1
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Derivative of $(\sin x)^{x}$ with respect to $x^{(\sin x)}$ is
A
$\frac{(\sin x)^{x-1}[(\sin x) \log (\sin x)+x \cos x]}{x^{(\sin x-1)}[x \cos x(\log x)+\sin x]}$
B
$\frac{(\sin x)^{x}[(\sin x)(\log (\sin x)+x \cos x)]}{x^{(\sin x)}[x \cos x(\log x)+\sin x]}$
C
$\frac{x^{\sin x-1}[x \cos x(\log x)+\sin x]}{(\sin x)^{x-1}[(\sin x) \log (\sin x)+x \cos x]}$
D
$\frac{x^{\sin x}[x \cos x(\log x)+\sin x]}{(\sin x)^{x}[(\sin x) \log (\sin x)+x \cos x]}$
2
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\log \left(x-\sqrt{x^{2}-1}\right)$, then $\left(x^{2}-1\right) y^{\prime \prime}+x y^{\prime}+e^{y}+\sqrt{x^{2}-1}=$
A
0
B
1
C
$\sqrt{x^{2}-1}$
D
$x$
3
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\log \left[\tan \sqrt{\frac{2^x-1}{2^x+1}}\right], x>0$, then $\left(\frac{d y}{d x}\right)_{x=1}=$
A
$\frac{4 \sqrt{2} \log 2}{9 \sin \left(\frac{2}{\sqrt{3}}\right)}$
B
$\frac{4 \sqrt{3} \log 2}{9 \sin \left(\frac{\sqrt{3}}{2}\right)}$
C
$\frac{4 \sqrt{3} \log 2}{9 \sin \left(\frac{2}{\sqrt{3}}\right)}$
D
$\frac{4 \sqrt{2} \log 2}{9 \sin \left(\frac{\sqrt{3}}{2}\right)}$
4
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\log y=y^{\log x}$, then $\frac{d y}{d x}=$
A
$\frac{y(\log y)^2}{x(1-\log x \log y)}$
B
$\frac{x(\log x)^2}{y(1-\log x \log y)}$
C
$\frac{x(1-\log x \log y)}{y(\log y)^2}$
D
$\frac{y(1-\log x \log y)}{x(\log x)^2}$
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