NTA JEE Mains 8th April Shift 2 2026

Consider the relation R on the set $$\{-2, -1, 0, 1, 2\}$$ defined by $$(a, b) \in R$$ if and only if $$1 + ab > 0$$. Then, among the statements :
I. The number of elements in R is 17
II. R is an equivalence relation

The number of values of $$z \in \mathbb{C}$$, satisfying the equations $$|z - (4 + 8i)| = \sqrt{10}$$ and $$|z - (3 + 5i)| + |z - (5 + 11i)| = 4\sqrt{5}$$, is :

If the system of linear equations :
$$x + y + z = 6$$,
$$x + 2y + 5z = 10$$,
$$2x + 3y + \lambda z = \mu$$
has infinitely many solutions, then the value of $$\lambda + \mu$$ equals :

Let $$A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix}$$ and $$B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -5\alpha & 0 \\ 0 & 4\alpha & -2\alpha \end{bmatrix} + \text{adj}(A)$$. If $$\det(B) = 66$$, then $$\det(\text{adj}(A))$$ equals :

Let $$\alpha = 3 + 4 + 8 + 9 + 13 + 14 + ...$$ upto 40 terms. If $$(\tan\beta)^{\frac{\alpha}{1020}}$$ is a root of the equation $$x^2 + x - 2 = 0$$, $$\beta \in \left(0, \frac{\pi}{2}\right)$$, then $$\sin^2\beta + 3\cos^2\beta$$ is equal to :

A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are $$\frac{2}{5}$$, $$\frac{1}{5}$$ and $$\frac{2}{5}$$. The probabilities that the candidate reaches late at the examination centre are $$\frac{1}{5}$$, $$\frac{1}{3}$$ and $$\frac{1}{4}$$ if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is :

A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to :

If $$26\left(\frac{2^3}{3} {^{12} C_{2}} + \frac{2^5}{5} {^{12} C_{4}} + \frac{2^7}{7} {^{12} C_{6}} + \cdots + \frac{2^{13}}{13} {^{12} C_{12}}\right) = 3^{13} - \alpha$$, then $$\alpha$$ is equal to :

A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is :

If a straight line drawn through the point of intersection of the lines $$4x + 3y - 1 = 0$$ and $$3x + 4y - 1 = 0$$, meets the co-ordinate axes at the points P and Q, then the locus of the mid point of PQ is :