NTA JEE Main 5th September 2020 Shift 2
For the following questions answer them individually
NTA JEE Main 5th September 2020 Shift 2 - Question 51
If $$\alpha$$ and $$\beta$$ are the roots of the equation, $$7x^2 - 3x - 2 = 0$$, then the value of $$\frac{\alpha}{1-\alpha^2} + \frac{\beta}{1-\beta^2}$$ is equal to:
NTA JEE Main 5th September 2020 Shift 2 - Question 52
The value of $$\left(\frac{-1+i\sqrt{3}}{1-i}\right)^{30}$$ is:
NTA JEE Main 5th September 2020 Shift 2 - Question 53
There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:
NTA JEE Main 5th September 2020 Shift 2 - Question 54
If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is:
NTA JEE Main 5th September 2020 Shift 2 - Question 55
If the sum of the first 20 terms of the series $$\log_{(7^{1/2})} x + \log_{(7^{1/3})} x + \log_{(7^{1/4})} x + \ldots$$ is 460, then $$x$$ is equal to:
NTA JEE Main 5th September 2020 Shift 2 - Question 56
If $$L = \sin^2\left(\frac{\pi}{16}\right) - \sin^2\left(\frac{\pi}{8}\right)$$ and $$M = \cos^2\left(\frac{\pi}{16}\right) - \sin^2\left(\frac{\pi}{8}\right)$$
NTA JEE Main 5th September 2020 Shift 2 - Question 57
If the length of the chord of the circle, $$x^2 + y^2 = r^2$$ $$(r > 0)$$ along the line, $$y - 2x = 3$$ is $$r$$, then $$r^2$$ is equal to:
NTA JEE Main 5th September 2020 Shift 2 - Question 58
If the line $$y = mx + c$$ is a common tangent to the hyperbola $$\frac{x^2}{100} - \frac{y^2}{64} = 1$$ and the circle $$x^2 + y^2 = 36$$, then which one of the following is true?
NTA JEE Main 5th September 2020 Shift 2 - Question 59
$$\lim_{x \to 0} \frac{x\left(e^{(\sqrt{1+x^2+x^4}-1)/x} - 1\right)}{\sqrt{1+x^2+x^4} - 1}$$
NTA JEE Main 5th September 2020 Shift 2 - Question 60
The statement $$(p \to (q \to p)) \to (p \to (p \vee q))$$ is:
