Let $C$ be the centre of the circle $x^{2}+y^{2}-x+2y=\dfrac{11}{4}$ and $P$ be a point on the circle. A line passes through the point $C$, makes an angle of $\dfrac{\pi}{4}$ with the line $CP$ and intersects the circle at the points $Q$ and $R$. Then the area of the triangle $PQR$ (in unit$^{2}$) is :
Next 10 Questions — JEE Main 2022 (28 July Morning Shift)
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Let the solution curve of the differential equation
$x,dy = \left(\sqrt{x^{2}+y^{2}}+y\right)dx,; x>0,$
intersect the l…
Topic: JEE Main 2022 (28 July Morning Shift)
Considering only the principal values of the inverse trigonometric functions, the domain of the function
$f(x)=\cos^{-1…
Topic: JEE Main 2022 (28 July Morning Shift)
Let the vectors $\vec a=(1+t)\hat i+(1-t)\hat j+\hat k$, $\vec b=(1-t)\hat i+(1+t)\hat j+2\hat k$ and $\vec c=t\hat i-t…
Topic: JEE Main 2022 (28 July Morning Shift)
Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation
$…
Topic: JEE Main 2022 (28 July Morning Shift)
Let a vector $\vec{a}$ has magnitude $9$. Let a vector $\vec{b}$ be such that for every $(x,y)\in\mathbb{R}\times\mathb…
Topic: JEE Main 2022 (28 July Morning Shift)
For $t\in(0,2\pi)$, if $\triangle ABC$ is an equilateral triangle with vertices $A(\sin t,-\cos t)$, $B(\cos t,\sin t)$…
Topic: JEE Main 2022 (28 July Morning Shift)
For $\alpha \in \mathbb{N}$, consider a relation $R$ on $\mathbb{N}$ given by
$R={(x,y):3x+\alpha y \text{ is a multipl…
Topic: JEE Main 2022 (28 July Morning Shift)
Out of $60%$ female and $40%$ male candidates appearing in an exam, $60%$ candidates qualify it. The number of females …
Topic: JEE Main 2022 (28 July Morning Shift)
If $y=y(x),\; x\in(0,\pi/2)$ be the solution curve of the differential equation
$$(\sin^{2}2x)\dfrac{dy}{dx}+(8\sin^…
Topic: JEE Main 2022 (28 July Morning Shift)
The remainder when $7^{2022}+3^{2022}$ is divided by $5$ is :
Topic: JEE Main 2022 (28 July Morning Shift)
