1

### 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
$$6$$
2

### 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
$${1 \over 3}$$
3

### 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 $$\left( {\pi /e,\infty } \right)$$
4

### IIT-JEE 1994

Which one of the following curves cut the parabola $${y^2} = 4ax$$ at right angles?
A
$${x^2} + {y^2} = {a^2}$$
B
$$y = {e^{ - x/2a}}$$
C
$$y = ax$$
D
$${x^2} = 4ay$$

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Class 12