NTA JEE Main 22nd April 2013 Online

If $$\alpha$$ and $$\beta$$ are roots of the equation $$x^2 + px + \frac{3p}{4} = 0$$, such that $$|\alpha - \beta| = \sqrt{10}$$, then $$p$$ belongs to the set :

If a complex number $$z$$ satisfies the equation $$x + \sqrt{2}|z + 1| + i = 0$$, then $$|z|$$ is equal to :

The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is :

Given sum of the first $$n$$ terms of an A.P. is $$2n + 3n^2$$. Another A.P. is formed with the same first term and double of the common difference, the sum of $$n$$ terms of the new A.P. is :

The sum $$\frac{3}{1^2} + \frac{5}{1^2+2^2} + \frac{7}{1^2+2^2+3^2} + \ldots$$ upto 11-terms is:

If the 7th term in the binomial expansion of $$\left(\frac{3}{\sqrt[3]{84}} + \sqrt{3}\ln x\right)^9$$, $$x \gt 0$$, is equal to 729, then $$x$$ can be:

The number of solutions of the equation, $$\sin^{-1}x = 2\tan^{-1}x$$ (in principal values) is :

Statement-1: The number of common solutions of the trigonometric equations $$2\sin^2\theta - \cos 2\theta = 0$$ and $$2\cos^2\theta - 3\sin\theta = 0$$ in the interval $$[0, 2\pi]$$ is two.
Statement-2: The number of solutions of the equation, $$2\cos^2\theta - 3\sin\theta = 0$$ in the interval $$[0, \pi]$$ is two.

If the $$x$$-intercept of some line $$L$$ is double as that of the line, $$3x + 4y = 12$$ and the $$y$$-intercept of $$L$$ is half as that of the same line, then the slope of $$L$$ is :

The acute angle between two lines such that the direction cosines $$l, m, n$$, of each of them satisfy the equations $$l + m + n = 0$$ and $$l^2 + m^2 - n^2 = 0$$ is :