IIT-JEE 1995 Screening | Application of Derivatives Question 78 | Mathematics

IIT-JEE 1995 Screening

MCQ (Single Correct Answer)

-0.25

On the interval $$\left[ {0,1} \right]$$ the function $${x^{25}}{\left( {1 - x} \right)^{75}}$$ takes its maximum value at the point

$$0$$

$${1 \over 4}$$

$${1 \over 2}$$

$${1 \over 3}$$

IIT-JEE 1995 Screening

MCQ (Single Correct Answer)

-0.25

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

$${5 \over 6}$$

$${6 \over 5}$$

$${1 \over 6}$$

$$6$$

IIT-JEE 1994

MCQ (Single Correct Answer)

-0.25

The function defined by $$f\left( x \right) = \left( {x + 2} \right){e^{ - x}}$$

decreasing for all $$x$$

decreasing in $$\left( { - \infty , - 1} \right)$$ and increasing in $$\left( { - 1,\infty } \right)$$

increasing for all $$x$$

decreasing in $$\left( { - 1,\infty } \right)$$ and increasing in $$\left( { - \infty , - 1} \right)$$

IIT-JEE 1994

MCQ (Single Correct Answer)

-0.25

Which one of the following curves cut the parabola $${y^2} = 4ax$$ at right angles?

$${x^2} + {y^2} = {a^2}$$

$$y = {e^{ - x/2a}}$$

$$y = ax$$

$${x^2} = 4ay$$

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