NTA JEE Main 9th April 2014 Online

If $$\frac{1}{\sqrt{\alpha}}$$, $$\frac{1}{\sqrt{\beta}}$$ are the roots of the equation $$ax^2 + bx + 1 = 0$$, $$(a \neq 0, a, b \in R)$$, then the equation $$x(x + b^3) + (a^3 - 3abx) = 0$$ has roots:

If equations $$ax^2 + bx + c = 0$$, $$(a, b, c \in R, a \neq 0)$$ and $$2x^2 + 3x + 4 = 0$$ have a common root, then $$a : b : c$$ equals:

Let $$w(Im\ w \neq 0)$$ be a complex number. Then, the set of all complex numbers $$z$$ satisfying the equation $$w - \bar{w}z = k(1 - z)$$, for some real number $$k$$, is:

The sum of the digits in the unit's place of all the 4-digit numbers formed by using the numbers 3, 4, 5 and 6, without repetition is:

Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4$$^{th}$$ term is:

If the sum $$\frac{3}{1^2} + \frac{5}{1^2+2^2} + \frac{7}{1^2+2^2+3^2} + \ldots$$ + up to 20 terms is equal to $$\frac{k}{21}$$, then $$k$$ is equal to:

The number of terms in the expansion of $$(1+x)^{101}(1-x+x^2)^{100}$$ in powers of $$x$$ is:

If $$\operatorname{cosec} \theta = \frac{p+q}{p-q}$$ ($$p \neq q, p \neq 0$$), then $$\left|\cot\left(\frac{\pi}{4} + \frac{\theta}{2}\right)\right|$$ is equals to:

The number of values of $$\alpha$$ in $$[0, 2\pi]$$ for which $$2\sin^3\alpha - 7\sin^2\alpha + 7\sin\alpha = 2$$, is:

Given three points $$P$$, $$Q$$, $$R$$ with $$P(5, 3)$$ and $$R$$ lies on the $$x$$-axis. If the equation of $$RQ$$ is $$x - 2y = 2$$ and $$PQ$$ is parallel to the $$x$$-axis, then the centroid of $$\Delta PQR$$ lies on the line: