1
JEE Main 2022 (Online) 29th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\mathrm{A}(\alpha,-2), \mathrm{B}(\alpha, 6)$$ and $$\mathrm{C}\left(\frac{\alpha}{4},-2\right)$$ be vertices of a $$\triangle \mathrm{ABC}$$. If $$\left(5, \frac{\alpha}{4}\right)$$ is the circumcentre of $$\triangle \mathrm{ABC}$$, then which of the following is NOT correct about $$\triangle \mathrm{ABC}$$?

A
area is 24
B
perimeter is 25
C
circumradius is 5
D
inradius is 2
2
JEE Main 2022 (Online) 29th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $$Q$$ be the foot of perpendicular drawn from the point $$P(1,2,3)$$ to the plane $$x+2 y+z=14$$. If $$R$$ is a point on the plane such that $$\angle P R Q=60^{\circ}$$, then the area of $$\triangle P Q R$$ is equal to :

A
$$\frac{\sqrt{3}}{2}$$
B
$$ \sqrt{3}$$
C
$$2 \sqrt{3}$$
D
3
3
JEE Main 2022 (Online) 29th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If $$(2,3,9),(5,2,1),(1, \lambda, 8)$$ and $$(\lambda, 2,3)$$ are coplanar, then the product of all possible values of $$\lambda$$ is:

A
$$\frac{21}{2}$$
B
$$\frac{59}{8}$$
C
$$\frac{57}{8}$$
D
$$\frac{95}{8}$$
4
JEE Main 2022 (Online) 29th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is :

A
$$\frac{4}{9}$$
B
$$\frac{5}{18}$$
C
$$\frac{1}{6}$$
D
$$\frac{3}{10}$$
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