1
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $\left|\frac{\bar{z}-i}{2 \bar{z}+i}\right|=\frac{1}{3}, z \in C$, be the equation of a circle with center at $C$. If the area of the triangle, whose vertices are at the points $(0,0), C$ and $(\alpha, 0)$ is 11 square units, then $\alpha^2$ equals:

A
$\frac{121}{25}$
B
100
C
$\frac{81}{25}$
D
50
2
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $\mathrm{I}(x)=\int \frac{d x}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}}$. If $\mathrm{I}(37)-\mathrm{I}(24)=\frac{1}{4}\left(\frac{1}{\mathrm{~b}^{\frac{1}{13}}}-\frac{1}{\mathrm{c}^{\frac{1}{13}}}\right), \mathrm{b}, \mathrm{c} \in \mathcal{N}$, then $3(\mathrm{~b}+\mathrm{c})$ is equal to

A
39
B
22
C
40
D
26
3
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the line $3 x-2 y+12=0$ intersects the parabola $4 y=3 x^2$ at the points $A$ and $B$, then at the vertex of the parabola, the line segment AB subtends an angle equal to

A
$\frac{\pi}{2}-\tan ^{-1}\left(\frac{3}{2}\right)$
B
$\tan ^{-1}\left(\frac{9}{7}\right)$
C
$\tan ^{-1}\left(\frac{11}{9}\right)$
D
$\tan ^{-1}\left(\frac{4}{5}\right)$
4
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

A
$-120$
B
$-1200$
C
$-1080$
D
$-1020$
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