GATE CE 2017 Set 2 | GATE CE Year Wise Previous Years Questions

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

-0.3

Let $$\,\,W = f\left( {x,y} \right),\,\,$$ where $$x$$ and $$y$$ are functions of $$t.$$ Then, according to the chain rule, $${{dw} \over {dt}}$$ is equal to

$${{dw} \over {dx}}{{dx} \over {dt}} + {{dw} \over {dy}}{{dt} \over {dt}}$$

$${{\partial w} \over {\partial x}}{{\partial x} \over {\partial t}} + {{\partial w} \over {\partial y}}{{\partial y} \over {\partial t}}$$

$${{\partial w} \over {\partial x}}{{dx} \over {dt}} + {{\partial w} \over {\partial y}}{{dy} \over {dt}}$$

$${{dw} \over {dx}}{{\partial x} \over {\partial t}} + {{dw} \over {dy}}{{\partial y} \over {\partial t}}$$

GATE CE 2017 Set 2

Numerical

-0

A two-faced fair coin has its faces designated as head $$(H)$$ and tail $$(T)$$. This coin is tossed three times in succession to record the following outcomes: $$H, H,H.$$ If the coin is tossed one more time, the probability (up to one decimal place ) of obtaining $$H$$ again, given the previous realizations of $$H, H$$ and $$H$$, would be _____.

Your input ____

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

-0.6

The tangent to the curve represented by $$y=x$$ $$ln$$ $$x$$ is required to have $${45^ \circ }$$ inclination with the $$x-$$axis. The coordinates of the tangent point would be

$$(1, 0)$$

$$(0,1)$$

$$(1,1)$$

$$\left( {\sqrt {2,} \sqrt 2 } \right)$$

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

-0.6

Consider the following definite integral $$${\rm I} = \int\limits_0^1 {{{{{\left( {{{\sin }^{ - 1}}x} \right)}^2}} \over {\sqrt {1 - {x^2}} }}dx} $$$
The value of the integral is

$${{{\pi ^3}} \over {24}}$$

$${{{\pi ^3}} \over {12}}$$

$${{{\pi ^3}} \over {48}}$$

$${{{\pi ^3}} \over {64}}$$

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