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1
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1 English
Hindi

Let $${{x - 2} \over 3} = {{y + 1} \over { - 2}} = {{z + 3} \over { - 1}}$$ lie on the plane $$px - qy + z = 5$$, for some p, q $$\in$$ R. The shortest distance of the plane from the origin is :

A
$$\sqrt {{3 \over {109}}}$$
B
$$\sqrt {{5 \over {142}}}$$
C
$${5 \over {\sqrt {71} }}$$
D
$${1 \over {\sqrt {142} }}$$
2
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1 English
Hindi

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line $$\overrightarrow r = - \widehat k + \lambda \left( {\widehat i + \widehat j + 2\widehat k} \right),\,\lambda \in R$$. Then, which of the following points lies on T ?

A
(2, 1, 0)
B
(1, 2, 1)
C
(1, 2, 2)
D
(1, 3, 2)
3
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1 English
Hindi
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 Morning Shift
+4
-1 English
Hindi

If the mirror image of the point (2, 4, 7) in the plane 3x $$-$$ y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to:

A
54
B
50
C
$$-$$6
D
$$-$$42
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