NTA JEE Main 8th January 2020 Shift 2

The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is

The sum, $$\sum_{n=1}^{7} \frac{n(n+1)(2n+1)}{4}$$, is equal to

If $$\frac{\sqrt{2}\sin\alpha}{\sqrt{1+\cos 2\alpha}} = \frac{1}{7}$$ and $$\sqrt{\frac{1-\cos 2\beta}{2}} = \frac{1}{\sqrt{10}}$$, $$\alpha, \beta \in \left(0, \frac{\pi}{2}\right)$$, then $$\tan(\alpha + 2\beta)$$ is equal to

Let a line $$y = mx$$ $$(m \gt 0)$$, intersect the parabola, $$y^2 = x$$, at a point P, other than the origin. Let the tangent to it at P, meet the x-axis at the point Q. If area ($$\triangle OPQ$$) = 4 square unit, then m is equal to

Let $$f(x)$$, be a polynomial of degree 3, such that $$f(-1) = 10$$, $$f(1) = -6$$, $$f(x)$$, has a critical point at $$x = -1$$ and $$f'(x)$$, has a critical point at $$x = 1$$. Then $$f(x)$$, has local minima at $$x =$$