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Physics

The volume of an ideal gas increases $ 8 $ times and temperature becomes $( \frac{1}{4} $)th of initial temperature during a reversible change. If there is no exchange of heat in this process $ (\Delta Q = 0) $ then identify the gas from the following options (Assuming the gases given in the options are ideal gases):

27.

The minimum frequency of photon required to break a particle of mass $ 15.348 $ amu into $ 4 \alpha $ particles is __________ kHz.
[ mass of He nucleus $=4.002$ amu, $1$ amu $=1.66\times 10^{-27}$ kg, $ h=6.6\times 10^{-34} $ J.s and $ c=3\times 10^{8} $ m/s ]

28.

A meter bridge with two resistances $ R_1 $ and $ R_2 $ as shown in figure was balanced (null point) at $ 40 $ cm from the point $ P $. The null point changed to $ 50 $ cm from the point $ P $, when $ 16\,\Omega $ resistance is connected in parallel to $ R_2 $. The Q. values of resistances $ R_1 $ and $ R_2 $ are __________.

29.

Net gravitational force at the center of a square is found to be $ F_1 $ when four particles having mass $ M, 2M, 3M $ and $ 4M $ are placed at the four corners of the square as shown in figure and it is $ F_2 $ when the positions of $ 3M $ and $ 4M $ are interchanged. The ratio $ \frac{F_1}{F_2} $ is $ \frac{\alpha}{\sqrt{5}} $. The value of $ \alpha $ is __________.

30.

A solid sphere of mass $ 5 \, \text{kg} $ and radius $ 10 \, \text{cm} $ is kept in contact with another solid sphere of mass $ 10 \, \text{kg} $ and radius $ 20 \, \text{cm} $. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is ______ $ \mathrm{kg \, m^2} $.

31.

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

32.

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

33.

A cylindrical tube $ AB $ of length $ l $, closed at both ends contains an ideal gas of $ 1 \, \text{mol} $ having molecular weight $ M $. The tube is rotated in a horizontal plane with constant angular velocity $ \omega $ about an axis perpendicular to $ AB $ and passing through the edge at end $ A $, as shown in the figure. If $ P_{A} $ and $ P_{B} $ are the pressures at $ A $ and $ B $ respectively, then: (Consider the temperature is same at all points in the tube)

34.

Electric field in a region is given by $ \vec{E}=Ax\,\hat{i}+By\,\hat{j} $, where $ A=10 \, \mathrm{V/m^{2}} $ and $ B=5 \, \mathrm{V/m^{2}} $. If the electric potential at a point $ (10,20) $ is $ 500 \, \mathrm{V} $, then the electric potential at origin is ______ $ \mathrm{V} $.

35.

Three identical coils $ C_1 $, $ C_2 $ and $ C_3 $ are closely placed such that they share a common axis. $ C_2 $ is exactly midway. $ C_1 $ carries current $ I $ in anti-clockwise direction while $ C_3 $ carries current $ I $ in clockwise direction. An induced current flows through $ C_2 $ will be in clockwise direction when:

36.

Find the correct combination of $ A $, $ B $, $ C $ and $ D $ inputs which can cause the LED to glow.

37.

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 _______ $ \text{m/s} $. ($ g = $ acceleration due to gravity)

38.

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

39.

A thin convex lens of focal length $ 5 \, \text{cm} $ and a thin concave lens of focal length $ 4 \, \text{cm} $ are combined together (without any gap) and this combination has magnification $ m_1 $ when an object is placed $ 10 \, \text{cm} $ before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of $ 1 \, \text{cm} $ is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to $ m_2 $. The value of $ \left| \dfrac{m_1}{m_2} \right| $ is ________.

40.

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

41.

Six point charges are kept $60^\circ$ apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is ________. ($\epsilon_0$ is permittivity of free space)

42.

Consider an equilateral prism (refractive index $\sqrt{2}$). A ray of light is incident on its one surface at a certain angle $i$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to _________.

43.

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 $\vec{E}$ 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)

44.

$7.9\text{ MeV}$ $\alpha$-particle scatters from a target material of atomic number $79$. From the given data the estimated diameter of nuclei of the target material is (approximately) _________ $\text{m}$.
$\left[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^9\text{ Nm}^2/\text{C}^2 \text{ and electron charge} = 1.6 \times 10^{-19}\text{ C} \right]$

45.

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ dare maintained at $100^\circ\text{C}$ and $40^\circ\text{C}$ respectively. Given the thermal conductivity of rod $x$ is three times of that of rod $y$. the temperature at junction points $B$ and $E$ are (close to):

46.

Two loudspeakers ( $L_1$ and $L_2$ ) are placed with a separation of $10\text{ m}$, 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 $25\text{ m}$ 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 _________ $\text{Hz}$

(Speed of sound in air is $324\text{ m/s}$ and $\sqrt{5} = 2.23$)

47.

Inductance of a coil with $10^4$ turns is $10\text{ mH}$ and it is connected to a dc source of $10\text{ V}$ with internal resistance of $10\ \Omega$. The energy density in the inductor when the current reaches $\left( \frac{1}{\text{e}} \right)$ of its maximum value is $\alpha\pi \times \frac{1}{\text{e}^2}\text{ J/m}^3$. The value of $\alpha$ is _________.
$(\mu_0 = 4\pi \times 10^{-7}\text{ Tm / A})$

48.

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 $ then $ \frac{T_1}{T_2} = \frac{1}{\alpha} $. The value of $ \alpha $ is __________.

49.

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) \, \text{V} / \text{m} $ (where $ x $, $ t $ and other values have S.I units). The dielectric constant of the medium is _______. (speed of light in free space is $ 3 \times 10^8 \, \text{m} / \text{s} $)

50.

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

JEE MAIN 2026 22nd Jan Morning Shift

Mathematics Physics Chemistry

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