen atom is _____ T.

A $$20$$ cm long metallic rod is rotated with $$210$$ rpm about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field $$0.2$$ T parallel to the axis exists everywhere. The emf developed between the centre and the ring is _____ mV.
(Take $$\pi = \frac{22}{7}$$)

The refractive index of a transparent liquid filled in an equilateral hollow prism is $$\sqrt{2}$$. The angle of minimum deviation for the liquid will be _____°.

As per given figure $$A$$, $$B$$ and $$C$$ are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths (i.e. $$\frac{\lambda_1}{\lambda_2}$$) is $$\frac{7}{4n}$$, then the value of $$n$$ will be _____.