Let $\sqrt{3}\,\hat{i}+\hat{j}$, $\ \hat{i}+\sqrt{3}\,\hat{j}$ and $\ \beta\,\hat{i}+(1-\beta)\,\hat{j}$ respectively be the position vectors of the points $A$, $B$ and $C$ with respect to the origin $O$. If the distance of $C$ from the bisector of the acute angle between $\overrightarrow{OA}$ and $\overrightarrow{OB}$ is $\dfrac{3}{\sqrt{2}}$, then the sum of all possible values of $\beta$ is:
Previous 10 Questions — JEE Main 2019 (11 January Evening Shift)
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All $x$ satisfying the inequality $(\cot^{-1}x)^2 - 7(\cot^{-1}x) + 10 > 0$ lie in the interval:
Topic: JEE Main 2019 (11 January Evening Shift)
A circle cuts a chord of length $4a$ on the $x$-axis and passes through a point on the $y$-axis, distant $2b$ from the …
Topic: JEE Main 2019 (11 January Evening Shift)
If the area of the triangle whose one vertex is at the vertex of the parabola, $y^{2}+4(x-a^{2})=0$ and the other two v…
Topic: JEE Main 2019 (11 January Evening Shift)
If in a parallelogram $ABDC$, the coordinates of $A, B$ and $C$ are respectively $(1,2)$, $(3,4)$ and $(2,5)$, then the…
Topic: JEE Main 2019 (11 January Evening Shift)
he solution of the differential equation,
$\dfrac{dy}{dx}=(x-y)^{2}$, when $y(1)=1$, is
Topic: JEE Main 2019 (11 January Evening Shift)
The number of functions $f$ from $\{1,2,3,\ldots,20\}$ onto $\{1,2,3,\ldots,20\}$ such that $f(k)$ is a multiple of $3$…
Topic: JEE Main 2019 (11 January Evening Shift)
Let $K$ be the set of all real values of $x$ where the function $f(x)=\sin|x|-|x|+2(x-\pi)\cos|x|$ is not differentiabl…
Topic: JEE Main 2019 (11 January Evening Shift)
If $19^{\text{th}}$ term of a non-zero A.P. is zero, then its $(49^{\text{th}}\ \text{term}) : (29^{\text{th}}\ \text{t…
Topic: JEE Main 2019 (11 January Evening Shift)
Let $z$ be a complex number such that $|z|+z=3+i$ (where $i=\sqrt{-1}$). Then $|z|$ is equal to :
Topic: JEE Main 2019 (11 January Evening Shift)
Let $\alpha$ and $\beta$ be the roots of the quadratic equation
$x^{2}\sin\theta-x(\sin\theta\cos\theta+1)+\cos\theta=…
Topic: JEE Main 2019 (11 January Evening Shift)
