1
JEE Main 2025 (Online) 23rd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the range of the function $f(x)=6+16 \cos x \cdot \cos \left(\frac{\pi}{3}-x\right) \cdot \cos \left(\frac{\pi}{3}+x\right) \cdot \sin 3 x \cdot \cos 6 x, x \in \mathbf{R}$ be $[\alpha, \beta]$. Then the distance of the point $(\alpha, \beta)$ from the line $3 x+4 y+12=0$ is :

A
11
B
10
C
8
D
9
2
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of $\left(\sin 70^{\circ}\right)\left(\cot 10^{\circ} \cot 70^{\circ}-1\right)$ is

A
0
B
2/3
C
1
D
3/2
3
JEE Main 2024 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the value of $$\frac{3 \cos 36^{\circ}+5 \sin 18^{\circ}}{5 \cos 36^{\circ}-3 \sin 18^{\circ}}$$ is $$\frac{a \sqrt{5}-b}{c}$$, where $$a, b, c$$ are natural numbers and $$\operatorname{gcd}(a, c)=1$$, then $$a+b+c$$ is equal to :

A
54
B
52
C
50
D
40
4
JEE Main 2024 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$\sin x=-\frac{3}{5}$$, where $$\pi< x <\frac{3 \pi}{2}$$, then $$80\left(\tan ^2 x-\cos x\right)$$ is equal to

A
109
B
108
C
19
D
18
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