1
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
$$(\sim p) \wedge(\sim q)$$
2
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
$$\frac{126}{81}$$
3
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
$$\frac{1}{2} \log _{e}\left|\frac{\tan \left(\frac{x}{2}-\frac{\pi}{12}\right)}{\tan \left(\frac{x}{2}-\frac{\pi}{6}\right)}\right|+C $$
4
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area bounded by the curves $$y=\left|x^{2}-1\right|$$ and $$y=1$$ is

A
$$\frac{2}{3}(\sqrt{2}+1)$$
B
$$\frac{4}{3}(\sqrt{2}-1)$$
C
$$2(\sqrt{2}-1)$$
D
$$\frac{8}{3}(\sqrt{2}-1)$$
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