NTA JEE Main 6th September 2020 Shift 2

If $$\alpha$$ and $$\beta$$ are the roots of the equation $$2x(2x+1) = 1$$, then $$\beta$$ is equal to:

Let $$z = x + iy$$ be a non-zero complex number such that $$z^2 = i|z|^2$$, where $$i = \sqrt{-1}$$, then $$z$$ lies on the:

The common difference of the A.P. $$b_1, b_2, \ldots, b_m$$ is 2 more than common difference of A.P. $$a_1, a_2, \ldots, a_n$$. If $$a_{40} = -159$$, $$a_{100} = -399$$ and $$b_{100} = a_{70}$$, then $$b_1$$ is equal to:

If the constant term in the binomial expansion of $$\left(\sqrt{x} - \frac{k}{x^2}\right)^{10}$$ is 405, then $$|k|$$ equals:

Let $$L$$ denote the line in the $$xy$$-plane with $$x$$ and $$y$$ intercepts as 3 and 1 respectively. Then the image of the point $$(-1, -4)$$ in the line is:

The centre of the circle passing through the point $$(0, 1)$$ and touching the parabola $$y = x^2$$ at the point $$(2, 4)$$ is:

If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity $$e$$ of the ellipse satisfies:

Consider the statement: "For an integer n, if $$n^3 - 1$$ is even, then $$n$$ is odd". The contrapositive statement of this statement is:

The angle of elevation of the summit of a mountain from a point on the ground is $$45^\circ$$. After climbing up one km towards the summit at an inclination of $$30^\circ$$ from the ground, the angle of elevation of the summit is found to be $$60^\circ$$. Then the height (in km) of the summit from the ground is:

Let $$\theta = \frac{\pi}{5}$$ and $$A = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$$. If $$B = A + A^4$$, then $$\det(B)$$: