1
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\ldots \infty,}}}$ then $\frac{d y}{d x}=$
A
$\frac{\cos (\log 2 x)}{2 x(2 y-1)}$
B
$\frac{\cos (\log 2 x)}{(2 y-1)}$
C
$\frac{\cos (\log 2 x)}{x(2 y-1)}$
D
$\frac{\sin (\log 2 x)}{x(2 y-1)}$
2
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\tan ^{-1}\left[\frac{\sin ^{3}(2 x)-3 x^{2} \sin (2 x)}{3 x \sin ^{2}(2 x)-x^{3}}\right]$, then $\frac{d y}{d x}=$
A
$\frac{6 x \cos (2 x)-3 \sin (2 x)}{x^{2}-\sin ^{2}(2 x)}$
B
$\frac{6 x \sin (2 x)-3 \cos (2 x)}{x^{2}+\sin ^{2}(2 x)}$
C
$\frac{2 x \cos (2 x)-\sin (2 x)}{x^{2}+\sin ^{2}(2 x)}$
D
$\frac{6 x \cos (2 x)-3 \sin (2 x)}{x^{2}+\sin ^{2}(2 x)}$
3
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
$\frac{x^{\sin x}[x \cos x(\log x)+\sin x]}{(\sin x)^{x}[(\sin x) \log (\sin x)+x \cos x]}$
4
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
$x$
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