1
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the plane $$P:\overrightarrow r \,.\,\overrightarrow a = d$$ contain the line of intersection of two planes $$\overrightarrow r \,.\,\left( {\widehat i + 3\widehat j - \widehat k} \right) = 6$$ and $$\overrightarrow r \,.\,\left( { - 6\widehat i + 5\widehat j - \widehat k} \right) = 7$$. If the plane P passes through the point $$\left( {2,3,{1 \over 2}} \right)$$, then the value of $${{|13\overrightarrow a {|^2}} \over {{d^2}}}$$ is equal to :

A
90
B
93
C
95
D
97
2
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The probability, that in a randomly selected 3-digit number at least two digits are odd, is :

A
$${{19} \over {36}}$$
B
$${{15} \over {36}}$$
C
$${{13} \over {36}}$$
D
$${{23} \over {36}}$$
3
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let $${\pi \over 8}$$ and $$\theta$$ be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then tan2$$\theta$$ is equal to

A
$${{3 - 2\sqrt 2 } \over 2}$$
B
$${{3 + \sqrt 2 } \over 2}$$
C
$${{3 - 2\sqrt 2 } \over 4}$$
D
$${{3 - \sqrt 2 } \over 4}$$
4
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let p, q, r be three logical statements. Consider the compound statements

$${S_1}:(( \sim p) \vee q) \vee (( \sim p) \vee r)$$ and

$${S_2}:p \to (q \vee r)$$

Then, which of the following is NOT true?

A
If S2 is True, then S1 is True
B
If S2 is False, then S1 is False
C
If S2 is False, then S1 is True
D
If S1 is False, then S2 is False
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