Yukti Vault

JEE Mathematics / Practice

Question Bank

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IIT-JEE 1979Question 31

Find the derivative of $$f(x)=\begin{cases}\dfrac{x-1}{2x^{2}-7x+5}, & x\neq1\\[4pt] -\dfrac13, & x=1\end{cases}$$ at $x=1$.

Differentiation and its Application

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IIT-JEE 1983Question 32

Find the coordinates of the point on the curve $y=\dfrac{x}{1+x^{2}}$ where the tangent to the curve has the greatest slope.

Differentiation and its Application

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IIT-JEE 1982Question 33

Let $f$ be a twice differentiable function such that $f''(x)=-f(x)$ and $f'(x)=g(x)$, $h(x)=[f(x)]^{2}+[g(x)]^{2}$. Find $h(10)$ if $h(5)=11$.

Differentiation and its Application

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IIT-JEE 1981Question 34

Use the function $f(x)=x^{1/x}$, $x>0$, to determine the bigger of the two numbers $e^{\pi}$ and $\pi^{e}$.

Differentiation and its Application

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IIT-JEE 1981Question 35

Let $y=e^{x\sin x^{3}}+(\tan x)^{x}$. Find $\dfrac{dy}{dx}$.

Differentiation and its Application

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