NTA JEE Mains 5th April Shift 2 2026

Let $$A = \{1, 4, 7\}$$ and $$B = \{2, 3, 8\}$$.  Then the number of elements, in the relation $$R = \{((a_1, b_1), (a_2, b_2)) \in (A \times B) \times (A \times B) : a_1 + b_2 \text{ divides } a_2 + b_1\}$$. is :

From the point $$(-1, -1)$$, two rays are sent making angle  of $$45°$$ with the line $$x + y = 0$$. The rays get reflected from the mirror $$x + 2y = 1$$. If the equations of the reflected rays are $$ax + by = 9$$ and $$cx + dy = 7$$,$$a,b,c,d \in \mathbb{Z}$$ thenthe value of  $$ad + bc$$ is :

Let $$S = \left\{\theta \in [-\pi, \pi] : \cos\theta \cos\left(\frac{5\theta}{2}\right) = \cos 7\theta \cos\left(\frac{7\theta}{2}\right)\right\}$$. Then $$n(S)$$ is equal to :

Let $$f : \mathbb{R} \to \mathbb{R}$$ be a function such that $$f(x) + 3f\left(\frac{\pi}{2} - x\right) = \sin x, x \in R$$.Let  the maximum value of $$f$$ on $$\mathbb{R}$$ be  $$\alpha$$. The area of the region bounded by the curves $$g(x) = x^2$$ and $$h(x) = \beta x^3$$, $$\beta > 0$$, is $$\alpha^2$$. Then $$30\beta^3$$ is equal to :

Let $$y = y(x)$$ be the solution of $$(\tan x)^{1/2}\,dy = (\sec^3 x - (\tan x)^{3/2}\,y)\,dx$$, $$0 < x < \frac{\pi}{2}$$. If $$y\left(\frac{\pi}{4}\right) = \frac{6\sqrt{2}}{5}$$, and $$y\left(\frac{\pi}{3}\right) = \frac{4}{5}\alpha$$, then $$\alpha^4$$ is equal to :

Match the List I With List II:

Where (Plank's constant), G(gravitational constant) and c (speed of light in vacuum) as fundamental units.
Choose the  correct answer from the options given below:

In an experiment to determine the resistance of a given wire using Ohm’s law, the voltmeter and ammeter readings are noted as $$10 V$$ and $$5 A$$, respectively. The least counts of voltmeter and ammeter are $$500 mV$$ and $$200 mA$$, respectively. The estimated error in the resistance measurement  is_______Ω.

A mass of 1 kg is kept on a inclined plane with 30° inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of 4 m/s. The work done by the frictional force in time 2 s is ________ J. (Take g = 10 m/s²)

The velocity (v) versus time (t) plot of a particle is shown in the figure, for a time interval of 40 s. The total distance travelled by the particle and the and the average velocity during this period are, respectively___________, 

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s  it rotates through an angle $$\theta_1$$. In the next 2 s it rotates through an angle $$\theta_2$$. Then ratio $$\frac{\theta_2}{\theta_1}$$ is :