NTA JEE Main 13th April 2023 Shift 1

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $$\pi : 22$$ then, the value of its angular speed will be _____ rad s$$^{-1}$$.

The elastic potential energy stored in a steel wire of length $$20$$ m stretched through $$2$$ cm is $$80$$ J. The cross sectional area of the wire is _____ mm$$^2$$. (Given, $$Y = 2.0 \times 10^{11}$$ N m$$^{-2}$$)

At a given point of time the value of displacement of a simple harmonic oscillator is given as $$y = A \cos(30°)$$. If amplitude is $$40$$ cm and kinetic energy at that time is $$200$$ J, the value of force constant is $$1.0 \times 10^x$$ N m$$^{-1}$$. The value of $$x$$ is _____.

A thin infinite sheet charge and an infinite line charge of respective charge densities $$+\sigma$$ and $$+\lambda$$ are placed parallel at $$5$$ m distance from each other. Points P and Q are at $$\frac{3}{\pi}$$ m and $$\frac{4}{\pi}$$ m perpendicular distances from line charge towards sheet charge, respectively. $$E_P$$ and $$E_Q$$ are the magnitudes of resultant electric field intensities at point P and Q respectively. If $$\frac{E_P}{E_Q} = \frac{4}{a}$$ for $$2|\sigma| = |\lambda|$$, then the value of $$a$$ is _____.

A potential $$V_0$$ is applied across a uniform wire of resistance $$R$$. The power dissipation is $$P_1$$. The wire is then cut into two equal halves and a potential of $$V_0$$ is applied across the length of each half. The total power dissipation across two wires is $$P_2$$. The ratio of $$P_2 : P_1$$ is $$\sqrt{x} : 1$$. The value of $$x$$ is _____.

When a resistance of $$5 \ \Omega$$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of $$250$$ mA, however when $$1050 \ \Omega$$ resistance is connected with it in series, it gives full scale deflection for $$25$$ volt. The resistance of galvanometer is _____ $$\Omega$$.

In the given figure, an inductor and resistor are connected in series with a battery of emf $$E$$ volt. $$\frac{E^a}{2b}$$ J s$$^{-1}$$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $$\frac{b}{a}$$ will be _____.

A fish rising vertically upward with a uniform velocity of $$8$$ m s$$^{-1}$$, observes that a bird is diving vertically downward towards the fish with the velocity of $$12$$ m s$$^{-1}$$. If the refractive index of water is $$\frac{4}{3}$$, then the actual velocity of the diving bird to pick the fish, will be _____ m s$$^{-1}$$.

The radius of 2$$^{\text{nd}}$$ orbit of He$$^+$$ of Bohr's model is $$r_1$$ and that of fourth orbit of Be$$^{3+}$$ is represented as $$r_2$$. Now the ratio $$\frac{r_2}{r_1}$$ is $$x : 1$$. The value of $$x$$ is _____.

From the given transfer characteristic of a transistor in CE configuration, the value of power gain of this configuration is $$10^x$$, for $$R_B = 10$$ k$$\Omega$$, and $$R_C = 1$$ k$$\Omega$$. The value of $$x$$ is _____.