NTA JEE Main 25th July 2021 Shift 2
For the following questions answer them individually
NTA JEE Main 25th July 2021 Shift 2 - Question 61
The number of real solutions of the equation, $$x^2 - |x| - 12 = 0$$ is:
NTA JEE Main 25th July 2021 Shift 2 - Question 62
The sum of all those terms which are rational numbers in the expansion of $$\left(2^{\frac{1}{3}} + 3^{\frac{1}{4}}\right)^{12}$$ is:
NTA JEE Main 25th July 2021 Shift 2 - Question 63
If the greatest value of the term independent of $$x$$ in the expansion of $$\left(x \sin \alpha + a\frac{\cos \alpha}{x}\right)^{10}$$ is $$\frac{10!}{(5!)^2}$$, then the value of $$a$$ is equal to:
NTA JEE Main 25th July 2021 Shift 2 - Question 64
The lowest integer which is greater than $$\left(1 + \frac{1}{10^{100}}\right)^{10^{100}}$$ is
NTA JEE Main 25th July 2021 Shift 2 - Question 65
If $$^nP_r = ^nP_{r+1}$$ and $$^nC_r = ^nC_{r-1}$$, then the value of $$r$$ is equal to:
NTA JEE Main 25th July 2021 Shift 2 - Question 66
The value of $$\cot \frac{\pi}{24}$$ is:
NTA JEE Main 25th July 2021 Shift 2 - Question 67
The number of distinct real roots of $$\begin{vmatrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \end{vmatrix} = 0$$ in the interval $$-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}$$ is:
NTA JEE Main 25th July 2021 Shift 2 - Question 68
Let the equation of the pair of lines, $$y = px$$ and $$y = qx$$, can be written as $$(y - px)(y - qx) = 0$$. Then the equation of the pair of the angle bisectors of the lines $$x^2 - 4xy - 5y^2 = 0$$ is:
NTA JEE Main 25th July 2021 Shift 2 - Question 69
If a tangent to the ellipse $$x^2 + 4y^2 = 4$$ meets the tangents at the extremities of its major axis at $$B$$ and $$C$$, then the circle with $$BC$$ as diameter passes through the point.
NTA JEE Main 25th July 2021 Shift 2 - Question 70
Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following:
