IIT-JEE 1981Question 36
Let $x$ and $y$ be two real variables such that $x>0$ and $xy=1$. Find the minimum value of $x+y$.
Differentiation and its Application
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JEE Mathematics / Practice
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IIT-JEE 1981Question 37
Find the value of $\cos\left(2\cos^{-1}x+\sin^{-1}x\right)$ at $x=\dfrac15$, where $0\le\cos^{-1}x\le\pi$ and $-\pi/2\le\sin^{-1}x\le\pi/2$.
Inverse Trigonometric Functions
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IIT-JEE 1983Question 38
Evaluate: $\displaystyle\int_{0}^{\pi/4}\frac{\sin x+\cos x}{9+16\sin2x}\,dx$.
Definite Integration
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IIT-JEE 1983Question 39
Evaluate: $\displaystyle\int\frac{(x-1)e^{x}}{(x+1)^{3}}\,dx$.
Indefinite Integration
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IIT-JEE 1978Question 40
Evaluate $\displaystyle\int\frac{\sin x}{\sin x-\cos x}\,dx$.
Indefinite Integration
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