1
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The statement $$(p \wedge(\sim q)) \vee((\sim p) \wedge q) \vee((\sim p) \wedge(\sim q))$$ is equivalent to _________.

A
$$(\sim p) \vee(\sim q)$$
B
$$p \vee(\sim q)$$
C
$$\mathrm{p} \vee \mathrm{q}$$
D
$$(\sim p) \vee q$$
2
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of $${{{e^{ - {\pi \over 4}}} + \int\limits_0^{{\pi \over 4}} {{e^{ - x}}{{\tan }^{50}}xdx} } \over {\int\limits_0^{{\pi \over 4}} {{e^{ - x}}({{\tan }^{49}}x + {{\tan }^{51}}x)dx} }}$$ is

A
51
B
50
C
25
D
49
3
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The random variable $$\mathrm{X}$$ follows binomial distribution $$\mathrm{B}(\mathrm{n}, \mathrm{p})$$, for which the difference of the mean and the variance is 1 . If $$2 \mathrm{P}(\mathrm{X}=2)=3 \mathrm{P}(\mathrm{X}=1)$$, then $$n^{2} \mathrm{P}(\mathrm{X}>1)$$ is equal to :

A
15
B
12
C
11
D
16
4
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The range of $$f(x)=4 \sin ^{-1}\left(\frac{x^{2}}{x^{2}+1}\right)$$ is

A
$$[0,2 \pi]$$
B
$$[0,2 \pi)$$
C
$$[0, \pi)$$
D
$$[0, \pi]$$
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