NTA JEE Main 16 th April 2018 Online

Let p, q and r be real numbers ($$p \neq q, r \neq 0$$), such that the roots of the equation $$\frac{1}{x+p} + \frac{1}{x+q} = \frac{1}{r}$$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to:

If an angle A of a $$\triangle ABC$$ satisfies $$5\cos A + 3 = 0$$, then the roots of the quadratic equation $$9x^2 + 27x + 20 = 0$$ are:

The least positive integer n for which $$\left(\frac{1 + i\sqrt{3}}{1 - i\sqrt{3}}\right)^n = 1$$ is:

The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is:

Let $$\frac{1}{x_1}, \frac{1}{x_2}, \ldots, \frac{1}{x_n}$$ ($$x_i \neq 0$$ for i = 1, 2, ..., n) be in A.P. such that $$x_1 = 4$$ and $$x_{21} = 20$$. If n is the least positive integer for which $$x_n \gt 50$$, then $$\sum_{i=1}^{n}\left(\frac{1}{x_i}\right)$$ is equal to:

The sum of the first 20 terms of the series $$1 + \frac{3}{2} + \frac{7}{4} + \frac{15}{8} + \frac{31}{16} + \ldots$$ is:

The coefficient of $$x^2$$ in the expansion of the product $$(2 - x^2)\left\{(1 + 2x + 3x^2)^6 + (1 - 4x^2)^6\right\}$$ is:

The locus of the point of intersection of the lines $$\sqrt{2}x - y + 4\sqrt{2}k = 0$$ and $$\sqrt{2}kx + ky - 4\sqrt{2} = 0$$ (k is any non-zero real parameter) is:

If a circle C, whose radius is 3, touches externally the circle $$x^2 + y^2 + 2x - 4y - 4 = 0$$ at the point (2, 2), then the length of the intercept cut by this circle C on the x-axis is equal to:

Let P be a point on the parabola $$x^2 = 4y$$. If the distance of P from the center of the circle $$x^2 + y^2 + 6x + 8 = 0$$ is minimum, then the equation of the tangent to the parabola at P is: