NTA JEE Main 10th April 2016 Online

Equation of the tangent to the circle, at the point $$(1, -1)$$, whose center is the point of intersection of the straight lines $$x - y = 1$$ and $$2x + y = 3$$ is:

$$P$$ and $$Q$$ are two distinct points on the parabola, $$y^2 = 4x$$, with parameters $$t$$ and $$t_1$$, respectively. If the normal at $$P$$ passes through $$Q$$, then the minimum value of $$t_1^2$$, is

A hyperbola whose transverse axis is along the major axis of the conic $$\frac{x^2}{3} + \frac{y^2}{4} = 4$$ and has vertices at the foci of the conic. If the eccentricity of the hyperbola is $$\frac{3}{2}$$, then which of the following points does not lie on the hyperbola?

$$\lim_{x \to 0} \frac{(1 - \cos 2x)^2}{2x\tan x - x\tan 2x}$$ is

The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is

The mean of 5 observations is 5 and their variance is 12.4. If three of the observations are 1, 2 & 6; then the value of the remaining two is:

The angle of elevation of the top of a vertical tower from a point A, due east of it is 45°. The angle of elevation of the top of the same tower from a point B, due south of A is 30°. If the distance between A and B is $$54\sqrt{2}$$ m, then the height of the tower (in meters), is:

Let $$A$$, be a $$3 \times 3$$ matrix, such that $$A^2 - 5A + 7I = O$$.
Statement - I: $$A^{-1} = \frac{1}{7}(5I - A)$$.
Statement - II: The polynomial $$A^3 - 2A^2 - 3A + I$$, can be reduced to $$5(A - 4I)$$. Then:

If $$A = \begin{bmatrix} -4 & -1 \\ 3 & 1 \end{bmatrix}$$, then the determinant of the matrix $$(A^{2016} - 2A^{2015} - A^{2014})$$ is:

Let $$a, b \in R$$, $$(a \neq 0)$$. If the function $$f$$, defined as
$$f(x) = \begin{cases} \frac{2x^2}{a}, & 0 \leq x \lt 1 \\ a, & 1 \leq x \lt \sqrt{2} \\ \frac{2b^2 - 4b}{x^3}, & \sqrt{2} \leq x \lt 8 \end{cases}$$
is continuous in the interval $$[0, \infty)$$, then an ordered pair $$(a, b)$$ can be