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In a vernier callipers, \( 50 \) vernier scale divisions are equal to \( 48 \) main scale divisions. If one main scale division \( = 0.05 \, \text{mm} \), then the least count of the vernier callipers is ____________ \( \text{mm} \).

A cubical block of density \( \rho_b = 600 \, \text{kg/m}^3 \) floats in a liquid of density \( \rho_e = 900 \, \text{kg/m}^3 \). If the height of block is \( H = 8.0 \, \text{cm} \) then height of the submerged part is ________________ \( \text{cm} \).

A thin uniform rod (X) of mass \( M \) and length \( L \) is pivoted at a height \( \left( \dfrac{L}{3} \right) \) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is ____________ . \( (g = \text{gravitational acceleration}) \).

The reading of the ammeter (\( A \)) in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is __________________ \( A \).

In case of vertical circular motion of a particle by a thread of length \( r \) if the tension in the thread is zero at an angle \( 30^{\circ} \) shown in figure, the velocity at the bottom point \( (A) \) of the circular path is: \( (g = \text{gravitational acceleration}) \).

Identify the correct truth table of the given logic circuit.

A flexible chain of mass \( m \) hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is \( 30^\circ \). Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is ____________ .

In the Young’s double slit experiment the intensity produced by each one of the individual slits is \( I_0 \). The distance between two slits is \( 2 \, \text{mm} \). The distance of screen from slits is \( 10 \, \text{m} \). The wavelength of light is \(6000 \mathring A\) . The intensity of light on the screen in front of one the slits is ____________ .

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is \( 3.2 \, \text{V} \). If a second light having wavelength twice of first light is used, the stopping potential drops to \( 0.7 \, \text{V} \). The wavelength of first light is __________ m.
\( (h = 6.63 \times 10^{-34} \, \text{J}\cdot\text{s}, \; e = 1.6 \times 10^{-19} \, \text{C}, \; c = 3 \times 10^{8} \, \text{m/s}) \)

Five persons \( P_1 , P_2 , P_3 , P_4 \) and \( P_5 \) recorded object distance \( (u) \) and image distance \( (v) \) using same convex lens having power \( +5 \, D \) as \( (25, 96) \), \( (30, 62) \), \( (35, 37) \), \( (45, 35) \) and \( (50, 32) \) respectively. Identify correct statement.

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is \( \frac{5}{x} \). The value of \( x \) is __________ .

The binding energy for the following nuclear reactions are expressed in \( \text{MeV} \).
\( {}_{2}\mathrm{He}^{3} + {}_{0}\mathrm{n}^{1} \rightarrow {}_{2}\mathrm{He}^{4} + 20 \, \text{MeV} \)
\( {}_{2}\mathrm{He}^{4} + {}_{0}\mathrm{n}^{1} \rightarrow {}_{2}\mathrm{He}^{5} - 0.9 \, \text{MeV} \)
If \( x_{3}, x_{4}, x_{5} \) denote the stability of \( {}_{2}\mathrm{He}^{3}, {}_{2}\mathrm{He}^{4} \) and \( {}_{2}\mathrm{He}^{5} \), respectively, then the correct order is:

\( 10 \) mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from \( P_1 \) to \( P_2 \) is \( a \) Joule \( ( P_1 = 21.7 \, \text{Pa} \text{ and } P_2 = 30 \, \text{Pa}, \, C_v = 21 \, \text{J} / \text{K} \cdot \text{mol} \, R = 8.3 \, \text{J} / \text{molK} ) \). The value of \( a \) is ________ .

Distance between an object and three times magnified real image is \( 40 \, \text{cm} \). The focal length of the mirror used is _______________ cm.

A moving coil galvanometer of resistance \( 100 \, \Omega \) shows a full scale deflection for a current of \( 1 \, \text{mA} \). The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of \( 5 \, \text{mA} \), is ____________ \( \Omega \).

A regular hexagon is formed by six wires each of resistance \( r \, \Omega \) and the corners are joined to the center by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be:

Two identical circular loops \( P \) and \( Q \) each of radius \( r \) are lying in parallel planes such that they have common axis. The current through \( P \) and \( Q \) are \( I \) and \( 4I \) respectively in clockwise direction as seen from \( O \). The net magnetic field at \( O \) is:

Three parallel plate capacitors each with area \( A \) and separation \( d \) are filled with two dielectric \( (k_1 \text{ and } k_2) \) in the following fashion. Which of the following is true? \( (k_1 > k_2) \).

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by \( 8 \) times, the intensity will:

The velocity \( (v) \) – Distance \( (x) \) graph is shown in figure. Which graph represents acceleration \( (a) \) versus distance \( (x) \) variation of this system.

When \( 300 \, \text{J} \) of heat given to an ideal gas with \( C_{p} = \dfrac{7}{2} R \) its temperature raises from \( 20^\circ \text{C} \) to \( 50^\circ \text{C} \) keeping its volume constant. The mass of the gas is (approximately) __________ \( \text{g} \). \( ( R = 8.314/\text{mol.K} ) \).

In a meter bridge experiment to determine the value of unknown resistance, first the resistance \( 2 \, \Omega \) and \( 3 \, \Omega \) are connected in the left and right gaps of the bridge and the null point is obtained at a distance \( l \) cm from the left. Now when an unknown resistance \( x \, \Omega \) is connected in parallel to \( 3 \, \Omega \) resistance, the null point is shifter by \( 10 \, \text{cm} \) to the right of wire. The value of unknown resistance \( x \) is ________________ \( \Omega \).

A soap bubble of surface tension \( 0.04 \, \text{N/m} \) is blown to a diameter of \( 7 \, \text{cm} \). If \( (15000 - x) \, \mu \text{J} \) of work is done in blowing it further to make its diameter \( 14 \, \text{cm} \), then the value of \( x \) is ____________ . \( \left( \pi = \dfrac{22}{7} \right) \).

A point charge \( q = 1 \, \mu \text{C} \) is located at a distance \( 2 \, \text{cm} \) from one end of a thin insulating wire of length \( 10 \, \text{cm} \) having a charge \( Q = 24 \, \mu \text{C} \), distributed uniformly along its length, as shown in figure. Force between \( q \) and wire is ______________ \( \text{N} \).
(Use: \( \dfrac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} \, \text{N m}^{2} / \text{C}^{2} )\)

A uniform solid cylinder of length \( L \) and radius \( R \) has moment of inertia about its axis equal to \( I_1 \). A small co-centric cylinder of length \( L / 3 \) and radius \( R / 3 \) carved from this cylinder has moment of inertia about its axis equals to \( I_2 \). The ratio \( {I_1}/{I_2} \) is _____________.

JEE Main 2026 24th Jan Evening Shift

Mathematics Physics Chemistry

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Identify the correct truth table of the given logic circuit.