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

The number of choices for $$\Delta \in \{ \wedge , \vee , \Rightarrow , \Leftrightarrow \} $$, such that

$$(p\Delta q) \Rightarrow ((p\Delta \sim q) \vee (( \sim p)\Delta q))$$ is a tautology, is :

A
1
B
2
C
3
D
4
4
JEE Main 2022 (Online) 24th June Morning Shift
Numerical
+4
-1
Change Language

The number of one-one functions f : {a, b, c, d} $$\to$$ {0, 1, 2, ......, 10} such

that 2f(a) $$-$$ f(b) + 3f(c) + f(d) = 0 is ___________.

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