1
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$0 < x < {1 \over {\sqrt 2 }}$$ and $${{{{\sin }^{ - 1}}x} \over \alpha } = {{{{\cos }^{ - 1}}x} \over \beta }$$, then the value of $$\sin \left( {{{2\pi \alpha } \over {\alpha + \beta }}} \right)$$ is :

A
$$4 \sqrt{\left(1-x^{2}\right)}\left(1-2 x^{2}\right)$$
B
$$4 x \sqrt{\left(1-x^{2}\right)}\left(1-2 x^{2}\right)$$
C
$$2 x \sqrt{\left(1-x^{2}\right)}\left(1-4 x^{2}\right)$$
D
$$4 \sqrt{\left(1-x^{2}\right)}\left(1-4 x^{2}\right)$$
2
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Negation of the Boolean expression $$p \Leftrightarrow(q \Rightarrow p)$$ is

A
$$(\sim p) \wedge q$$
B
$$p \wedge(\sim q)$$
C
$$(\sim p) \vee(\sim q)$$
D
$$(\sim p) \wedge(\sim q)$$
3
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $$X$$ be a binomially distributed random variable with mean 4 and variance $$\frac{4}{3}$$. Then, $$54 \,P(X \leq 2)$$ is equal to :

A
$$\frac{73}{27}$$
B
$$\frac{146}{27}$$
C
$$\frac{146}{81}$$
D
$$\frac{126}{81}$$
4
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$ \text { The integral } \int \frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}} \sin 2 x\right)} d x \text { is equal to } $$

A
$$\frac{1}{2} \log _{e}\left|\frac{\tan \left(\frac{x}{2}+\frac{\pi}{12}\right)}{\tan \left(\frac{x}{2}+\frac{\pi}{6}\right)}\right|+C$$
B
$$\frac{1}{2} \log _{e}\left|\frac{\tan \left(\frac{x}{2}+\frac{\pi}{6}\right)}{\tan \left(\frac{x}{2}+\frac{\pi}{3}\right)}\right|+C$$
C
$$ \log _{e}\left|\frac{\tan \left(\frac{x}{2}+\frac{\pi}{6}\right)}{\tan \left(\frac{x}{2}+\frac{\pi}{12}\right)}\right|+C$$
D
$$\frac{1}{2} \log _{e}\left|\frac{\tan \left(\frac{x}{2}-\frac{\pi}{12}\right)}{\tan \left(\frac{x}{2}-\frac{\pi}{6}\right)}\right|+C $$
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