1
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $$\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$$ is equal to :

A
0
B
1
C
$$\frac{1}{2}$$
D
$$-\frac{1}{2}$$
2
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the operations $$*, \odot \in\{\wedge, \vee\}$$. If $$(\mathrm{p} * \mathrm{q}) \odot(\mathrm{p}\, \odot \sim \mathrm{q})$$ is a tautology, then the ordered pair $$(*, \odot)$$ is :

A
$$(\vee, \wedge)$$
B
$$(\vee, \vee)$$
C
$$(\wedge, \wedge)$$
D
$$(\wedge, \vee)$$
3
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a vector $$\vec{a}$$ has magnitude 9. Let a vector $$\vec{b}$$ be such that for every $$(x, y) \in \mathbf{R} \times \mathbf{R}-\{(0,0)\}$$, the vector $$(x \vec{a}+y \vec{b})$$ is perpendicular to the vector $$(6 y \vec{a}-18 x \vec{b})$$. Then the value of $$|\vec{a} \times \vec{b}|$$ is equal to :

A
$$9 \sqrt{3}$$
B
$$27 \sqrt{3}$$
C
9
D
81
4
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

For $$\mathrm{t} \in(0,2 \pi)$$, if $$\mathrm{ABC}$$ is an equilateral triangle with vertices $$\mathrm{A}(\sin t,-\cos \mathrm{t}), \mathrm{B}(\operatorname{cost}, \sin t)$$ and $$C(a, b)$$ such that its orthocentre lies on a circle with centre $$\left(1, \frac{1}{3}\right)$$, then $$\left(a^{2}-b^{2}\right)$$ is equal to :

A
$$\frac{8}{3}$$
B
8
C
$$\frac{77}{9}$$
D
$$\frac{80}{9}$$
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