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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