NTA JEE Main 11th April 2015 Online

If the two roots of the equation, $$(a-1)(x^4 + x^2 + 1) + (a+1)(x^2 + x + 1)^2 = 0$$ are real and distinct, then the set of all values of $$a$$ is equal to

If $$z$$ is a non-real complex number, then the minimum value of $$\frac{Im\ z^5}{(Im\ z)^5}$$ is (Where $$Im\ z$$ = Imaginary part of $$z$$)

Let $$A = \{x_1, x_2, \ldots, x_7\}$$ and $$B = \{y_1, y_2, y_3\}$$ be two sets containing seven and three distinct elements respectively. Then the total number of functions $$f : A \rightarrow B$$ that are onto, if there exist exactly three elements $$x$$ in $$A$$ such that $$f(x) = y_2$$, is equal to:

If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is:

The sum of the 3$$^{rd}$$ and the 4$$^{th}$$ terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its 7$$^{th}$$ term is:

If $$\sum_{n=1}^{5}\frac{1}{n(n+1)(n+2)(n+3)} = \frac{k}{3}$$, then $$k$$ is equal to:

The term independent of $$x$$ in the binomial expansion of $$\left(1 - \frac{1}{x} + 3x^5\right)\left(2x^2 - \frac{1}{x}\right)^8$$ is

If $$\cos \alpha + \cos \beta = \frac{3}{2}$$ and $$\sin \alpha + \sin \beta = \frac{1}{2}$$ and $$\theta$$ is the arithmetic mean of $$\alpha$$ and $$\beta$$, then $$\sin 2\theta + \cos 2\theta$$ is equal to:

A straight line $$L$$ through the point $$(3, -2)$$ is inclined at an angle of $$60^\circ$$ to the line $$\sqrt{3}x + y = 1$$. If $$L$$ also intersects the X-axis, then the equation of $$L$$ is: