NTA JEE Main 16 th April 2018 Online

Let M and m be respectively the absolute maximum and the absolute minimum values of the function, $$f(x) = 2x^3 - 9x^2 + 12x + 5$$ in the interval [0, 3]. Then M - m is equal to:

If $$\int \frac{\tan x}{1 + \tan x + \tan^2 x} dx = x - \frac{K}{\sqrt{A}} \tan^{-1}\left(\frac{K\tan x + 1}{\sqrt{A}}\right) + C$$, (C is a constant of integration), then the ordered pair (K, A) is equal to:

If $$f(x) = \int_0^x t(\sin x - \sin t)dt$$, then:

If the area of the region bounded by the curves, $$y = x^2$$, $$y = \frac{1}{x}$$ and the lines $$y = 0$$ and $$x = t$$ (t > 1) is 1 sq. unit, then t is equal to:

The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, center at the origin and passing through the point (0, 3) is:

Let $$\vec{a} = \hat{i} + \hat{j} + \hat{k}$$, $$\vec{c} = \hat{j} - \hat{k}$$ and a vector $$\vec{b}$$ be such that $$\vec{a} \times \vec{b} = \vec{c}$$ and $$\vec{a} \cdot \vec{b} = 3$$. Then $$|\vec{b}|$$ equals:

The sum of the intercepts on the coordinate axes of the plane passing through the point (-2, -2, 2) and containing the line joining the points (1, -1, 2) and (1, 1, 1) is:

If the angle between the lines $$\frac{x}{2} = \frac{y}{2} = \frac{z}{1}$$ and $$\frac{5-x}{-2} = \frac{7y-14}{P} = \frac{z-3}{4}$$ is $$\cos^{-1}\left(\frac{2}{3}\right)$$, then P is equal to:

Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is $$\frac{1}{12}$$, then the number of children in each family is:

Let A, B and C be three events, which are pair-wise independent and $$\bar{E}$$ denotes the complement of an event E. If $$P(A \cap B \cap C) = 0$$ and $$P(C) > 0$$, then $$P\left[(\bar{A} \cap \bar{B}) | C\right]$$ is equal to: