NTA JEE Mains 4th April Shift 1 2026

The two projectiles are projected with the same initial velocities at the $$15°$$ and $$30°$$ with respect to the horizontal. The ratio of their ranges is $$1:x$$. The value of $$x$$ is :

The graph shows variation of stopping potential $$V_0$$ with the frequency $$\nu$$ of the incident radiation for three photosensitive metals $$X_1$$, $$X_2$$ and $$X_3$$. Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation?

A slit of width $$a$$ is illuminated by light of wavelength $$\lambda$$. The linear separation between 1st and 3rd minima in the diffraction pattern produced on a screen placed at a distance $$D$$ from the slit system is :

A string A of length 0.314 m and Young's modulus $$2 \times 10^{10}$$ N/m² is connected to another string B of length and Young's modulus both twice of those of A. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg. The net change in length of the combination is _____ mm.
(radius of both the strings is 0.2 mm and acceleration due to gravity = 10 $$m/s^{2}$$) 
(Mass of both strings is to be neglected as compared to the mass of load )

One gas of $$n_1$$ mole of molecules at temperature $$T_1$$, volume $$V_1$$, and pressure $$P_1$$, and another gas of $$n_2$$ mole of molecules at temperature $$T_2$$, volume $$V_2$$, and pressure $$P_2$$, are mixed resulting in pressure $$P$$ and volume $$V$$ of the mixture. The temperature of the mixture is :

An ideal gas undergoes a process maintaining relation between pressure $$(P)$$ and volume $$(V)$$ as $$P = P_0\left(1 + \left(\frac{V_0}{V}\right)^2\right)^{-1}$$, where $$P_0$$ and $$V_0$$ are constants. If two samples A and B (two moles each) with initial volumes $$V_0$$ and $$3V_0$$ respectively undergo above mentioned process and attain same pressure, then the difference of the temperatures of these samples, $$T_B - T_A$$ is :
(R = gas constant)

A voltmeter with internal resistance of $$x \; \Omega$$ can be used to measure upto 20 V. In order to increase its measuring range to 30 V, the required modification is :

Two 4 bits binary numbers, $$A = 1101$$ and $$B = 1010$$ are given in the inputs of a logic circuit shown in figure below . The output $$(Y)$$ will be :

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is _____ cm.

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $$v$$. If $$x$$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $$x^{\alpha}$$, where $$\alpha$$ is :