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

Let a triangle ABC be inscribed in the circle $${x^2} - \sqrt 2 (x + y) + {y^2} = 0$$ such that $$\angle BAC = {\pi \over 2}$$. If the length of side AB is $$\sqrt 2 $$, then the area of the $$\Delta$$ABC is equal to :

A
1
B
$$\left( {\sqrt 6 + \sqrt 3 } \right)/2$$
C
$$\left( {3 + \sqrt 3 } \right)/4$$
D
$$\left( {\sqrt 6 + 2\sqrt 3 } \right)/4$$
2
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The distance of the origin from the centroid of the triangle whose two sides have the equations $$x - 2y + 1 = 0$$ and $$2x - y - 1 = 0$$ and whose orthocenter is $$\left( {{7 \over 3},{7 \over 3}} \right)$$ is :

A
$$\sqrt 2 $$
B
2
C
2$$\sqrt 2 $$
D
4
3
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let A, B, C be three points whose position vectors respectively are

$$\overrightarrow a = \widehat i + 4\widehat j + 3\widehat k$$

$$\overrightarrow b = 2\widehat i + \alpha \widehat j + 4\widehat k,\,\alpha \in R$$

$$\overrightarrow c = 3\widehat i - 2\widehat j + 5\widehat k$$

If $$\alpha$$ is the smallest positive integer for which $$\overrightarrow a ,\,\overrightarrow b ,\,\overrightarrow c $$ are noncollinear, then the length of the median, in $$\Delta$$ABC, through A is :

A
$${{\sqrt {82} } \over 2}$$
B
$${{\sqrt {62} } \over 2}$$
C
$${{\sqrt {69} } \over 2}$$
D
$${{\sqrt {66} } \over 2}$$
4
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :

A
$${5 \over {16}}$$
B
$${9 \over {16}}$$
C
$${11 \over {16}}$$
D
$${13 \over {16}}$$
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