NTA JEE Mains 6th April Shift 2 2026

Let $$f: \mathbb{R} \to \mathbb{R}$$ be defined as $$f(x) = \dfrac{2x^2 - 3x + 2}{3x^2 + x + 3}$$. Then $$f$$ is :

Consider the quadratic equation $$(n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0, n \in \mathbb{R}$$. Let $$\alpha$$ be the minimum value of the product of its roots and $$\beta$$ be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is $$\alpha$$ and the common ratio is $$\dfrac{\alpha}{\beta}$$, is :

Let $$S = \{z \in \mathbb{C} : z^2 + \sqrt{6}\,iz - 3 = 0\}$$. Then $$\displaystyle\sum_{z \in S} z^8$$ is equal to :

The sum of all possible values of $$\theta \in [0, 2\pi]$$, for which the system of equations :
$$x\cos 3\theta - 8y - 12z = 0$$
$$x\cos 2\theta + 3y + 3z = 0$$
$$x + y + 3z = 0$$
has a non-trivial solution, is equal to :

Let $$A = \begin{bmatrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1 \end{bmatrix}$$ and $$B = [b_{ij}], 1 \le i, j \le 3$$. If $$B = A^{99} - I$$, then the value of $$\dfrac{b_{31} - b_{21}}{b_{32}}$$ is :

The sum $$1 + \dfrac{1}{2}(1^2 + 2^2) + \dfrac{1}{3}(1^2 + 2^2 + 3^2) + \ldots$$ upto 10 terms is equal to :

A building has ground floor and 10 more floors. Nine persons enter a lift at the ground floor. The lift goes up to the 10th floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to :

Let the mean and the variance of seven observations 2, 4, $$\alpha$$, 8, $$\beta$$, 12, 14, $$\alpha < \beta$$, be 8 and 16 respectively. Then the quadratic equation whose roots are $$3\alpha + 2$$ and $$2\beta + 1$$ is :

A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :

Let C be a circle having centre in the first quadrant and touching the $$x$$-axis at a distance of 3 units from the origin. If the circle C has an intercept of length $$6\sqrt{3}$$ on $$y$$-axis, then the length of the chord of the circle C on the line $$x - y = 3$$ is :