NTA JEE Main 8th April 2019 Shift 1
For the following questions answer them individually
NTA JEE Main 8th April 2019 Shift 1 - Question 71
If the tangents on the ellipse $$4x^{2} + y^{2} = 8$$ at the points (1, 2) and (a, b) are perpendicular to each other, then $$a^{2}$$ is equal to:
NTA JEE Main 8th April 2019 Shift 1 - Question 72
$$\lim_{x \to 0} \frac{\sin^{2}x}{\sqrt{2} - \sqrt{1 + \cos x}}$$ equals:
NTA JEE Main 8th April 2019 Shift 1 - Question 73
The contrapositive of the statement "If you are born in India, then you are a citizen of India", is:
NTA JEE Main 8th April 2019 Shift 1 - Question 74
The mean and variance for seven observations are 8 and 16 respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is:
NTA JEE Main 8th April 2019 Shift 1 - Question 75
Let $$A = \begin{pmatrix} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{pmatrix}$$, $$a \in R$$ such that $$A^{32} = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$$. Then, a value of $$\alpha$$ is:
NTA JEE Main 8th April 2019 Shift 1 - Question 76
The greatest value of $$c \in R$$ for which the system of linear equations $$x - cy - cz = 0$$, $$cx - y + cz = 0$$, $$cx + cy - z = 0$$ has a non-trivial solution, is:
NTA JEE Main 8th April 2019 Shift 1 - Question 77
If $$\alpha = \cos^{-1}\frac{3}{5}$$, $$\beta = \tan^{-1}\frac{1}{3}$$, where $$0 < \alpha, \beta < \frac{\pi}{2}$$, then $$\alpha - \beta$$ is equal to:
NTA JEE Main 8th April 2019 Shift 1 - Question 78
If $$f(x) = \log_e\frac{1-x}{1+x}$$, $$|x| < 1$$, then $$f\left(\frac{2x}{1+x^{2}}\right)$$ is equal to:
NTA JEE Main 8th April 2019 Shift 1 - Question 79
If $$2y=\left(\cot^{-1}\left(\frac{\sqrt{3}\cos x+\sin x}{\cos x-\sqrt{3}\sin x}\right)^{ }\right)^2$$, $$\forall x \in \left(0, \frac{\pi}{2}\right)$$, then $$\frac{dy}{dx}$$ is equal to:
NTA JEE Main 8th April 2019 Shift 1 - Question 80
The shortest distance between the line $$y = x$$ and the curve $$y^{2} = x - 2$$ is:
