NTA JEE Main 9th April 2013 Online

Statement-1: The slope of the tangent at any point P on a parabola, whose axis is the axis of x and vertex is at the origin, is inversely proportional to the ordinate of the point P.
Statement-2: The system of parabolas $$y^2 = 4ax$$ satisfies a differential equation of degree 1 and order 1.

Equation of the line passing through the points of intersection of the parabola $$x^2 = 8y$$ and the ellipse $$\frac{x^2}{3} + y^2 = 1$$ is :

If $$a$$ and $$c$$ are positive real numbers and the ellipse $$\frac{x^2}{4c^2} + \frac{y^2}{c^2} = 1$$ has four distinct points in common with the circle $$x^2 + y^2 = 9a^2$$, then

The value of $$\lim_{x \to 0} \frac{1}{x}\left[\tan^{-1}\left(\frac{x+1}{2x+1}\right) - \frac{\pi}{4}\right]$$ is :

Statement-1: The statement $$A \rightarrow (B \rightarrow A)$$ is equivalent to $$A \rightarrow (A \vee B)$$.
Statement-2: The statement $$\sim [(A \wedge B) \rightarrow (\sim A \vee B)]$$ is a Tautology.

The mean of a data set consisting of 20 observations is 40. If one observation 53 was wrongly recorded as 33, then the correct mean will be:

The matrix $$A^2 + 4A - 5I$$, where $$I$$ is identity matrix and $$A = \begin{bmatrix} 1 & 2 \\ 4 & -3 \end{bmatrix}$$, equals :

If $$a, b, c$$ are sides of a scalene triangle, then the value of $$\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$$ is :

Let $$A = \{1, 2, 3, 4\}$$ and $$R : A \rightarrow A$$ be the relation defined by $$R = \{(1,1), (2,3), (3,4), (4,2)\}$$. The correct statement is :

Let $$f(x) = \frac{x^2 - x}{x^2 + 2x}$$, $$x \neq 0, -2$$. Then $$\frac{d}{dx}\left[f^{-1}(x)\right]$$ (wherever it is defined) is equal to: