NTA JEE Main 12th April 2019 Shift 2

If $$\alpha$$, $$\beta$$ and $$\gamma$$ are three consecutive terms of a non-constant G.P. Such that the equations $$\alpha x^2 + 2\beta x + \gamma = 0$$ and $$x^2 + x - 1 = 0$$ have a common root, then $$\alpha(\beta + \gamma)$$ is equal to:

Let $$z \in C$$ with Im(z) = 10 and it satisfies $$\frac{2z - n}{2z + n} = 2i - 1$$ for some natural number n. Then

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to

If $$a_1, a_2, a_3, \ldots$$ are in A.P. such that $$a_1 + a_7 + a_{16} = 40$$, then the sum of the first 15 terms of this A.P is:

If $$^{20}C_1 + (2^2)\,^{20}C_2 + (3^2)\,^{20}C_3 + \ldots + (20^2)\,^{20}C_{20} = A(2^\beta)$$, then the ordered pair $$(A, \beta)$$ is equal to

The term independent of x in the expansion of $$\left(\frac{1}{60} - \frac{x^8}{81}\right) \cdot \left(2x^2 - \frac{3}{x^2}\right)^6$$ is equal to

Let S be the set of all $$\alpha \in R$$ such that the equation, $$\cos 2x + \alpha \sin x = 2\alpha - 7$$ has a solution. Then S is equal to:

A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (-1, 1) and (2, 3). Then the centroid of this triangle is:

A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of 60° with the line x + y = 0. Then an equation of the line L is:

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point: