NTA JEE Main 10th April 2015 Online

The largest value of $$r$$, for which the region represented by the set $$\{\omega \in C | |\omega - 4 - i| \leq r\}$$ is contained in the region represented by the set $$\{z \in C | |z - 1| \leq |z + i|\}$$, is equal to:

If $$2 + 3i$$ is one of the roots of the equation $$2x^3 - 9x^2 + kx - 13 = 0$$, $$k \in R$$, then the real root of this equation (where $$i^2 = -1$$):

The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman is

The value of $$\sum_{r=16}^{30}(r+2)(r-3)$$ is equal to:

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is:

If the coefficient of the three successive terms in the binomial expansion of $$(1 + x)^n$$ are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is

In a $$\Delta ABC$$, $$\frac{a}{b} = 2 + \sqrt{3}$$, and $$\angle C = 60^\circ$$. Then the ordered pair $$(\angle A, \angle B)$$ is equal to:

Let $$L$$ be the line passing through the point $$P(1, 2)$$ such that its intercepted segment between the co-ordinate axes is bisected at $$P$$. If $$L_1$$ is the line perpendicular to $$L$$ and passing through the point $$(-2, 1)$$, then the point of intersection of $$L$$ and $$L_1$$ is

The points $$\left(0, \frac{8}{3}\right)$$, $$(1, 3)$$ and $$(82, 30)$$

If $$y + 3x = 0$$ is the equation of a chord of the circle $$x^2 + y^2 - 30x = 0$$, then the equation of the circle with this chord as diameter is: