1
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The set of all values of $a^{2}$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $\mathrm{P}\left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x^{2}+2 y^{2}-(1+a) x-(1-a) y=0$, is equal to :
A
$(0,4]$
B
$(4, \infty)$
C
$(2,12]$
D
$(8, \infty)$
2
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language
Let A be a $n \times n$ matrix such that $|\mathrm{A}|=2$. If the determinant of the matrix $\operatorname{Adj}\left(2 \cdot \operatorname{Adj}\left(2 \mathrm{~A}^{-1}\right)\right) \cdot$ is $2^{84}$, then $\mathrm{n}$ is equal to :
Your input ____
3
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language
Let $\mathrm{S}$ be the set of all $\mathrm{a} \in \mathrm{N}$ such that the area of the triangle formed by the tangent at the point $\mathrm{P}(\mathrm{b}$, c), b, c $\in \mathbb{N}$, on the parabola $y^{2}=2 \mathrm{a} x$ and the lines $x=\mathrm{b}, y=0$ is $16 $ unit2, then $\sum\limits_{\mathrm{a} \in \mathrm{S}} \mathrm{a}$ is equal to :
Your input ____
4
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Change Language
Let the area of the region

$\left\{(x, y):|2 x-1| \leq y \leq\left|x^{2}-x\right|, 0 \leq x \leq 1\right\}$ be $\mathrm{A}$.

Then $(6 \mathrm{~A}+11)^{2}$ is equal to
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