NTA JEE Mains 22nd Jan 2026 Shift 1

A projectile is thrown upward at an angle $$60 ^{o}$$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $$45 ^{o}$$ with the horizontal. The initial speed of the projectile is ______ m/s.

$$XPQY$$ is a vertical smooth long loop having a total resistance $$R$$ where $$PX$$ is parallel to $$QY$$ and separation between them is $$l$$. A constant magnetic field $$B$$ perpendicular to the plane of the loop exists in the entire space. A rod $$CD$$ of length $$L (L > l)$$ and mass $$m$$ is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is _______ $$m/s. (g$$ = acceleration due to gravity)

Given below are two statements:

Statement I : Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.

In the light of the above statements, choose the correct answer from the options given below

The escape velocity from a spherical planet $$A$$ is $$10 km/s.$$ The escape velocity from another planet $$B$$ whose density and radius are 10% of those of planet $$A$$, is ______$$m/s.$$

A simple pendulum has a bob with mass $$m$$ and charge $$q$$. The pendulum string has negligible mass. When a uniform and horizontal electric field it is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ______.
($$g$$: acceleration due to gravity)

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,

$$ E_{y}=20 \sin (3\times 10^{6}x - 4.5\times 10^{14}t)V/m $$
(where $$x, t$$ and other values have S.I. units). The dielectric constant of the medium iS_________
(speed oflight in free space is $$ 3\times 10^{8} m/s $$)

Inductance of a coil with $$ 10^{4} $$ tums is $$10 mH$$ and it is connected to a dc source of $$10 V$$ with internal resistance of $$10\Omega $$ The energy density in the inductor when the
current reaches $$ \left( \frac{1}{e} \right) $$ of its maximum value is $$ \alpha\pi \times \frac{1}{e^{2}}J/m^{3} $$. The value of $$ \alpha$$ is_______.
$$ (\mu_{o}=4\pi\times 10^{-7}Tm/A). $$

A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm. Refractive index of glass is 1.5. The rays converge to a point at a distance $$x$$ cm from the centre of the curvature of the spherical surface. The value of $$x$$ is ____ cm

Two loudspeakers $$(L_{1} and L_{2})$$ are placed with a separation of 10 m , as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $$A$$ , at equidistance to both loud speakers, is moved by 25 m along the line $$AB$$ while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is ________Hz
(Speed of sound in air is 324 m/s and $$ \sqrt{5}=2.23 $$)

A circular disc has radius $$R_{1}$$ and thickness $$T_{1}$$. Another circular disc made of the same material has radius $$R_{2} and thickness $$T_{2}. If the moment of inertia of both discs are same and $$ \frac{R_{1}}{R_{2}}=2 \text { then }\frac{T_{1}}{T_{2}}=\frac{1}{\alpha} $$. The value of $$\alpha$$ is__________.