1
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

Let $$f(x) = \int\limits_0^x {{e^t}(t - 1)(t - 2)dt} $$. Then f(x) decreases in the interval.

A
x $$\in$$ (1, 2)
B
x $$\in$$ (2, 3)
C
x $$\in$$ (0, 1)
D
x $$\in$$ (0.5, 1)
2
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

Let R be a region in the first quadrant of the xy plane enclosed by a closed curve C considered in counter-clockwise direction. Which of the following expressions does not represent the area of the region R?

GATE EE 2022 Engineering Mathematics - Calculus Question 1 English

A
$$\int\!\!\!\int\limits_R {dxdy} $$
B
$$\oint\limits_C {xdy} $$
C
$$\oint\limits_C {ydx} $$
D
$${1 \over 2}\oint\limits_C {(xdy - ydx)} $$
3
GATE EE 2017 Set 1
Numerical
+1
-0
Let $${\rm I} = c\int {\int {_Rx{y^2}dxdy,\,\,} } $$ where $$R$$ is the region shown in the figure and $$c = 6 \times {10^{ - 4}}.\,\,$$ The value of $${\rm I}$$ equals ___________. GATE EE 2017 Set 1 Engineering Mathematics - Calculus Question 3 English
Your input ____
4
GATE EE 2017 Set 2
Numerical
+1
-0
Let $$\,{y^2} - 2y + 1 = x$$ and $$\,\sqrt x + y = 5.\,\,$$ The value of $$\,x + \sqrt y \,\,$$ equals ________. (Given the answer up to three decimal places)
Your input ____
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