1
VITEEE 2024
MCQ (Single Correct Answer)
+1
-0

If $(\cos x)^y=(\sin y)^x$, then $\frac{d y}{d x}$ equals

A
$\frac{\log \sin y-y \tan x}{\log \cos x+x \cot y}$
B
$\frac{\log \sin y+y \tan x}{\log \cos x-x \cot y}$
C
$\frac{\log \sin y+y \tan x}{\log \cos x+x \cot y}$
D
$\frac{\log \sin y+y \tan x}{\log \cos y-y \cot x}$
2
VITEEE 2024
MCQ (Single Correct Answer)
+1
-0

If the curves $\frac{x^2}{a}+\frac{y^2}{4}=1$ and $y^3=16 x$ intersect at right angles, then ' $a$ ' equals to

A
$\frac{3}{4}$
B
$\frac{1}{2}$
C
$\frac{4}{3}$
D
$2$
3
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

If $$y=1+\frac{x}{1 !}+\frac{x^2}{2 !}+\frac{x^3}{3 !} \ldots$$, then $$\frac{d y}{d x}$$ is equal to

A
$$e^x$$
B
$$\sin x$$
C
y
D
x
4
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

The value of $$\frac{d}{d x}\left(x^n \log _a x e^x\right)$$ is

A
$$e^x \log _a x+\frac{x^{n-1}}{\log _e a}$$
B
$$e^x x^{n-1}\left\{x \log _a x+\frac{1}{\log _e a}+n \log _a x\right\}$$
C
$$n x^{n-1} \log _a x e^x$$
D
$$x^n \log _a x \cdot e^x$$
VITEEE Subjects
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