A hyperbola whose transverse axis is along the major axis of the conic $\dfrac{x^2}{3} + \dfrac{y^2}{4} = 4$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\dfrac{3}{2}$, then which of the following points does NOT lie on it?

1

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)

2

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)

3

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)

4

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)

5

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)

6

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

Topic: JEE Main 2016 (10 April Morning Shift)

7

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)

8

If $x$ is a solution of the equation $\sqrt{2x+1} - \sqrt{2x-1} = 1,\ (x \ge \tfrac12)$, then $\sqrt{4x^{2}-1}$ is eq…

Topic: JEE Main 2016 (10 April Morning Shift)

9

Let $A$ be a $3 \times 3$ matrix such that $A^{2} - 5A + 7I = 0$. \textbf{Statement I:} $A^{-1} = \dfrac{1}{7}(5I - …

Topic: JEE Main 2016 (10 April Morning Shift)

10

If $A = \begin{bmatrix} -4 & -1 \\ 3 & 1 \end{bmatrix}$, then the determinant of the matrix $(A^{2016} - 2A^{2015} - A…

Topic: JEE Main 2016 (10 April Morning Shift)

1

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)

2

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)

3

The value of the integral $\int\limits_4^{10} {{{\left[ {{x^2}} \right]dx} \over {\left[ {{x^2} - 28x + 196} \right] + …

Topic: JEE Main 2016 (10 April Morning Shift)

4

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

Topic: JEE Main 2016 (10 April Morning Shift)

5

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)

6

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)

7

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

Topic: JEE Main 2016 (10 April Morning Shift)