NTA JEE Main 3rd April 2016 Offline

The sum of all real values of $$x$$ satisfying the equation $$\left(x^2 - 5x + 5\right)^{x^2 + 4x - 60} = 1$$ is

A value of $$\theta$$ for which $$\frac{2 + 3i\sin\theta}{1 - 2i\sin\theta}$$ is purely imaginary, is

If all the words (with or without meaning) having five letters, formed using the letters of the word $$SMALL$$ and arranged as in a dictionary; then the position of the word $$SMALL$$ is

If the $$2^{nd}$$, $$5^{th}$$ and $$9^{th}$$ terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is

If the sum of the first ten terms of the series $$\left(1\frac{3}{5}\right)^2 + \left(2\frac{2}{5}\right)^2 + \left(3\frac{1}{5}\right)^2 + 4^2 + \left(4\frac{4}{5}\right)^2 + \ldots$$, is $$\frac{16}{5}m$$, then $$m$$ is equal to

If the number of terms in the expansion of $$\left(1 - \frac{2}{x} + \frac{4}{y^2}\right)^n$$, $$x, y \neq 0$$, is 28, then the sum of the coefficients of all the terms in this expansion is

If $$0 \leq x < 2\pi$$, then the number of real values of $$x$$, which satisfy the equation $$\cos x + \cos 2x + \cos 3x + \cos 4x = 0$$, is

Two sides of a rhombus are along the lines, $$x - y + 1 = 0$$ and $$7x - y - 5 = 0$$. If its diagonals intersect at $$(-1, -2)$$, then which one of the following is a vertex of this rhombus?

The centres of those circles which touch the circle, $$x^2 + y^2 - 8x - 8y - 4 = 0$$, externally and also touch the x-axis, lie on

If one of the diameters of the circle, given by the equation, $$x^2 + y^2 - 4x + 6y - 12 = 0$$, is a chord of a circle $$S$$, whose centre is at $$(-3, 2)$$, then the radius of $$S$$ is