NTA JEE Main 22nd April 2013 Online

If a circle C passing through (4, 0) touches the circle $$x^2 + y^2 + 4x - 6y - 12 = 0$$ externally at a point (1, -1), then the radius of the circle C is :

Statement-1: The line $$x - 2y = 2$$ meets the parabola, $$y^2 + 2x = 0$$ only at the point (-2, -2).
Statement-2: The line $$y = mx - \frac{1}{2m}$$ ($$m \neq 0$$) is tangent to the parabola, $$y^2 = -2x$$ at the point $$\left(-\frac{1}{2m^2}, -\frac{1}{m}\right)$$

Let the equations of two ellipses be
$$E_1 : \frac{x^2}{3} + \frac{y^2}{2} = 1$$ and $$E_2 : \frac{x^2}{16} + \frac{y^2}{b^2} = 1$$,
If the product of their eccentricities is $$\frac{1}{2}$$, then the length of the minor axis of ellipse $$E_2$$ is :

The statement $$p \rightarrow (q \rightarrow p)$$ is equivalent to :

Mean of 5 observations is 7. If four of these observations are 6, 7, 8, 10 and one is missing, then the variance of all the five observations is :

If two vertices of an equilateral triangle are $$A(-a, 0)$$ and $$B(a, 0)$$, $$a > 0$$, and the third vertex C lies above x-axis then the equation of the circumcircle of $$\triangle ABC$$ is :

Let $$R = \{(3,3)(5,5),(9,9),(12,12),(5,12),(3,9),(3,12),(3,5)\}$$ be a relation on the set $$A = \{3, 5, 9, 12\}$$. Then, R is :

If $$p, q, r$$ are 3 real numbers satisfying the matrix equation, $$[p \ q \ r]\begin{bmatrix} 3 & 4 & 1 \\ 3 & 2 & 3 \\ 2 & 0 & 2 \end{bmatrix} = [3 \ 0 \ 1]$$ then $$2p + q - r$$ equals :

If the system of linear equations :
$$x_1 + 2x_2 + 3x_3 = 6$$
$$x_1 + 3x_2 + 5x_3 = 9$$
$$2x_1 + 5x_2 + ax_3 = b$$
is consistent and has infinite number of solutions, then :

Let $$f(x) = -1 + |x - 2|$$, and $$g(x) = 1 - |x|$$; then the set of all points where $$f \circ g$$ is discontinuous is :