NTA JEE Main 9th April 2017 Online

The sum of all the real values of $$x$$ satisfying the equation $$2^{(x-1)(x^2+5x-50)} = 1$$ is:

The equation $$Im\left(\frac{iz - 2}{z - i}\right) + 1 = 0$$, $$z \in \mathbb{C}$$, $$z \neq i$$ represents a part of a circle having radius equal to:

The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy $$B_1$$ and a particular girl $$G_1$$ never sit adjacent to each other, is:

If three positive numbers $$a$$, $$b$$ and $$c$$ are in A.P. such that $$abc = 8$$, then the minimum possible value of $$b$$ is:

Let $$S_n = \frac{1}{1^3} + \frac{1+2}{1^3+2^3} + \frac{1+2+3}{1^3+2^3+3^3} + \ldots + \frac{1+2+\ldots+n}{1^3+2^3+\ldots+n^3}$$. If 100 $$S_n = n$$, then $$n$$ is equal to:

The coefficient of $$x^{-5}$$ in the binomial expansion of $$\left(\frac{x+1}{x^{\frac{2}{3}} - x^{\frac{1}{3}} + 1} - \frac{x-1}{x - x^{\frac{1}{2}}}\right)^{10}$$ where $$x \neq 0, 1$$ is

The lengths of two adjacent sides of a cyclic quadrilateral are 2 units and 5 units and the angle between them is 60°. If the area of the quadrilateral is $$4\sqrt{3}$$ sq. units, then the perimeter of the quadrilateral is

A square, of each side 2, lies above the x-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30° with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is:

A line drawn through the point $$P(4, 7)$$ cuts the circle $$x^2 + y^2 = 9$$ at the points $$A$$ and $$B$$. Then $$P_A \cdot P_B$$ is equal to.

If $$y = mx + c$$ is the normal at a point on the parabola $$y^2 = 8x$$ whose focal distance is 8 units, then $$|c|$$ is equal to: