1
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The equations of the sides $$\mathrm{AB}, \mathrm{BC}$$ and CA of a triangle ABC are $$2 x+y=0, x+\mathrm{p} y=39$$ and $$x-y=3$$ respectively and $$\mathrm{P}(2,3)$$ is its circumcentre. Then which of the following is NOT true?

A
$$(\mathrm{AC})^{2}=9 \mathrm{p}$$
B
$$(\mathrm{AC})^{2}+\mathrm{p}^{2}=136$$
C
$$32<\operatorname{area}\,(\Delta \mathrm{ABC})<36$$
D
$$34<\operatorname{area}\,(\triangle \mathrm{ABC})<38$$
2
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

A circle $$C_{1}$$ passes through the origin $$\mathrm{O}$$ and has diameter 4 on the positive $$x$$-axis. The line $$y=2 x$$ gives a chord $$\mathrm{OA}$$ of circle $$\mathrm{C}_{1}$$. Let $$\mathrm{C}_{2}$$ be the circle with $$\mathrm{OA}$$ as a diameter. If the tangent to $$\mathrm{C}_{2}$$ at the point $$\mathrm{A}$$ meets the $$x$$-axis at $$\mathrm{P}$$ and $$y$$-axis at $$\mathrm{Q}$$, then $$\mathrm{QA}: \mathrm{AP}$$ is equal to :

A
1 : 4
B
1 : 5
C
2 : 5
D
1 : 3
3
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If the length of the latus rectum of a parabola, whose focus is $$(a, a)$$ and the tangent at its vertex is $$x+y=a$$, is 16, then $$|a|$$ is equal to :

A
$$2 \sqrt{2}$$
B
$$2 \sqrt{3}$$
C
$$4 \sqrt{2}$$
D
4
4
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the length of the perpendicular drawn from the point $$P(a, 4,2)$$, a $$>0$$ on the line $$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}$$ is $$2 \sqrt{6}$$ units and $$Q\left(\alpha_{1}, \alpha_{2}, \alpha_{3}\right)$$ is the image of the point P in this line, then $$\mathrm{a}+\sum\limits_{i=1}^{3} \alpha_{i}$$ is equal to :

A
7
B
8
C
12
D
14
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