NTA JEE Mains 6th April Shift 1 2026

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 _______.