NTA JEE Main 7th April 2013 Online

The circle passing through (1, -2) and touching the axis of $$x$$ at (3, 0) also passes through the point

Given : A circle, $$2x^2 + 2y^2 = 5$$ and a parabola, $$y^2 = 4\sqrt{5}x$$.
Statement - I : An equation of a common tangent to these curves is $$y = x + \sqrt{5}$$.
Statement - II : If the line, $$y = mx + \frac{\sqrt{5}}{m}$$ $$(m \neq 0)$$ is their common tangent, then $$m$$ satisfies $$m^4 - 3m^2 + 2 = 0$$.

The equation of the circle passing through the foci of the ellipse $$\frac{x^2}{16} + \frac{y^2}{9} = 1$$, and having centre at (0, 3) is

The value of $$\lim_{x \to 0} \frac{(1 - \cos 2x)(3 + \cos x)}{x \tan 4x}$$ is equal to

Consider :
Statement - I : $$(p \wedge \sim q) \wedge (\sim p \wedge q)$$ is a fallacy.
Statement - II : $$(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$$ is a tautology.

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

$$ABCD$$ is a trapezium such that $$AB$$ and $$CD$$ are parallel and $$BC \perp CD$$. If $$\angle ADB = \theta$$, $$BC = p$$ and $$CD = q$$, then $$AB$$ is equal to

Let $$A$$ and $$B$$ be two sets containing 2 elements and 4 elements respectively. The number of subsets of $$A \times B$$ having 3 or more elements is :

If $$P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$$ is the adjoint of a $$3 \times 3$$ matrix $$A$$ and $$|A| = 4$$, then $$\alpha$$ is equal to

The number of values of $$k$$, for which the system of equations :
$$(k+1)x + 8y = 4k$$
$$kx + (k+3)y = 3k - 1$$
has no solution, is :