If $2\displaystyle\int_{0}^{1} \tan^{-1} x , dx = \displaystyle\int_{0}^{1} \cot^{-1} (1 - x + x^{2}) , dx,$ then $\displaystyle\int_{0}^{1} \tan^{-1} (1 - x + x^{2}) , dx$ is equal to :
Previous 10 Questions — JEE Main 2016 (9 April Morning Shift)
Nearest first
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If $f(x)$ is a differentiable function in the interval $(0,\infty)$ such that $f(1) = 1$ and
$\displaystyle \lim_{t \to…
Topic: JEE Main 2016 (9 April Morning Shift)
If a variable line drawn through the intersection of the lines
$\dfrac{x}{3} + \dfrac{y}{4} = 1$ and $\dfrac{x}{4} + \d…
Topic: JEE Main 2016 (9 April Morning Shift)
The area (in sq. units) of the region described by
$A = {(x,y)\mid y \ge x^{2} - 5x + 4,\ x + y \ge 1,\ y \le 0}$ is:
Topic: JEE Main 2016 (9 April Morning Shift)
The point $(2,1)$ is translated parallel to the line $L : x - y = 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in…
Topic: JEE Main 2016 (9 April Morning Shift)
The shortest distance between the lines
$\dfrac{x}{2} = \dfrac{y}{2} = \dfrac{z}{1}$
and
$\dfrac{x + 2}{-1} = \dfrac{y …
Topic: JEE Main 2016 (9 April Morning Shift)
If the mean deviation of the numbers
$1,, 1 + d,, \ldots,, 1 + 100d$
from their mean is $255$, then a value of $d$ is:
Topic: JEE Main 2016 (9 April Morning Shift)
If $A$ and $B$ are any two events such that $P(A) = \dfrac{2}{5}$ and $P(A \cap B) = \dfrac{3}{20}$, then the condition…
Topic: JEE Main 2016 (9 April Morning Shift)
In a triangle $ABC$, right angled at the vertex $A$, if the position vectors of $A,B$ and $C$ are respectively
$3\hat{i…
Topic: JEE Main 2016 (9 April Morning Shift)
Let $a$ and $b$ respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies …
Topic: JEE Main 2016 (9 April Morning Shift)
If $m$ and $M$ are the minimum and the maximum values of
$4 + \dfrac{1}{2}\sin^{2} 2x - 2\cos^{4} x,; x \in \mathbb{R}$…
Topic: JEE Main 2016 (9 April Morning Shift)
Next 10 Questions — JEE Main 2016 (9 April Morning Shift)
Ascending by ID
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The minimum distance of a point on the curve $y = x^{2} - 4$ from the origin is :
Topic: JEE Main 2016 (9 April Morning Shift)
If
$\displaystyle \int \frac{dx}{\cos^{3}x\sqrt{2\sin 2x}} = (\tan x)^{A} + C(\tan x)^{B} + k,$
where $k$ is a constan…
Topic: JEE Main 2016 (9 April Morning Shift)
If the function
f(x) = $\left\{ {\matrix{
{ - x} & {x < 1} \cr
{a + {{\cos }^{ - 1}}\left( {x + b} \rig…
Topic: JEE Main 2016 (9 April Morning Shift)
If
$\displaystyle \lim_{x \to \infty} \left(1 + \frac{a}{x} - \frac{4}{x^{2}}\right)^{2x} = e^{3}$,
then $a$ is equal t…
Topic: JEE Main 2016 (9 April Morning Shift)
