The locus of the mid-points of the chords of the circle $C_{1} : (x-4)^{2}+(y-5)^{2}=4$ which subtend an angle $\theta_{i}$ at the centre of the circle $C_{1}$, is a circle of radius $r_{i}$. If $\theta_{1}=\dfrac{\pi}{3}$, $\theta_{3}=\dfrac{2\pi}{3}$ and $r_{1}^{2}=r_{2}^{2}+r_{3}^{2}$, then $\theta_{2}$ is equal to:
Previous 10 Questions — JEE Main 2023 (24 January Evening Shift)
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The set of all values of $a$ for which
$\displaystyle \lim_{x\to a}\big([x-5]-[2x+2]\big)=0$, where $[\alpha]$ denotes…
Topic: JEE Main 2023 (24 January Evening Shift)
If the system of equations
$x + 2y + 3z = 3$
$4x + 3y - 4z = 4$
$8x + 4y - \lambda z = 9 + \mu$
has infinitel…
Topic: JEE Main 2023 (24 January Evening Shift)
Let $\vec{\alpha}=4\hat{i}+3\hat{j}+5\hat{k}$ and $\vec{\beta}=\hat{i}+2\hat{j}-4\hat{k}$.
Let $\vec{\beta}_{1}$ be p…
Topic: JEE Main 2023 (24 January Evening Shift)
The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is :
Topic: JEE Main 2023 (24 January Evening Shift)
The number of real solutions of the equation
$3\left(x^{2}+\dfrac{1}{x^{2}}\right)-2\left(x+\dfrac{1}{x}\right)+5=0$ i…
Topic: JEE Main 2023 (24 January Evening Shift)
Let $f(x)$ be a function such that $f(x+y)=f(x)\cdot f(y)$ for all $x,y\in \mathbb{N}$.
If $f(1)=3$ and $\displaystyl…
Topic: JEE Main 2023 (24 January Evening Shift)
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Let $y=y(x)$ be the solution of the differential equation $(x^{2}-3y^{2})\,dx+3xy\,dy=0$, with $y(1)=1$.
Then $6y^{2}…
Topic: JEE Main 2023 (24 January Evening Shift)
If $f(x)=\dfrac{2^{2x}}{2^{2x}+2},\ x\in\mathbb{R}$, then
$f\!\left(\dfrac{1}{2023}\right)+f\!\left(\dfrac{2}{2023}\ri…
Topic: JEE Main 2023 (24 January Evening Shift)
The number of square matrices of order $5$ with entries from the set $\{0,1\}$, such that the sum of all the elements i…
Topic: JEE Main 2023 (24 January Evening Shift)
Let the six numbers $a_{1},a_{2},a_{3},a_{4},a_{5},a_{6}$ be in A.P. and $a_{1}+a_{3}=10$.
If the mean of these six n…
Topic: JEE Main 2023 (24 January Evening Shift)
The value of
$\left(\dfrac{\,1+\sin\frac{2\pi}{9}+i\cos\frac{2\pi}{9}\,}{\,1+\sin\frac{2\pi}{9}-i\cos\frac{2\pi}{9}\,}…
Topic: JEE Main 2023 (24 January Evening Shift)
If $f(x)=x^{3}-x^{2}f'(1)+x f''(2)-f'''(3),\ x\in\mathbb{R}$, then:
Topic: JEE Main 2023 (24 January Evening Shift)
$\displaystyle \int_{\tfrac{3\sqrt{2}}{4}}^{\tfrac{3\sqrt{3}}{4}} \dfrac{48}{\sqrt{9-4x^{2}}}\,dx$ is equal to:
Topic: JEE Main 2023 (24 January Evening Shift)
