NTA JEE Main 9th April 2016 Online

If the function $$f(x) = \begin{cases} -x, & x < 1 \\ a + \cos^{-1}(x+b), & 1 \leq x \leq 2 \end{cases}$$ is differentiable at $$x = 1$$, then $$\frac{a}{b}$$ is equal to

The minimum distance of a point on the curve $$y = x^2 - 4$$ from the origin is

If the tangent at a point P, with parameter $$t$$, on the curve $$x = 4t^2 + 3$$, $$y = 8t^3 - 1$$, $$t \in R$$, meets the curve again at a point Q, then the coordinates of Q are:

If $$\int \frac{dx}{\cos^3 x \sqrt{2\sin 2x}} = (\tan x)^A + C(\tan x)^B + k$$, where k is a constant of integration, then $$A + B + C$$ equals

If $$2\int_0^1 \tan^{-1} x\,dx = \int_0^1 \cot^{-1}(1 - x + x^2)\,dx$$, then $$\int_0^1 \tan^{-1}(1 - x + x^2)\,dx$$ is equal to

The area (in sq. units) of the region described by $$A = \{(x, y) | y \geq x^2 - 5x + 4, x + y \geq 1, y \leq 0\}$$ is

In a triangle $$ABC$$, right angle at vertex $$A$$, if the position vectors of $$A$$, $$B$$ and $$C$$ are respectively $$3\hat{i} + \hat{j} - \hat{k}$$, $$-\hat{i} + 3\hat{j} + p\hat{k}$$ and $$5\hat{i} + q\hat{j} - 4\hat{k}$$, then the point $$(p, q)$$ lies on a line:

The shortest distance between the lines $$\frac{x}{2} = \frac{y}{2} = \frac{z}{1}$$ and $$\frac{x+2}{-1} = \frac{y-4}{8} = \frac{z-5}{4}$$, lies in the interval:

The distance of the point $$(1, -2, 4)$$ from the plane passing through the point $$(1, 2, 2)$$ and perpendicular to the planes $$x - y + 2z = 3$$ and $$2x - 2y + z + 12 = 0$$, is:

If A and B are any two events such that $$P(A) = \frac{2}{5}$$ and $$P(A \cap B) = \frac{3}{20}$$, then the conditional probability, $$P(A|(A' \cup B'))$$, where $$A'$$ denotes the complement of A, is equal to: