NTA JEE Main 4th April 2015 Offline

Let $$\alpha$$ and $$\beta$$ be the roots of equation $$x^2 - 6x - 2 = 0$$. If $$a_n = \alpha^n - \beta^n$$, $$\forall n \geq 1$$, then the value of $$\frac{a_{10} - 2a_8}{2a_9}$$ is equal to

A complex number $$z$$ is said to be unimodular if $$|z| = 1$$. Let $$z_1$$ and $$z_2$$ are complex numbers such that $$\frac{z_1 - 2z_2}{2 - z_1\bar{z_2}}$$ is unimodular and $$z_2$$ is not unimodular, then the point $$z_1$$ lies on a

The number of integers greater than 6000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition is

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0) is

Let $$A$$ and $$B$$ be two sets containing four and two elements respectively. Then the number of subsets of the set $$A \times B$$, each having at least three elements is

The sum of first 9 terms of the series $$\frac{1^3}{1} + \frac{1^3 + 2^3}{1+3} + \frac{1^3 + 2^3 + 3^3}{1+3+5} + \ldots$$ is

If $$m$$ is the A.M. of two distinct real numbers $$l$$ and $$n$$ $$(l, n > 1)$$ and $$G_1$$, $$G_2$$ and $$G_3$$ are three geometric means between $$l$$ and $$n$$, then $$G_1^4 + 2G_2^4 + G_3^4$$ equals

The sum of coefficients of integral powers of $$x$$ in the binomial expansion of $$(1 - 2\sqrt{x})^{50}$$ is

Locus of the image of the point (2, 3) in the line $$(2x - 3y + 4) + k(x - 2y + 3) = 0$$, k $$\in \mathbb{R}$$, is a

The number of common tangents to the circles $$x^2 + y^2 - 4x - 6y - 12 = 0$$ and $$x^2 + y^2 + 6x + 18y + 26 = 0$$, is