NTA JEE Mains 6th April Shift 1 2026

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

Let one root of the quadratic equation in x:
$$(k^2 - 15k + 27)x^2 + 9(k - 1)x + 18 = 0$$
be twice the other. Then the length of the latus rectum of the parabola $$y^2 = 6kx$$ is equal to:

Let $$e_1$$ and $$e_2$$ be two distinct roots of the equation $$x^2 - ax + 2 = 0$$. Let the sets
$$\{a \in \mathbb{R} : e_1, e_2 \text{ are the eccentricities of hyperbolas}\} = (\alpha, \beta)$$, and
$$\{a \in \mathbb{R} : e_1, e_2 \text{ are the eccentricities of an ellipse and a hyperbola, respectively}\} = (\gamma, \infty)$$.
Then $$\alpha^2 + \beta^2 + \gamma^2$$ is equal to:

Let the set of all values of $$k \in \mathbb{R}$$ such that the equation $$z(\bar{z} + 2 + i) + k(2 + 3i) = 0$$, $$z \in \mathbb{C}$$, has at least one solution, be the interval $$[\alpha, \beta]$$. Then $$9(\alpha + \beta)$$ is equal to:

The value of $$1^3 - 2^3 + 3^3 - ... + 15^3$$ is:

The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is:

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:

If the coefficients of the middle terms in the binomial expansions of $$(1 + \alpha x)^{26}$$ and $$(1 - \alpha x)^{28}$$, $$\alpha \neq 0$$, are equal, then the value of $$\alpha$$ is:

A data consists of 20 observations $$x_1, x_2, ..., x_{20}$$. If $$\sum_{i=1}^{20}(x_i + 5)^2 = 2500$$ and $$\sum_{i=1}^{20}(x_i - 5)^2 = 100$$, then the ratio of mean to standard deviation of this data is:

A bag contains (N + 1) coins - N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is $$\frac{9}{16}$$, then N is equal to: