NTA JEE Main 5th September 2020 Shift 1
For the following questions answer them individually
NTA JEE Main 5th September 2020 Shift 1 - Question 51
The product of the roots of the equation $$9x^2 - 18|x| + 5 = 0$$ is:
NTA JEE Main 5th September 2020 Shift 1 - Question 52
If the four complex numbers $$z$$, $$\overline{z}$$, $$\overline{z} - 2\,\text{Re}(\overline{z})$$ and $$z - 2\,\text{Re}(z)$$ represent the vertices of a square of side 4 units in the Argand plane, then $$|z|$$ is equal to:
NTA JEE Main 5th September 2020 Shift 1 - Question 53
If $$2^{10} + 2^9 \cdot 3^1 + 2^8 \cdot 3^2 + \ldots + 2 \cdot 3^9 + 3^{10} = S - 2^{11}$$, then $$S$$ is equal to:
NTA JEE Main 5th September 2020 Shift 1 - Question 54
If $$3^{2\sin 2\alpha - 1}$$, 14 and $$3^{4 - 2\sin 2\alpha}$$ are the first three terms of an A.P. for some $$\alpha$$, then the sixth term of this A.P. is:
NTA JEE Main 5th September 2020 Shift 1 - Question 55
If the common tangent to the parabolas, $$y^2 = 4x$$ and $$x^2 = 4y$$ also touches the circle, $$x^2 + y^2 = c^2$$, then $$c$$ is equal to:
NTA JEE Main 5th September 2020 Shift 1 - Question 56
If the co-ordinates of two points $$A$$ and $$B$$ are $$\left(\sqrt{7}, 0\right)$$ and $$\left(-\sqrt{7}, 0\right)$$ respectively and $$P$$ is any point on the conic, $$9x^2 + 16y^2 = 144$$, then $$PA + PB$$ is equal to:
NTA JEE Main 5th September 2020 Shift 1 - Question 57
If the point $$P$$ on the curve, $$4x^2 + 5y^2 = 20$$ is farthest from the point $$Q(0, -4)$$, then $$PQ^2$$ is equal to:
NTA JEE Main 5th September 2020 Shift 1 - Question 58
If $$\alpha$$ is the positive root of the equation, $$p(x) = x^2 - x - 2 = 0$$, then $$\lim_{x \to \alpha^+} \frac{\sqrt{1 - \cos(p(x))}}{x + \alpha - 4}$$ is equal to:
NTA JEE Main 5th September 2020 Shift 1 - Question 59
The negation of the Boolean expression $$x \leftrightarrow \sim y$$ is equivalent to:
NTA JEE Main 5th September 2020 Shift 1 - Question 60
The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14 then the absolute difference of the remaining two observations is:
