1
IIT-JEE 1983
Subjective
+4
-0
Find the coordinates of the point on the curve $$y = {x \over {1 + {x^2}}}$$
where the tangent to the curve has the greatest slope.
2
IIT-JEE 1982
Subjective
+2
-0
If $$f(x)$$ and $$g(x)$$ are differentiable function for $$0 \le x \le 1$$ such that $$f(0)=2$$, $$g(0)=0$$, $$f(1)=6$$; $$g(1)=2$$, then show that there exist $$c$$ satisfying $$0 < c < 1$$ and $$f'(c)=2g'(c)$$.
3
IIT-JEE 1982
Subjective
+2
-0
If $$a{x^2} + {b \over x} \ge c$$ for all positive $$x$$ where $$a>0$$ and $$b>0$$ show that $$27a{b^2} \ge 4{c^3}$$.
4
IIT-JEE 1981
Subjective
+4
-0
Use the function $$f\left( x \right) = {x^{1/x}},x > 0$$. to determine the bigger of the two numbers $${e^\pi }$$ and $${\pi ^e}$$
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