NTA JEE Main 9th January 2019 Shift 1

Let $$\alpha$$ and $$\beta$$ be the roots of the equation $$x^2 + 2x + 2 = 0$$, then $$\alpha^{15} + \beta^{15}$$ is equal to:

Let $$A = \{\theta \in (-\frac{\pi}{2}, \pi): \frac{3 + 2i\sin\theta}{1 - 2i\sin\theta}$$ is purely imaginary$$\}$$. Then the sum of the elements in $$A$$ is:

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:

If $$a$$, $$b$$ and $$c$$ be three distinct real numbers in G.P. and $$a + b + c = xb$$, then $$x$$ cannot be:

Let $$a_1, a_2, \ldots, a_{30}$$ be an A.P., $$S = \sum_{i=1}^{30} a_i$$ and $$T = \sum_{i=1}^{15} a_{(2i-1)}$$. If $$a_5 = 27$$ and $$S - 2T = 75$$, then $$a_{10}$$ is equal to:

If the fractional part of the number $$\frac{2^{403}}{15}$$ is $$\frac{k}{15}$$, then $$k$$ is equal to:

For any $$\theta \in \frac{\pi}{4}, \frac{\pi}{2}$$, the expression $$3\sin\theta - \cos\theta^4 + 6\sin\theta + \cos\theta^2 + 4\sin^6\theta$$ equals:

Consider the set of all lines $$px + qy + r = 0$$ such that $$3p + 2q + 4r = 0$$. Which one of the following statements is true?

Three circles of radii $$a$$, $$b$$, $$c$$ ($$a < b < c$$) touch each other externally. If they have $$x$$-axis as a common tangent, then:

Axis of a parabola lies along $$x$$-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive $$x$$-axis then which of following points does not lie on it?