NTA JEE Mains 4th April Shift 1 2026

An insulated wire is wound so that it forms a flat coil with $$N = 200$$ turns. The radius of the innermost turn is $$r_1 = 3$$ cm, and of the outermost turn $$r_2 = 6$$ cm. If 20 mA current flows in it then the magnetic moment will be $$\alpha \times 10^{-2}$$ A·m². The value of $$\alpha$$ is :

Consider a circuit consisting of a capacitor (20 $$\mu$$F), resistor (100 $$\Omega$$) and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is 10 $$\Omega$$. The time constant of the circuit is $$\alpha \times 10^{-3}$$ s. The value of $$\alpha$$ is :

The voltage and the current between A and B points shown in the circuit are :

A telescope with objective diameter $$R$$ is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $$5 \times 10^{-7}$$ radian. The value of $$R$$ is _____ cm.

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

A 1 kg block subjected to two simultaneous forces $$(2\hat{i} + 3\hat{j} + 4\hat{k})$$ N and $$(3\hat{i} - \hat{j} - 2\hat{k})$$ N is moved a distance of 25 m along $$(3\hat{i} - 4\hat{j})$$ direction. The work done in this process is _____ J.

The surface tension of a soap solution is $$3.5 \times 10^{-2}$$ N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $$\alpha \times 10^{-6}$$ J. The value of $$\alpha$$ is _____. $$(\pi = 22/7)$$

The velocity of a particle executing simple harmonic motion along $$x$$-axis is described as $$v^2 = 50 - x^2$$, where $$x$$ represents displacement. If the time period of motion is $$\frac{x}{7}$$ s, the value of $$x$$ is _____.

A body of mass 2 kg begins to move under the influence of time dependent force $$\vec{F} = (2t\hat{i} + 6t^2\hat{j})$$ N, where $$\hat{i}$$ and $$\hat{j}$$ are unit vectors along $$x$$ and $$y$$-axis respectively. The power produced by the force at $$t = 2$$ s is _____ W.

An inductor of 10 mH, capacitor of 0.1 $$\mu$$F and a resistor of 100 $$\Omega$$ are connected in series across an a.c power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitance reactance is $$\sqrt{3}\,\alpha$$ $$\Omega$$. The value of $$\alpha$$ is _____.