GATE CE 2022 Set 2 | Calculus Question 12 | Engineering Mathematics | GATE CE - ExamSIDE.com

1

GATE CE 2022 Set 2

MCQ (Single Correct Answer)

+1

-0.33

$$\int {\left( {x - {{{x^2}} \over 2} + {{{x^3}} \over 3} - {{{x^4}} \over 4} + ....} \right)dx} $$ is equal to :

A

$$ - {1 \over {1 - {x^2}}} + $$ Constant

B

$$ - {1 \over {1 - x}} + $$ Constant

C

$${1 \over {1 + {x^2}}} + $$ Constant

D

$${1 \over {1 + x}} + $$ Constant

2

GATE CE 2022 Set 1

MCQ (More than One Correct Answer)

+1

-0

Let max {a, b} denote the maximum of two real numbers a and b. Which of the following statements is/are TRUE about the function f(x) = max{3 $$-$$ x, x $$-$$ 1}?

A

It is continuous on its domain.

B

It has a local minimum at x = 2.

C

It has a local maximum at x = 2.

D

It is differentiable on its domain.

3

GATE CE 2022 Set 1

Numerical

+1

-0

A set of observations of independent variable (x) and the corresponding dependent variable (y) is given below.

x	5	2	4	3
y	16	10	13	12

Based on the data, the coefficient a of the linear regression model

y = a + bx

is estimated as 6.1. The coefficient b is _________. (round off to one decimal place)

Your input ____

4

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

+1

-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

A

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

B

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

C

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

D

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

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