NTA JEE Main 11th April 2023 Shift 1

A projectile fired at 30$$^\circ$$ to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is _______ m s$$^{-1}$$.
(Given $$g = 10$$ m s$$^{-2}$$)

A force $$\vec{F} = (2 + 3x)\hat{i}$$ acts on a particle in the $$x$$ direction where $$F$$ is in Newton and $$x$$ is in meter. The work done by this force during a displacement from $$x = 0$$ to $$x = 4$$ m is _______ J.

A solid sphere of mass 500 g radius 5 cm is rotated about one of its diameter with angular speed of 10 rad s$$^{-1}$$. If the moment of inertia of the sphere about its tangent is $$x \times 10^{-2}$$ times its angular momentum about the diameter. Then the value of $$x$$ will be _______

The length of a wire becomes $$l_1$$ and $$l_2$$ when 100 N and 120 N tension are applied respectively. If $$10l_2 = 11l_1$$, then the natural length of wire will be $$\frac{1}{x}l_1$$. Here the value of $$x$$ is _______

The equation of wave is given by $$Y = 10^{-2}\sin 2\pi(160t - 0.5x + \frac{\pi}{4})$$, where $$x$$ and $$Y$$ are in m and $$t$$ in s. The speed of the wave is _______ km h$$^{-1}$$.

As shown in the figure, a configuration of two equal point charges $$q_0 = +2\mu C$$ is placed on an inclined plane. Mass of each point charge is 20 g. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $$h = x \times 10^{-3}$$ m. The value of x is _______
Take $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$$ N m$$^2$$ C$$^{-2}$$, $$g = 10$$ m s$$^{-2}$$

In the circuit diagram shown in figure given below, the current flowing through resistance 3 $$\Omega$$ is $$\frac{x}{3}$$ A. The value of $$x$$ is _______.

The magnetic field B crossing normally a square metallic plate of area 4 m$$^2$$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $$t = 2$$ s to $$t = 4$$ s, is _______ mV.

The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be $$x$$ : 1. The value of $$x$$ is _______

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $$x \times 10^{15}$$ Hz. The value of x is _______.
(Given $$h = 4.25 \times 10^{-15}$$ eVs)