In a triangle $ABC$, right angled at the 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:
Previous 10 Questions — JEE Main 2016 (9 April Morning Shift)
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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)
A circle passes through $(-2,4)$ and touches the $y$-axis at $(0,2)$. Which one of the following equations can represen…
Topic: JEE Main 2016 (9 April Morning Shift)
The value of
$\displaystyle \sum_{r=1}^{15} r^{2} \left( \dfrac{{}^{15}C_{r}}{{}^{15}C_{r-1}} \right)$ is equal to:
Topic: JEE Main 2016 (9 April Morning Shift)
For $x \in \mathbb{R}, x \ne 0$, let $f_{0}(x) = \dfrac{1}{1 - x}$ and $f_{n+1}(x) = f_{0}(f_{n}(x)),; n = 0,1,2,\ldots…
Topic: JEE Main 2016 (9 April Morning Shift)
If $P = \begin{bmatrix} \dfrac{\sqrt{3}}{2} & \dfrac{1}{2} \\ -\dfrac{1}{2} & \dfrac{\sqrt{3}}{2} \end{bmatrix}$
and $A…
Topic: JEE Main 2016 (9 April Morning Shift)
The point represented by $2 + i$ in the Argand plane moves $1$ unit eastwards, then $2$ units northwards and finally fr…
Topic: JEE Main 2016 (9 April Morning Shift)
If the equations $x^{2} + bx - 1 = 0$ and $x^{2} + x + b = 0$ have a common root different from $-1$, then $|b|$ is equ…
Topic: JEE Main 2016 (9 April Morning Shift)
The number of distinct real roots of the equation
$ \begin{vmatrix}
\cos x & \sin x & \sin x \\
\sin x & \cos x & \si…
Topic: JEE Main 2016 (9 April Morning Shift)
If the four-letter words (need not be meaningful) are to be formed using the letters from the word “MEDITERRANEAN” such…
Topic: JEE Main 2016 (9 April Morning Shift)
Next 10 Questions — JEE Main 2016 (9 April Morning Shift)
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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)
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)
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)
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 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)
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)
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
$2\displaystyle\int_{0}^{1} \tan^{-1} x , dx = \displaystyle\int_{0}^{1} \cot^{-1} (1 - x + x^{2}) , dx,$
then
$\dis…
Topic: JEE Main 2016 (9 April Morning Shift)
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)
