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Physics

A particle of mass $ m $ falls from rest though a resistive medium having resistive force, $ F = -kv $, where $ v $ is the velocity of the particle and $ k $ is a constant. Which of the following graphs represents velocity $ (v) $ versus time $ (t) $?

27.

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $ -20^\circ \text{C} $ to $ 120^\circ \text{C} $?

28.

Two circular discs of radius each $ 10 \, \text{cm} $ are joined at their centres by a rod of length $ 30 \, \text{cm} $ and mass $ 600 \, \text{gm} $ as shown in figure. If the mass of each disc is $ 600 \, \text{gm} $ and applied torque between two discs is $ 43 \times 10^{5} \, \text{dyne}\!\cdot\!\text{cm} $, the angular acceleration of the discs about the given axis $ AB $ is _________ $ \text{rad}/ \text{s}^{2} $.

29.

$ 10 \, \text{kg} $ of ice at $ -10^\circ \text{C} $ is added to $ 100 \, \text{kg} $ of water to lower its temperature from $ 25^\circ \text{C} $. Consider no heat exchange to surroundings. The decrement to the temperature of water is _________ $ ^\circ \text{C} $. (specific heat of ice $ = 2100 \, \text{J/kg}\!\cdot\!^\circ \text{C} $, specific heat of water $ = 4200 \, \text{J/kg}\!\cdot\!^\circ \text{C} $, latest heat of fusion of ice $ = 3.36 \times 10^{5} \, \text{J} / \text{kg} $ )

30.

For the two cells having same EMF $ E $ and internal resistance $ r $, the current passing through the external resistor $ 6\,\Omega $ is same when both the cells are connected either in parallel or in series. The value of internal resistance $ r $ is __________ $ \Omega $.

31.

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by $ 15 \, \text{cm} $ length of wire $ Q $ is ________________ . $ (\mu_{0} = 4\pi \times 10^{-7} \, \text{T}\!\cdot\!\text{m}/\text{A}) $

32.

Assuming in forward bias condition there is a voltage drop of $ 0.7 \, \text{V} $ across a silicon diode, the current through diode $ D_1 $ in the circuit is ________ $ \text{ma} $. (Assume all diodes in the given circuit are identical)

33.

Water drops fall from a tap on the floor, $ 5 \, \text{m} $ below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ________ $ \text{m} $. $ (g = 10 \, \text{m} / \text{s}^2) $

34.

The electric current in the circuit is given as $ i = i_0 \left( \dfrac{t}{T} \right) $. The r.m.s current for the period $ t = 0 $ to $ t = T $ is _________.

35.

The magnitudes of power of a biconvex lens (refractive index $ 1.5 $) and that of a plano-concave lens (refractive index $ = 1.7 $) are same. If the curvature of plano-concave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is ____________.

36.

The electric field of an electromagnetic wave travelling through a medium is given by $ \vec{E}(x,t) = 25 \sin \left( 2.0 \times 10^{15} t - 10^{7} x \right) \, \hat{n} $ then the refractive index of the medium is ________. (All given measurement are in SI units)

37.

Given below are two statements:
Statement I : A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave.
Statement II: The curvature of a spherical wave emerging from a slit will increase for increasing slit width.
In the light of the above statements, choose the correct answer from the options given below:

38.

An atom $ {}^{8}_{3}X $ is bombarded by shower of fundamental particles and in $ 10 \, \text{s} $ this atom absorbed $ 10 $ electrons, $ 10 $ protons and $ 9 $ neutrons. The percentage growth in the surface area of the nucleons is recorded by:

39.

In the potentiometer, when the cell in the secondary circuit is shunted with $ 4\Omega $ resistance, the balance is obtained at the length $ 120 \, \text{cm} $ of wire. Now when the same cell is shunted with $ 12\Omega $ resistance, the balance is shifted to a length of $ 180 \, \text{cm} $. The internal resistance of cell is ________ $ \Omega $.

40.

Two point charges of $ 1 \, \text{nC} $ and $ 2 \, \text{nC} $ are placed at the two corners of equilateral triangle of side $ 3 \, \text{cm} $. The work done in bringing a charge of $ 3 \, \text{nC} $ from infinity to the third corner of the triangle is ________ $ \mu \text{J} $.
$ \dfrac{1}{4\pi\varepsilon_{0}} = 9 \times 10^{9} \, \text{N}\cdot\text{m}^{2}\,/\text{C}^{2} $

41.

A block of mass $ 5 \, \text{kg} $ is moving on an inclined plane which makes an angle of $ 30^{\circ} $ with the horizontal. Friction coefficient between the block and inclined plane surface is $ \dfrac{\sqrt{3}}{2} $. The force to be applied on the block so that the block will move down without acceleration is________ $ \text{N} $. $ (g = 10 \, \text{m}/\text{s}^{2}) $.

42.

In the following $ p\! -\! V $ diagram the equation of state along the curved path is given by $ (V - 2)^{2} = 4 a p $ where $ a $ is a constant. The total work done in the closed path is:

43.

Two wires A and B made of different materials of lengths $ 6.0 \, \text{cm} $ and $ 5.4 \, \text{cm} $, respectively and area of cross sections $ 3.0 \times 10^{-5} \, \text{m}^{2} $ and $ 4.5 \times 10^{-5} \, \text{m}^{2} $, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is $ x : 3 $. The value of $ x $ is $ \underline{\phantom{0}} $.

44.

The magnetic field at the centre of a current carrying circular loop of radius $ R $ is $ 16 \, \mu \text{T} $. The magnetic field at a distance $ x = \sqrt{3} R $ on its axis from the centre is ______ $ \mu \text{T} $.

45.

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, $ 4^{\text{th}} $ mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes $ 15 $ divisions on main scale and $ 5^{\text{th}} $ division of vernier scale coincides with a main scale division. Measured length of cylinder is ________ $ \text{mm} $. (Least count of Vernier calliper = $ 0.1 \, \text{mm} $)

46.

A solid sphere of radius $ 10 \, \text{cm} $ is rotating about an axis which is at a distance $ 15 \, \text{cm} $ from its centre. The radius of gyration about this axis is $ \sqrt{n} \, \text{cm} $. The value of $ n $ is __________.

47.

A convex lens of refractive index $ 1.5 $ and focal length $ f = 18 \, \text{cm} $ is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is $ \alpha \times f $. The value of $ \alpha $ is __________. (refractive index of water $ = \frac{4}{3} $)

48.

The displacement of a particle, executing simple harmonic motion with time period $ T $, is expressed as $ x(t) = A \sin \omega t $, where $ A $ is the amplitude. The maximum value of potential energy of this oscillator is found at $ t = \frac{T}{2\beta} $. The value of $ \beta $ is __________.

49.

The equivalent resistance between the points $ A $ and $ B $ in the following circuit is $ \frac{x}{5} \, \Omega $. The value of $ x $ is ________.

50.

The ratio of de Broglie wavelength of a deutron with kinetic energy $E$ to that of an alpha particle with kinetic energy $2E$, is $n : 1$. The value of $n$ is ______________.

(Assume mass of proton = mass of neutron) :

JEE MAIN 2026 28TH Jan Morning Shift

Mathematics Physics Chemistry

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The equivalent resistance between the points $ A $ and $ B $ in the following circuit is $ \frac{x}{5} \, \Omega $. The value of $ x $ is ________.

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JEE Mains JEE Advance BITSAT
JEE Mains | PYQ