1
JEE Main 2024 (Online) 31st January Evening Shift
+4
-1

If $$a=\sin ^{-1}(\sin (5))$$ and $$b=\cos ^{-1}(\cos (5))$$, then $$a^2+b^2$$ is equal to

A
25
B
$$4 \pi^2+25$$
C
$$8 \pi^2-40 \pi+50$$
D
$$4 \pi^2-20 \pi+50$$
2
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

For $$\alpha, \beta, \gamma \neq 0$$, if $$\sin ^{-1} \alpha+\sin ^{-1} \beta+\sin ^{-1} \gamma=\pi$$ and $$(\alpha+\beta+\gamma)(\alpha-\gamma+\beta)=3 \alpha \beta$$, then $$\gamma$$ equals

A
$$\sqrt{3}$$
B
$$\frac{\sqrt{3}}{2}$$
C
$$\frac{1}{\sqrt{2}}$$
D
$$\frac{\sqrt{3}-1}{2 \sqrt{2}}$$
3
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

Let $$x=\frac{m}{n}$$ ($$m, n$$ are co-prime natural numbers) be a solution of the equation $$\cos \left(2 \sin ^{-1} x\right)=\frac{1}{9}$$ and let $$\alpha, \beta(\alpha >\beta)$$ be the roots of the equation $$m x^2-n x-m+ n=0$$. Then the point $$(\alpha, \beta)$$ lies on the line

A
$$3 x-2 y=-2$$
B
$$3 x+2 y=2$$
C
$$5 x+8 y=9$$
D
$$5 x-8 y=-9$$
4
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

Considering only the principal values of inverse trigonometric functions, the number of positive real values of $$x$$ satisfying $$\tan ^{-1}(x)+\tan ^{-1}(2 x)=\frac{\pi}{4}$$ is :

A
more than 2
B
2
C
0
D
1
EXAM MAP
Medical
NEET