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Physics

The density \( \rho \) of a uniform cylinder is determined by measuring its mass \( m \), length \( l \) and diameter \( d \). The measured values of \( m \), \( l \) and \( d \) are \( 97.42\pm0.02 \, \text{g} \), \( 8.35\pm0.05 \, \text{mm} \) and \( 20.20\pm0.02 \, \text{mm} \), respectively. Calculated percentage fractional error in \( \rho \) is ______.

27.

The potential energy of a particle changes with distance \( x \) from a fixed origin as \( V=\dfrac{A\sqrt{x}}{x+B} \), where \( A \) and \( B \) are constant with appropriate dimensions. The dimensions of \( AB \) are ______.

28.

The rain drop of mass \( 1\,\text{g} \) starts with zero velocity from a height of \( 1 \,\text{km} \). It hits the ground with a speed of \( 5\,\text{m/s} \). The work done by the unknown resistive force is ______ \( \text{J} \). (Take \( g=10\,\text{m/s}^2 \))

29.

Two blocks \( (P \text{ and } Q) \) with respectively masses \( 2 \,\text{kg} \) and \( 1.5 \,\text{kg} \) are joined by a massless thread. These blocks are mounted on a frictionless pully which is fixed on the edge of a cube \( (S) \), as shown in the figure below. Below \( P \) is positioned on the top surface which has no friction and block \( Q \) is in contact with side-surface, having coefficient friction \( \mu \). The cube \( (S) \) moves towards the right with acceleration of \( \frac{g}{2} \), where \( g \) is gravitational acceleration. During this movement the block \( P \) and \( Q \) remain stationary. The value of \( \mu \) is ______. (take \( g=10\,\text{m/s}^2 \))

30.

A lift of mass \( 1600 \, \text{kg} \) is supported by thick iron wire. If the maximum stress which the wire can withstand is \( 4 \times 10^8 \, \text{N}/\text{m}^2 \) and its radius is \( 4 \, \text{mm} \), then maximum acceleration the lift can take is _____ \( \text{m}/\text{s}^2 \).

(take \( g = 10 \, \text{m}/\text{s}^2 \) and \( \pi = 3.14 \))

31.

A solid sphere of radius \( 4 \, \text{cm} \) and mass \( 5 \, \text{kg} \) is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of \( 1200 \, \text{rpm} \). It is brought to rest in \( 10 \, \text{s} \) by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are ______ and ______ respectively.

32.

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height \( h \) as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height \( h = \alpha R \). The value of \( \alpha \) is:

33.

The position of center of mass of three masses \( 2 \, \text{kg} \), \( 3 \, \text{kg} \) and \( 15 \, \text{kg} \) placed with respect to mid point \( (p) \) of normal bisector, as shown in the figure is ______.

34.

The two wires \( A \) and \( B \) of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire \( A \) and wire \( B \) is \( 20/11 \). When the joined wire is kept under certain tension the elongations in the wires \( A \) and \( B \) are equal. If the length of wire \( A \) is \( 2.2 \, \text{m} \), then the length of wire \( B \) is ______ \( \text{m} \).

35.

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure \( 90 \, \text{kPa} \) and temperature \( 400 \, \text{K} \). Keeping the temperature of one vessel constant at \( 400 \, \text{K} \) the second vessel temperature is raised to \( 500 \, \text{K} \). The final pressure in the vessels is _____ \( \text{kPa} \).

36.

In interference experiment the path difference between two interfering waves at a point A on the screen is \( \frac{\lambda}{3} \), where \( \lambda \) is the wavelength of these waves, and at another point B the path difference is \( \frac{\lambda}{6} \). The ratio of intensities at points A and B is ______.

37.

A particle is executing simple harmonic motion. Its amplitude is \( A \) and time period is \( 5 \, \text{sec} \). The time required by it to move from \( x = A \) to \( x = \frac{A}{\sqrt{2}} \) is _____ \( \text{sec} \).

38.

A thin half ring of radius \( 35 \, \text{cm} \) is uniformly charged with a total charge of \( Q \) coulomb. If the magnitude of the electric field at centre of the half ring is \( 100 \, \text{V/m} \), then the value of \( Q \) is _____ \( \text{nC} \). \( (\varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 / \text{Nm}^2 \) and \( \pi = 3.14) \)

39.

The maximum rated power of the LED is \( 2 \, \text{mW} \) and it is used in the circuit with input voltage of \( 5 \, \text{V} \) as shown in the figure below. The current through resistance \( R_S \) is \( 0.5 \, \text{mA} \). The minimum value of the resistance of \( R_S \), to ensure that the LED is not damaged is _____ \( \text{k}\Omega \).

40.

A point light source emits E.M. waves in free space. A detector, placed at a distance of \( L \, \text{m} \), measure the intensity as \( I_0 \). The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as \( 45^\circ \). The measured intensity at new location will be ______.

41.

A spherical interface lens of radius \( R \) separates two media of refractive indices \( 1 \) and \( 1.4 \) respectively as shown in the figure below. A point source is placed at a distance of \( 4R \) in front of spherical interface. The magnitude of the magnification of point source image is _____.

42.

A small cube of side \( 1 \, \text{mm} \) is placed at the centre of a circular loop of radius \( 10 \, \text{cm} \) carrying a current of \( 2 \, \text{A} \). The magnetic energy stored inside the cube is \( \alpha \times 10^{-14} \, \text{J} \). The value of \( \alpha \) is _____.
\( (\mu_{0}=4\pi \times 10^{-7} \, \text{T m/A} , \ \pi = 3.14) \)

43.

An inductor of inductance \( 10 \, \text{mH} \) having resistance of \( 100\Omega \) is connected to battery of E.M.F. \( 1.0 \, \text{V} \) through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is \( 2 \, \text{mA} \) and \( 4 \, \text{mA} \) is _____.

44.

The ratio of momentum of the photons of the \( 1^{\text{st}} \) and \( 2^{\text{nd}} \) line of Balmer series of Hydrogen atoms is \( \alpha / \beta \). The possible values of \( \alpha \) and \( \beta \) are:

45.

A LCR series circuit driven with \( E_{\text{rms}}=90 \, \text{V} \) at frequency \( f_{d}=30 \, \text{Hz} \) has resistance \( R=80\Omega \), an inductance with inductive reactance \( X_{L}=20.0\Omega \) and capacitance with capacitive reactance \( X_{C}=80.0\Omega \). The power factor of the circuit is ____.

46.

Refer to the circuit diagram given below. The heat generated across the \( 6\Omega \) resistance in \( 100 \) second is \( \dfrac{\alpha}{100} \, \text{J} \). The value of \( \alpha \) is ______. (Nearest integer)

47.

An unpolarized light of intensity \( I_0 \) passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is \( 0^\circ \) and intensity of light emerged from analyser is \( \frac{3}{8} I_0 \), the angle of rotation of the light by the solution with respect to analyser is ______ degrees.

48.

The energy released when \( \frac{7}{17.13} \) \( \text{kg} \) of \( {}^{7}_{3}\mathrm{Li} \) is converted into \( {}^{4}_{2}\mathrm{He} \) by proton bombardment is \( \alpha \times 10^{32} \) \( \text{eV} \). The value of \( \alpha \) is _______. (Nearest integer) (Mass of \( {}^{7}_{3}\mathrm{Li} = 7.0183\,u \), mass of \( {}^{4}_{2}\mathrm{He} = 4.0004\,u \), mass of proton \( = 1.008\,u \) and \( 1u = 931\,\mathrm{MeV}/c^{2} \) and Avogadro number \( = 6.0 \times 10^{23} \))

49.

A three coulomb charge moves from the point \( (0,-2,-5) \) to the point \( (5,1,2) \) in an electric field expressed as \( \vec{E} = 2x\,\hat{i} + 3y^{2}\,\hat{j} + 4\,\hat{k}\ \mathrm{N/C} \). The work done in moving the charge is ______ \( \text{J} \).

50.

A certain gas is isothermally compressed to \( \left( \frac{1}{3} \right)^{\text{rd}} \) of its initial volume \( (V_0 = 3\,\text{litre}) \) by applying required pressure. If the bulk modulus of the gas is \( 3 \times 10^{5}\ \mathrm{N/m^{2}} \), the magnitude of work done on the gas is ______ \( \text{J} \).

JEE Main 2026 6th April Morning Shift

Mathematics Physics Chemistry

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A thin half ring of radius \( 35 \, \text{cm} \) is uniformly charged with a total charge of \( Q \) coulomb. If the magnitude of the electric field at centre of the half ring is \( 100 \, \text{V/m} \), then the value of \( Q \) is _____ \( \text{nC} \). \( (\varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 / \text{Nm}^2 \) and \( \pi = 3.14) \)

JEE MainsJEE AdvanceBITSATJEE Mains | PYQ

JEE Mains JEE Advance BITSAT
JEE Mains | PYQ