1
IIT-JEE 1996
Subjective
+3
-0
Let $$f\left( x \right) = \left\{ {\matrix{ {x{e^{ax}},\,\,\,\,\,\,\,x \le 0} \cr {x + a{x^2} - {x^3},\,x > 0} \cr } } \right.$$

Where a is a positive constant. Find the interval in which $$f'(x)$$ is increasing.

2
IIT-JEE 1996
Subjective
+2
-0
Evaluate $$\int {{{\left( {x + 1} \right)} \over {x{{\left( {1 + x{e^x}} \right)}^2}}}dx} $$.
3
IIT-JEE 1996
Fill in the Blanks
+2
-0
If for nonzero $$x$$, $$af(x)+$$ $$bf\left( {{1 \over x}} \right) = {1 \over x} - 5$$ where $$a \ne b,$$ then
$$\int_1^2 {f\left( x \right)dx} = .......$$
4
IIT-JEE 1996
Fill in the Blanks
+1
-0
For $$n>0,$$ $$\int_0^{2\pi } {{{x{{\sin }^{2n}}x} \over {{{\sin }^{2n}}x + {{\cos }^{2n}}x}}} dx = $$
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