IIT-JEE 2005 Mains | Application of Derivatives Question 48 | Mathematics

IIT-JEE 2005 Mains

MCQ (Single Correct Answer)

-1

If $$p(x)$$ be a polynomial of degree 3 satisfying $$p(-1)=10, p(1)=-6$$ and $$p(x)$$ has maximum at $$x=-1$$ and $$p'(x)$$ has minima at $$x=1$$. Find the distance between the local maximum and local minimum of the curve.

$$2\sqrt{65}$$

$$\sqrt{65}$$

$$4\sqrt{65}$$

$$4\sqrt{75}$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

If $$f\left( x \right) = {x^a}\log x$$ and $$f\left( 0 \right) = 0,$$ then the value of $$\alpha $$ for which Rolle's theorem can be applied in $$\left[ {0,1} \right]$$ is

$$-2$$

$$-1$$

$$0$$

$$1/2$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

If $$f\left( x \right) = {x^3} + b{x^2} + cx + d$$ and $$0 < {b^2} < c,$$ then in $$\left( { - \infty ,\infty } \right)$$

$$f\left( x \right)$$ is a strictly increasing function

$$f\left( x \right)$$ has a local maxima

$$f\left( x \right)$$ is a strictly decreasing function

$$f\left( x \right)$$ is bounded

IIT-JEE 2003 Screening

MCQ (Single Correct Answer)

-0.5

Tangent is drawn to ellipse
$${{{x^2}} \over {27}} + {y^2} = 1\,\,\,at\,\left( {3\sqrt 3 \cos \theta ,\sin \theta } \right)\left( {where\,\,\theta \in \left( {0,\pi /2} \right)} \right)$$.

Then the value of $$\theta $$ such that sum of intercepts on axes made by this tangent is minimum, is

$$\pi /3$$

$$\pi /6$$

$$\pi /8$$

$$\pi /4$$

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