NTA JEE Main 13th April 2023 Shift 1

Let $$s_1, s_2, s_3, \ldots, s_{10}$$ respectively be the sum of 12 terms of 10 A.P.s whose first terms are $$1, 2, 3, \ldots, 10$$ and the common differences are $$1, 3, 5, \ldots, 19$$ respectively. Then $$\sum_{i=1}^{10} s_i$$ is equal to

Fractional part of the number $$\frac{4^{2022}}{15}$$ is equal to

Let $$PQ$$ be a focal chord of the parabola $$y^2 = 36x$$ of length 100, making an acute angle with the positive $$x-$$axis. Let the ordinate of P be positive and M be the point on the line segment PQ such that $$PM : MQ = 3 : 1$$. Then which of the following points does NOT lie on the line passing through M and perpendicular to the line $$PQ$$?

Let the tangent and normal at the point $$(3\sqrt{3}, 1)$$ on the ellipse $$\frac{x^2}{36} + \frac{y^2}{4} = 1$$ meet the $$y-$$axis at the points $$A$$ and $$B$$ respectively. Let the circle $$C$$ be drawn taking $$AB$$ as a diameter and the line $$x = 2\sqrt{5}$$ intersect $$C$$ at the points P and Q. If the tangents at the points P and Q on the circle intersect at the point $$(\alpha, \beta)$$, then $$\alpha^2 - \beta^2$$ is equal to

The negation of the statement $$((A \wedge (B \vee C)) \Rightarrow (A \vee B)) \Rightarrow A$$ is

The number of symmetric matrices of order 3, with all the entries from the set $$\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$ is

Let $$B = \begin{bmatrix} 1 & 3 & \alpha \\ 1 & 2 & 3 \\ \alpha & \alpha & 4 \end{bmatrix}$$, $$\alpha > 2$$ be the adjoint of a matrix $$A$$ and $$|A| = 2$$. Then $$\begin{bmatrix} \alpha & -2\alpha & \alpha \end{bmatrix} B \begin{bmatrix} \alpha \\ -2\alpha \end{bmatrix}$$ is equal to

For the system of linear equations
$$2x + 4y + 2az = b$$
$$x + 2y + 3z = 4$$
$$2x + 5y + 2z = 8$$
which of the following is NOT correct?

For $$x \in \mathbb{R}$$, two real valued functions $$f(x)$$ and $$g(x)$$ are such that, $$g(x) = \sqrt{x} + 1$$ and $$fog(x) = x + 3 - \sqrt{x}$$. Then $$f(0)$$ is equal to

For the differentiable function $$f : \mathbb{R} - \{0\} - \mathbb{R}$$, let $$3f(x) + 2f\left(\frac{1}{x}\right) = \frac{1}{x} - 10$$, then $$\left|f(3) + f'\left(\frac{1}{4}\right)\right|$$ is equal to