NTA JEE Mains 6th April Shift 1 2026 - 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 $$\pm$$ 0.02 g, 8.35 $$\pm$$ 0.05 mm and 20.20 $$\pm$$ 0.02 mm, respectively. Calculated percentage fractional error in $$\rho$$ is _______.

The potential energy of a particle changes with distance $$x$$ from a fixed origin as $$V = \frac{A\sqrt{x}}{x + B}$$, where $$A$$ and $$B$$ are constants with appropriate dimensions. The dimensions of $$AB$$ are _______.

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

Two blocks (P and Q) with respectively masses 2 kg and 1.5 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. Block 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 m/s$$^2$$)

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $$4 \times 10^8$$ N/m$$^2$$ and its radius is 4 mm, then maximum acceleration the lift can take is _______ m/s$$^2$$.
(take g = 10 m/s$$^2$$ and $$\pi$$ = 3.14)

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

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 _______.

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

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 m, then the length of wire $$B$$ is _______ m.

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

In interference experiment the path difference between two interfering waves at a point $$A$$ on the screen is $$\lambda/3$$, where $$\lambda$$ is the wavelength of these waves, and at another point $$B$$ the path difference is $$\lambda/6$$. The ratio of intensities at points $$A$$ and $$B$$ is _______.

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

A thin half ring of radius 35 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 V/m, then the value of $$Q$$ is _______ nC.
$$(\varepsilon_0 = 8.85 \times 10^{-12}$$ C$$^2$$/Nm$$^2$$ and $$\pi = 3.14)$$

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

A point light source emits E.M. waves in free space. A detector, placed at a distance of $$L$$ m, measures 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 _______.

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 _______.

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $$\alpha \times 10^{-14}$$ J. The value of $$\alpha$$ is _______.
$$(\mu_0 = 4\pi \times 10^{-7}$$ Tm/A, $$\pi = 3.14)$$

An inductor of inductance 10 mH having resistance of 100 $$\Omega$$ is connected to battery of E.M.F. 1.0 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 mA and 4 mA is _______.

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

A LCR series circuit driven with $$E_{rms} = 90$$ V at frequency $$f_d = 30$$ 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 _______.

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

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.

The energy released when $$\frac{7}{17.13}$$ kg of $$^7_3$$Li is converted into $$^4_2$$He by proton bombardment is $$\alpha \times 10^{32}$$ eV. The value of $$\alpha$$ is _______. (Nearest integer)
(Mass of $$^7_3$$Li = 7.0183 u, mass of $$^4_2$$He = 4.004 u, mass of proton = 1.008 u and 1 u = 931 MeV/c$$^2$$ and Avogadro number = $$6.0 \times 10^{23}$$)

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

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