For $t\in(0,2\pi)$, if $\triangle ABC$ is an equilateral triangle with vertices $A(\sin t,-\cos t)$, $B(\cos t,\sin t)$ and $C(a,b)$ such that its orthocentre lies on a circle with centre $\left(1,\tfrac{1}{3}\right)$, then $(a^{2}-b^{2})$ is equal to:
Previous 10 Questions — JEE Main 2022 (28 July Morning Shift)
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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)
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 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 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 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)
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 th…
Topic: JEE Main 2022 (28 July Morning Shift)
Next 10 Questions — JEE Main 2022 (28 July Morning Shift)
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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)
Let $S_{1} = \{ z_{1} \in \mathbb{C} : |z_{1} - 3| = \tfrac{1}{2} \}$ and
$S_{2} = \{ z_{2} \in \mathbb{C} : |z_{2} -…
Topic: JEE Main 2022 (28 July Morning Shift)
If the minimum value of $f(x)=\dfrac{5x^{2}}{2}+\dfrac{\alpha}{x^{5}},; x>0,$ is $14$, then the value of $\alpha$ is eq…
Topic: JEE Main 2022 (28 July Morning Shift)
$ \text{Let } \alpha, \beta \text{ and } \gamma \text{ be three positive real numbers. Let } f(x) = \alpha x^{5} + \bet…
Topic: JEE Main 2022 (28 July Morning Shift)
The minimum value of the twice differentiable function $f(x)=\int_{0}^{x} e^{,x-t},f'(t),dt-(x^{2}-x+1)e^{x},; x\in\mat…
Topic: JEE Main 2022 (28 July Morning Shift)
