NTA JEE Mains 4th April Shift 1 2026

Let $$[\cdot]$$ denote the greatest integer function. If the domain of $$f(x) = \cos^{-1}\left(\frac{4x + 2[x]}{3}\right)$$ is $$[\alpha, \beta]$$, then $$12(\alpha + \beta)$$ is equal to :

If the set of all solutions of $$|x^2 + x - 9| = |x| + |x^2 - 9|$$ is $$[\alpha, \beta] \cup [\gamma, \infty)$$, then $$(\alpha^2 + \beta^2 + \gamma^2)$$ is equal to :

Let $$z$$ be complex such that $$|z + 2| = |z - 2|$$ and $$\arg\left(\frac{z+3}{z-i}\right) = \frac{\pi}{4}$$. Then $$|z|^2$$ is :

The number of functions $$f: \{1,2,3,4\} \to \{a,b,c\}$$, which are not onto, is :

Let $$S = \left\{A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} : a,b,c,d \in \{0,1,2,3,4\} \text{ and } A^2 - 4A + 3I = 0\right\}$$ be a set of $$2 \times 2$$ matrices. Then the number of matrices in $$S$$, for which the sum of the diagonal elements is equal to 4, is :

Let $$A = \begin{bmatrix} 1 & 1 & 2 \\ -2 & 0 & 1 \\ 1 & 3 & 5 \end{bmatrix}$$. Then the sum of all elements of the matrix $$\text{adj}\left(\text{adj}\left(2(\text{adj}\,A)^{-1}\right)\right)$$ is equal to :

The first term of an A.P. of 30 non-negative terms is $$\frac{10}{3}$$. If the sum of the A.P. is the cube of its last term, then its common difference is :

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is :

Let the smallest value of $$k \in \mathbb{N}$$, for which the coefficient of $$x^3$$ in $$(1+x)^3 + (1+x)^4 + \ldots + (1+x)^{99} + (1+kx)^{100}$$, $$x \neq 0$$, is $$\left(43n + \frac{101}{4}\right)\binom{100}{3}$$ for some $$n \in \mathbb{N}$$, be $$p$$. Then the value of $$p + n$$ is :

Suppose that the mean and median of the non-negative numbers $$21, 8, 17, a, 51, 103, b, 13, 67$$, $$(a > b)$$, are 40 and 21, respectively. If the mean deviation about the median is 26, then $$2a$$ is equal to :