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Physics

The given circuit works as:

A parallel plate capacitor has capacitance $C$, when there is vacuum within the parallel plates. A sheet having thickness $\left(\frac{1}{3}\right)^{\text{rd}}$ of the separation between the plates and relative permittivity $K$ is introduced between the plates. The new capacitance of the system is:

28.

A uniform rod of mass $ m $ and length $ l $ suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is __________. $ (g $ acceleration due to gravity$) $.

29.

The electric field in a plane electromagnetic wave is given by:

$E_y = 69 \sin \left[ 0.6 \times 10^3 x - 1.8 \times 10^{11} t \right] \text{V/m}.$

The expression for magnetic field associated with this electromagnetic wave is ________.

30.

A $4\text{ kg}$ mass moves under the influence of a force $\vec{F} = \left( 4t^3\hat{i} - 3t\hat{j} \right)\text{N}$ where $t$ is the time in second. If mass starts from origin at $t = 0$, the velocity and position after $t = 2\text{s}$ will be:

31.

If an alpha particle with energy $ 7.7 \, \text{MeV} $ is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ____________ $ \text{m} $. $ \text{(Atomic number of gold } = 79 \text{ and } \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^{9} \text{ in SI units)} $

32.

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is $ 5 \, \text{cm} $ and the area of cross-sections at A and B are $ 6 \, \text{cm}^{2} $ and $ 3 \, \text{cm}^{2} $ respectively. The rate of flow will be ______________ $ \text{cm}^{3} / \text{s} $. $ \text{(take } g = 10 \, \text{m} / \text{s}^{2} \text{)} $

33.

Consider a modified Bernoulli equation.
$ \left( P + \frac{A}{B t^{2}} \right) + \rho g (h + B t) + \frac{1}{2} \rho v^{2} = \text{constant}. $ If $ t $ has the dimension of time then the dimensions of $ A $ and $ B $ are ______ , ______ respectively.

34.

A point charge of $ 10^{-8} \, \text{C} $ is placed at origin. The work done in moving a point charge $ 2 \, \mu \text{C} $ from point $ A(4, 4, 2) \, \text{m} $ to $ B(2, 2, 1) \, \text{m} $ is ______________ $ \text{J} $. $ \left( \frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} \text{ in SI units} \right) $

35.

A gas based geyser heats water flowing at the rate of $ 5.0 $ litres per minute from $ 27^{\circ}\text{C} $ to $ 87^{\circ}\text{C} $. The rate of consumption of the gas is ____________ $ \text{g}/\text{s} $.
$ \text{(Take heat of combustion of gas } = 5.0 \times 10^{4} \, \text{J}/\text{g} \text{ ) specific heat capacity of water } = 4200 \, \text{J}/\text{kg}\cdot{}^{\circ}\text{C}. $

36.

Two strings $ (A, B) $ having linear densities $ \mu_A = 2 \times 10^{-4} \, \text{kg} / \text{m} $ and $ \mu_B = 4 \times 10^{-4} \, \text{kg} / \text{m} $ and lengths $ L_A = 2.5 \, \text{m} $ and $ L_B = 1.5 \, \text{m} $ respectively are joined. Free ends of $ A $ and $ B $ are tied to two rigid supports $ C $ and $ D $, respectively creating a tension of $ 500 \, \text{N} $ in the wire. Two identical pulses, sent from $ C $ and $ D $ ends, take time $ t_1 $ and $ t_2 $, respectively, to reach the joint. The ratio $ \frac{t_1}{t_2} $ is:

37.

Initially a satellite of $ 100 \, \text{kg} $ is in a circular orbit of radius $ 1.5 R_E $. This satellite can be moved to a circular orbit of radius $ 3 R_E $ by supplying $ \alpha \times 10^{6} \, \text{J} $ of energy. The value of $ \alpha $ is ______________.
$ \big(\text{Take Radius of Earth } R_E = 6 \times 10^{6} \, \text{m} \text{ and } g = 10 \, \text{m}/\text{s}^{2} \big) $

38.

A $ 1 \, \text{m} $ long metal rod $ AB $ completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of $ 0.10 \, \text{T} $. If the resistance of the total circuit is $ 2 \, \Omega $ then the force needed to move the rod towards right with constant speed $ (v) $ of $ 1.5 \, \text{m/s} $ is ______________ $ \text{N} $.

39.

A conducting circular loop of area $ 1.0 \, \text{m}^{2} $ is placed perpendicular to a magnetic field which varies as $ B = \sin(100 \, t) $ Tesla. If the resistance of the loop is $ 100 \, \Omega $, then the average thermal energy dissipated in the loop in one period is ______________ $ \text{J} $.

40.

In a double slit experiment the distance between the slits is $ 0.1 \, \text{cm} $ and the screen is placed at $ 50 \, \text{cm} $ from the slits plane. When one slit is covered with a transparent sheet having thickness $ t $ and refractive index n(= 1.5), the central fringe shifts by $ 0.2 \, \text{cm} $. The value of $ t $ is ______________ $ \text{cm} $.

41.

A light wave described by $ E = 60 \left[ \sin\!\left(3 \times 10^{15} \right) t+ \sin\!\left(12 \times 10^{15} \right)t \right] $ (in SI units) falls on a metal surface of work function $ 2.8 \, \text{eV} $. The maximum kinetic energy of ejected photoelectron is (approximately) ____________ $ \text{eV} $.
$ ( h = 6.6 \times 10^{-34} \, \text{J}\!\cdot\!\text{s}, \text{ and } e = 1.6 \times 10^{-19} \, \text{C} ) $

42.

A current carrying solenoid is placed vertically and a particle of mass $ m $ with charge $ Q $ is released from rest. The particle moves along the axis of solenoid. If $ g $ is acceleration due to gravity then the acceleration $ a $ of the charged particle will satisfy:

43.

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of $ 120 \, \text{cm} $ at $ 30^\circ\text{C} $. The coefficient of linear expansion of aluminium and steel are $ 24 \times 10^{-6} \, / \, ^\circ\text{C} $ and $ 1.2 \times 10^{-5} \, / \, ^\circ\text{C} $, respectively. The length of this composite rod when its temperature is raised to $ 100^\circ\text{C} $, is ________ $ \text{cm} $.

44.

In an experiment the values of two spring constants were measured as $ k_1 = (10 \pm 0.2) \, \text{N/m} $ and $ k_2 = (20 \pm 0.3) \, \text{N/m} $. If these springs are connected in parallel, then the percentage error in equivalent spring constant is:

45.

Potential energy $ (V) $ versus distance $ (x) $ is given by the graph. Rank various regions as per the magnitudes of the force $ (F) $ acting on a particle from high to low.

46.

Two identical thin rods of mass $ M $ $ \text{kg} $ and length $ L $ $ \text{m} $ are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point $ P $ and perpendicular to the plane of the rods is $ \frac{x}{12} \, M L^2 \, \text{kg m}^2 $. The value of $ x $ is _________________.

47.

$ 10 $ mole of oxygen is heated at constant volume from $ 30^\circ\text{C} $ to $ 40^\circ\text{C} $. The change in the internal energy of the gas is __________ $ \text{cal} $. (The molecular specific heat of oxygen at constant pressure, $ C_p = 7 \, \text{cal} / \text{mol}^\circ\text{C} $ and $ R = 2 \, \text{cal}./\text{mol}.^\circ\text{C} $)

48.

In a microscope the objective is having focal length $ f_o = 2 \, \text{cm} $ and eye-piece is having focal length $ f_e = 4 \, \text{cm} $. The tube length is $ 32 \, \text{cm} $. The magnification produced by this microscope for normal adjustment is __________.

49.

A collimated beam of light of diameter $ 2 \, \text{mm} $ is propagating along $ x $-axis. The beam is required to be expanded in a collimated beam of diameter $ 14 \, \text{mm} $ using a system of two convex lenses. If first lens has focal length $ 40 \, \text{mm} $, then the focal length of second lens is __________ $ \text{mm} $.

50.

The heat generated in $ 1 \, \text{minute} $ between points $ A $ and $ B $ in the given circuit, when a battery of $ 9 \, \text{V} $ with internal resistance of $ 1 \, \Omega $ is connected across these points is __________________$ \text{J} $.

JEE Main 2026 21st Jan Morning Shift

Mathematics Physics Chemistry

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The given circuit works as:

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