1

IIT-JEE 1997

If $$f\left( x \right) = {x \over {\sin x}}$$ and $$g\left( x \right) = {x \over {\tan x}}$$, where $$0 < x \le 1$$, then in this interval
A
both $$f(x)$$ and $$g(x)$$ are increasing functions
B
both $$f(x)$$ and $$g(x)$$ are decreasing functions
C
$$f(x)$$ is an increasing functions
D
$$g(x)$$ is an increasing functions
2

IIT-JEE 1995 Screening

The slope of the tangent to a curve $$y = f\left( x \right)$$ at $$\left[ {x,\,f\left( x \right)} \right]$$ is $$2x+1$$. If the curve passes through the point $$\left( {1,2} \right)$$, then the area bounded by the curve, the $$x$$-axis and the line $$x=1$$ is
A
$${5 \over 6}$$
B
$${6 \over 5}$$
C
$${1 \over 6}$$
D
$$6$$
3

IIT-JEE 1995 Screening

On the interval $$\left[ {0,1} \right]$$ the function $${x^{25}}{\left( {1 - x} \right)^{75}}$$ takes its maximum value at the point
A
$$0$$
B
$${1 \over 4}$$
C
$${1 \over 2}$$
D
$${1 \over 3}$$
4

IIT-JEE 1995 Screening

The function $$f\left( x \right) = {{in\,\left( {\pi + x} \right)} \over {in\,\left( {e + x} \right)}}$$ is
A
increasing on $$\left( {0,\infty } \right)$$
B
decreasing on $$\left( {0,\infty } \right)$$
C
increasing on $$\left( {0,\pi /e} \right),$$ decreasing on $$\left( {\pi /e,\infty } \right)$$
D
decreasing on $$\left( {0,\pi /e} \right),$$ increasing on $$\left( {\pi /e,\infty } \right)$$

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