NTA JEE Main 19th April 2014 Online

The equation $$\sqrt{3x^2 + x + 5} = x - 3$$, where x is real, has:

For all complex numbers z of the form $$1 + i\alpha$$, $$\alpha \in R$$, if $$z^2 = x + iy$$, then:

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval:

Let $$f(n) = \left[\frac{1}{3} + \frac{3n}{100}\right]n$$, where $$[n]$$ denotes the greatest integer less than or equal to n. Then $$\sum_{n=1}^{56} f(n)$$ is equal to:

The number of terms in an A.P. is even, the sum of the odd terms in it is 24 and that of the even terms is 30. If the last term exceeds the first term by $$10\frac{1}{2}$$, then the number of terms in the A.P. is:

The coefficient of $$x^{1012}$$ in the expansion of $$(1 + x^n + x^{253})^{10}$$, (where $$n \leq 22$$ is any positive integer), is:

If a line L is perpendicular to the line $$5x - y = 1$$, and the area of the triangle formed by the line L and the coordinate axes is 5 sq units, then the distance of the line L from the line $$x + 5y = 0$$ is:

The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points $$(a^2 + 1, a^2 + 1)$$ and $$(2a, -2a)$$, $$a \neq 0$$. Then for any a, the orthocentre of this triangle lies on the line:

The equation of the circle described on the chord $$3x + y + 5 = 0$$ of the circle $$x^2 + y^2 = 16$$ as the diameter is:

A chord is drawn through the focus of the parabola $$y^2 = 6x$$ such that its distance from the vertex of this parabola is $$\frac{\sqrt{5}}{2}$$, then its slope can be: