1
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\widehat a$$, $$\widehat b$$ be unit vectors. If $$\overrightarrow c $$ be a vector such that the angle between $$\widehat a$$ and $$\overrightarrow c $$ is $${\pi \over {12}}$$, and $$\widehat b = \overrightarrow c + 2\left( {\overrightarrow c \times \widehat a} \right)$$, then $${\left| {6\overrightarrow c } \right|^2}$$ is equal to :

A
$$6\left( {3 - \sqrt 3 } \right)$$
B
$$3 + \sqrt 3 $$
C
$$6\left( {3 + \sqrt 3 } \right)$$
D
$$6\left( {\sqrt 3 + 1} \right)$$
2
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If a random variable X follows the Binomial distribution B(33, p) such that

$$3P(X = 0) = P(X = 1)$$, then the value of $${{P(X = 15)} \over {P(X = 18)}} - {{P(X = 16)} \over {P(X = 17)}}$$ is equal to :

A
1320
B
1088
C
$${{120} \over {1331}}$$
D
$${{1088} \over {1089}}$$
3
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The domain of the function

$$f(x) = {{{{\cos }^{ - 1}}\left( {{{{x^2} - 5x + 6} \over {{x^2} - 9}}} \right)} \over {{{\log }_e}({x^2} - 3x + 2)}}$$ is :

A
$$( - \infty ,1) \cup (2,\infty )$$
B
$$(2,\infty )$$
C
$$\left[ { - {1 \over 2},1} \right) \cup (2,\infty )$$
D
$$\left[ { - {1 \over 2},1} \right) \cup (2,\infty ) - \left\{ 3,{{{3 + \sqrt 5 } \over 2},{{3 - \sqrt 5 } \over 2}} \right\}$$
4
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $$S = \left\{ {\theta \in [ - \pi ,\pi ] - \left\{ { \pm \,\,{\pi \over 2}} \right\}:\sin \theta \tan \theta + \tan \theta = \sin 2\theta } \right\}$$.

If $$T = \sum\limits_{\theta \, \in \,S}^{} {\cos 2\theta } $$, then T + n(S) is equal to :

A
7 + $$\sqrt 3 $$
B
9
C
8 + $$\sqrt 3 $$
D
10
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