Trigonometry
Trigonometric Ratio and Identites
NumericalMCQ (Single Correct Answer)
1
JEE Main 2025 (Online) 22nd January Morning Shift
MCQ (Single Correct Answer)
+4
-1

The product of all solutions of the equation $\mathrm{e}^{5\left(\log _{\mathrm{e}} x\right)^2+3}=x^8, x>0$, is :

A
$e^2$
B
$e$
C
$\mathrm{e}^{6 / 5}$
D
$\mathrm{e}^{8 / 5}$
2
JEE Main 2023 (Online) 11th April Morning Shift
MCQ (Single Correct Answer)
+4
-1

The number of integral solutions $$x$$ of $$\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^{2} \geq 0$$ is :

A
8
B
7
C
5
D
6
3
JEE Main 2023 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1

If the solution of the equation $$\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right)$$, is $$\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)$$, where $$\alpha$$, $$\beta$$ are integers, then $$\alpha+\beta$$ is equal to :

A
3
B
6
C
4
D
5
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