The value of the integral

$\int\limits_4^{10} {{{\left[ {{x^2}} \right]dx} \over {\left[ {{x^2} - 28x + 196} \right] + \left[ {{x^2}} \right]}}} ,$

where [x] denotes the greatest integer less than or equal to x, is :

1

A ray of light is incident along a line which meets another line $7x - y + 1 = 0$ at the point $(0,1)$. The ray is then…

Topic: JEE Main 2016 (10 April Morning Shift)

2

A straight line through origin $O$ meets the lines $3y = 10 - 4x$ and $8x + 6y + 5 = 0$ at points $A$ and $B$ respectiv…

Topic: JEE Main 2016 (10 April Morning Shift)

3

A hyperbola whose transverse axis is along the major axis of the conic $\dfrac{x^2}{3} + \dfrac{y^2}{4} = 4$ and has …

Topic: JEE Main 2016 (10 April Morning Shift)

4

ABC is a triangle in a plane with vertices $A(2,3,5)$, $B(-1,3,2)$ and $C(\lambda,5,\mu)$. If the median through $A$…

Topic: JEE Main 2016 (10 April Morning Shift)

5

Let $\triangle ABC$ be a triangle whose circumcentre is at $P$. If the position vectors of $A, B, C$ and $P$ are $\ve…

Topic: JEE Main 2016 (10 April Morning Shift)

6

The mean of $5$ observations is $5$ and their variance is $124$. If three of the observations are $1, 2$ and $6$, the…

Topic: JEE Main 2016 (10 April Morning Shift)

7

If $A>0,\ B>0$ and $A+B=\dfrac{\pi}{6}$, then the minimum value of $\tan A+\tan B$ is:

Topic: JEE Main 2016 (10 April Morning Shift)

8

For $x \in \mathbb{R},\ x \ne 0$, if $y(x)$ is a differentiable function such that $x \int_{1}^{x} y(t)\,dt = (x+1) …

Topic: JEE Main 2016 (10 April Morning Shift)

9

The sum $\displaystyle \sum_{r=1}^{10} (r^2 + 1)\,(r!)$ is equal to :

Topic: JEE Main 2016 (10 April Morning Shift)

10

Let $P = \{\theta : \sin\theta - \cos\theta = \sqrt{2}\cos\theta\}$ and $Q = \{\theta : \sin\theta + \cos\theta = \sq…

Topic: JEE Main 2016 (10 April Morning Shift)

1

The integral $\displaystyle \int \frac{dx}{(1+\sqrt{x})\sqrt{x - x^{2}}}$ is equal to :

Topic: JEE Main 2016 (10 April Morning Shift)

2

Let $f(x)=\sin^{4}x+\cos^{4}x$. Then $f$ is an increasing function in the interval :

Topic: JEE Main 2016 (10 April Morning Shift)

3

Let $a,b\in\mathbb{R}$, $(a\neq 0)$. If the function $f$ defined as $f(x)= \begin{cases} \dfrac{2x^{2}}{a}, & 0\le x

Topic: JEE Main 2016 (10 April Morning Shift)

4

$\displaystyle \lim_{x\to 0} \frac{(1-\cos 2x)^{2}}{2x\tan x - x\tan 2x}$ is :

Topic: JEE Main 2016 (10 April Morning Shift)