Let $\triangle ABC$ be a triangle whose circumcentre is at $P$. If the position vectors of $A, B, C$ and $P$ are $\vec a, \vec b, \vec c$ and $\dfrac{\vec a + \vec b + \vec c}{4}$ respectively, then the position vector of the orthocentre of this triangle is:
Previous 10 Questions — JEE Main 2016 (10 April Morning Shift)
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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)
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)
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)
The sum $\displaystyle \sum_{r=1}^{10} (r^2 + 1)\,(r!)$ is equal to :
Topic: JEE Main 2016 (10 April Morning Shift)
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)
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)
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)
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)
If the coefficients of $x^{-2}$ and $x^{-4}$ in the expansion of
$\left(x^{\tfrac13} + \dfrac{1}{2x^{\tfrac13}}\right)^…
Topic: JEE Main 2016 (10 April Morning Shift)
If $\dfrac{{}^{n+2}C_{6}}{{}^{n-2}P_{2}} = 11$, then $n$ satisfies the equation:
Topic: JEE Main 2016 (10 April Morning Shift)
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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)
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)
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)
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)
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)
The integral $\displaystyle \int \frac{dx}{(1+\sqrt{x})\sqrt{x - x^{2}}}$ is equal to :
Topic: JEE Main 2016 (10 April Morning Shift)
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)
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)
$\displaystyle \lim_{x\to 0} \frac{(1-\cos 2x)^{2}}{2x\tan x - x\tan 2x}$ is :
Topic: JEE Main 2016 (10 April Morning Shift)
