NDA MATHEMATICS QUIZ - 28

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Question 1:

If $x^{y}=\mathrm{e}^{x-y}$ then $\frac{d y}{d x}=\ldots \ldots$

Question 2:

If $x^{\mathrm{a}} \cdot \mathrm{y}^{\mathrm{b}}=(x+\mathrm{y})^{\mathrm{a}+\mathrm{b}} \cdot$ then $\frac{d y}{d x}$ equals

Question 3:

If $\mathrm{y}=e^{x+e^{x+\ldots+ up t o \infty}}$ then $\frac{d y}{d x}=\ldots . .$

Question 4:

If $x^{y}=y^{x}$ and $\frac{d y}{d x}=f(x, y)\left(\frac{x \log y-y}{y \log x-x}\right)$ then $f(x, y)=\ldots \ldots$

Question 5:

If $y=\cos ^{-1} \sqrt{\frac{\sqrt{1+x^{2}}+1}{2 \sqrt{1+x^{2}}}}$ then $\frac{d y}{d x}=\ldots \ldots$

Question 6:

If $y=\cos ^{-1}\left(\frac{x-x^{-1}}{x+x^{-1}}\right)$ then $\frac{d y}{d x}$ will be:

Question 7:

If $y=x \log y$ then which of the following is correct?

Question 8:

If $y=\sqrt{x}+\frac{1}{\sqrt{x}}$ then $2 x \frac{d y}{d x}+y$ is equal to

Question 9:

If $y=e^{\tan x}$ then the value of $\cos ^{2} x \frac{d^{2} y}{d x^{2}}-$ $(1+\sin 2 x) \frac{d y}{d x}=\ldots . .$

Question 10:

If $y=e^{\operatorname{ax}} \sin b x$ then $\frac{d^{2} y}{d x^{2}}-2 x \frac{d y}{d x}+k g=0$ where $\mathrm{k}$ equals: