AIEEE 2005 | Application of Derivatives Question 123 | Mathematics

AIEEE 2005

MCQ (Single Correct Answer)

-1

The normal to the curve
$$x = a\left( {\cos \theta + \theta \sin \theta } \right),y = a\left( {\sin \theta - \theta \cos \theta } \right)$$ at any point
$$\theta\, '$$ is such that

it passes through the origin

it makes an angle $${\pi \over 2} + \theta $$ with the $$x$$-axis

it passes through $$\left( {a{\pi \over 2}, - a} \right)$$

it is at a constant distance from the origin

AIEEE 2005

MCQ (Single Correct Answer)

-1

If the equation $${a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + ........... + {a_1}x = 0$$
$${a_1} \ne 0,n \ge 2,$$ has a positive root $$x = \alpha $$, then the equation
$$n{a_n}{x^{n - 1}} + \left( {n - 1} \right){a_{n - 1}}{x^{n - 2}} + ........... + {a_1} = 0$$ has a positive root, which is

greater than $$\alpha $$

smaller than $$\alpha $$

greater than or equal to smaller than $$\alpha $$

equal to smaller than $$\alpha $$

AIEEE 2004

MCQ (Single Correct Answer)

-1

A point on the parabola $${y^2} = 18x$$ at which the ordinate increases at twice the rate of the abscissa is

$$\left( {{9 \over 8},{9 \over 2}} \right)$$

$$(2, -4)$$

$$\left( {{-9 \over 8},{9 \over 2}} \right)$$

$$(2, 4)$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

A function $$y=f(x)$$ has a second order derivative $$f''\left( x \right) = 6\left( {x - 1} \right).$$ If its graph passes through the point $$(2, 1)$$ and at that point the tangent to the graph is $$y = 3x - 5$$, then the function is

$${\left( {x + 1} \right)^2}$$

$${\left( {x - 1} \right)^3}$$

$${\left( {x + 1} \right)^3}$$

$${\left( {x - 1} \right)^2}$$

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