GATE ME 2011 | GATE ME Year Wise Previous Years Questions

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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 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)

-0.6

An unbiased coin is tossed five times. The outcome of each loss is either a head or a tail. Probability of getting at least one head is _______.

$${1 \over {32}}$$

$${13 \over {32}}$$

$${16 \over {32}}$$

$${31 \over {32}}$$

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

Consider the differential equation $${{dy} \over {dx}} = \left( {1 + {y^2}} \right)x\,\,.$$ The general solution with constant $$'C'$$ is

$$y = \tan \left( {{{{x^2}} \over 2}} \right) + C$$

$$y = {\tan ^2}\left( {{x \over 2} + C} \right)$$

$$y = {\tan ^2}\left( {{x \over 2}} \right) + C$$

$$y = \tan \left( {{{{x^2}} \over 2} + C} \right)$$

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