GATE ME 2011 | Calculus Question 33 | Engineering Mathematics

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GATE ME 2011

MCQ (Single Correct Answer)

-0.3

A series expansion for the function $$\sin \theta $$ is _______.

$$1 - {{{\theta ^2}} \over {2!}} + {{{\theta ^4}} \over {4!}} - ......$$

$$\theta - {{{\theta ^3}} \over {3!}} + {{{\theta ^5}} \over {5!}} - ......$$

$$1 + \theta + {{{\theta ^2}} \over {2!}} + {{{\theta ^3}} \over {3!}} + ......$$

$$\theta + {{{\theta ^3}} \over {3!}} + {{{\theta ^5}} \over {5!}} + ......$$

GATE ME 2010

MCQ (Single Correct Answer)

-0.3

The parabolic are $$y = \sqrt x ,1 \le x \le 2$$ is revolved around the $$x$$-axis. The volume of the solid of revolution is

$${\pi \over 4}$$

$${\pi \over 2}$$

$${{3\pi } \over 4}$$

$${{3\pi } \over 2}$$

GATE ME 2010

MCQ (Single Correct Answer)

-0.3

The value of the integral $$\int\limits_{ - a}^a {{{dx} \over {1 + {x^2}}}} $$

$$-\pi $$

$${{ - \pi } \over 2}$$

$${{ \pi } \over 2}$$

$$\pi $$

GATE ME 2010

MCQ (Single Correct Answer)

-0.3

The function $$y = \left| {2 - 3x} \right|$$

is continuous $$\forall x \in R$$ and differentiable $$\forall x \in R$$

is continuous $$\forall x \in R$$ and differentiable $$\forall x \in R$$ except at $$x = {3 \over 2}$$

is continuous $$\forall x \in R$$ and differentiable $$\forall x \in R$$ except at $$x = {2 \over 3}$$

is continuous $$\forall x \in R$$ and except at $$x=3$$ and differentiable $$\forall x \in R$$

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