GATE ME 2011 | Calculus Question 31 | Engineering Mathematics

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

If $$f(x)$$ is even function and a is a positive real number , then $$\int\limits_{ - a}^a {f\left( x \right)dx\,\,} $$ equals ________.

$$0$$

$$a$$

$$2a$$

$$2\int\limits_0^a {f\left( x \right)dx\,\,} $$

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

What is $$\mathop {Lim}\limits_{\theta \to 0} {{\sin \theta } \over \theta }\,\,$$ equal to ?

$$\theta $$

$$sin$$$$\theta $$

$$0$$

$$1$$

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

$${\pi \over 4}$$

$${\pi \over 2}$$

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

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

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