NTA JEE Main 12th April 2019 Shift 2
For the following questions answer them individually
NTA JEE Main 12th April 2019 Shift 2 - Question 71
The tangents to the curve $$y = (x - 2)^2 - 1$$ at its points of intersection with the line $$x - y = 3$$, intersect at the point:
NTA JEE Main 12th April 2019 Shift 2 - Question 72
An ellipse, with foci at (0, 2) and (0, -2) and minor axis of length 4, passes through which of the following points?
NTA JEE Main 12th April 2019 Shift 2 - Question 73
The equation of a common tangent to the curves, $$y^2 = 16x$$ and $$xy = -4$$, is:
NTA JEE Main 12th April 2019 Shift 2 - Question 74
$$\lim_{x \to 0} \frac{x + 2\sin x}{\sqrt{x^2 + 2\sin x + 1} - \sqrt{\sin^2 x - x + 1}}$$ is
NTA JEE Main 12th April 2019 Shift 2 - Question 75
The Boolean expression $$\sim(p \Rightarrow (\sim q))$$ is equivalent to
NTA JEE Main 12th April 2019 Shift 2 - Question 76
The angle of the top of a vertical tower standing on a horizontal plane is observed to be 45° from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be 30°, then the distance (in m) of the foot of the tower from the point A is:
NTA JEE Main 12th April 2019 Shift 2 - Question 77
Let A, B and C be sets such that $$\phi \neq A \cap B \subseteq C$$. Then which of the following statements is not true?
NTA JEE Main 12th April 2019 Shift 2 - Question 78
A value of $$\theta \in \left(0, \frac{\pi}{3}\right)$$, for which $$\begin{vmatrix} 1 + \cos^2\theta & \sin^2\theta & 4\cos 6\theta \\ \cos^2\theta & 1 + \sin^2\theta & 4\cos 6\theta \\ \cos^2\theta & \sin^2\theta & 1 + 4\cos 6\theta \end{vmatrix} = 0$$, is
NTA JEE Main 12th April 2019 Shift 2 - Question 79
If [x] denotes the greatest integer $$\leq x$$, then the system of linear equations $$[\sin\theta]x + [-\cos\theta]y = 0$$, $$[\cot\theta]x + y = 0$$
NTA JEE Main 12th April 2019 Shift 2 - Question 80
The derivative of $$\tan^{-1}\left(\frac{\sin x - \cos x}{\sin x + \cos x}\right)$$ with respect to $$\frac{x}{2}$$, where $$x \in \left(0, \frac{\pi}{2}\right)$$, is
