1
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
$\tan ^{-1}\left(\frac{4}{5}\right)$
2
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
$-1020$
3
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the arc $A C$ of a circle subtend a right angle at the centre $O$. If the point $B$ on the arc $A C$, divides the arc $A C$ such that $\frac{\text { length of } \operatorname{arc} A B}{\text { length of } \operatorname{arc} B C}=\frac{1}{5}$, and $\overrightarrow{O C}=\alpha \overrightarrow{O A}+\beta \overrightarrow{O B}$, then $\alpha+\sqrt{2}(\sqrt{3}-1) \beta$ is equal to

A
$2 \sqrt{3}$
B
$5 \sqrt{3}$
C
$2+\sqrt{3}$
D
$2-\sqrt{3}$
4
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the area of a $\triangle P Q R$ with vertices $P(5,4), Q(-2,4)$ and $R(a, b)$ be 35 square units. If its orthocenter and centroid are $O\left(2, \frac{14}{5}\right)$ and $C(c, d)$ respectively, then $c+2 d$ is equal to

A
$3$
B
$\frac{7}{3}$
C
$2$
D
$\frac{8}{3}$
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