1
MHT CET 2023 9th May Evening Shift
+2
-0

If $$x^{\mathrm{k}}+y^{\mathrm{k}}=\mathrm{a}^{\mathrm{k}}(\mathrm{a}, \mathrm{k}>0)$$ and $$\frac{\mathrm{d} y}{\mathrm{~d} x}+\left(\frac{y}{x}\right)^{\frac{1}{3}}=0$$, then $$\mathrm{k}$$ has the value

A
$$\frac{1}{3}$$
B
$$\frac{2}{3}$$
C
$$\frac{1}{4}$$
D
$$\frac{2}{7}$$
2
MHT CET 2023 9th May Evening Shift
+2
-0

If $$\mathrm{g}$$ is the inverse of $$\mathrm{f}$$ and $$\mathrm{f}^{\prime}(x)=\frac{1}{1+x^3}$$, then $$\mathrm{g}^{\prime}(x)$$ is

A
$$\frac{1}{1+(g(x))^3}$$
B
$$1+(g(x))^3$$
C
$$\frac{g(x)}{1+(g(x))^3}$$
D
$$\frac{(\mathrm{g}(x))^3}{1+(\mathrm{g}(x))^3}$$
3
MHT CET 2023 9th May Morning Shift
+2
-0

The rate of change of $$\sqrt{x^2+16}$$ with respect to $$\frac{x}{x-1}$$ at $$x=5$$ is

A
$$\frac{-80}{\sqrt{41}}$$
B
$$\frac{80}{\sqrt{41}}$$
C
$$\frac{12}{5}$$
D
$$\frac{-12}{5}$$
4
MHT CET 2023 9th May Morning Shift
+2
-0

If $$x^2+y^2=\mathrm{t}+\frac{1}{\mathrm{t}}$$ and $$x^4+y^4=\mathrm{t}^2+\frac{1}{\mathrm{t}^2}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is equal to

A
$$\frac{y}{x}$$
B
$$\frac{-y}{x}$$
C
$$\frac{x}{y}$$
D
$$\frac{-x}{y}$$
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