1
GATE ECE 2024
MCQ (Single Correct Answer)
+2
-1.33

Consider the Earth to be a perfect sphere of radius $R$. Then the surface area of the region, enclosed by the 60°N latitude circle, that contains the north pole in its interior is _______.

A

$\left( 2 - \sqrt{3} \right) \pi R^2$

B

$\frac{\left( \sqrt{2} - 1 \right) \pi R^2}{2}$

C

$\frac{2 \pi R^2}{3}$

D

$\frac{\left( 2 + \sqrt{3} \right) \pi R^2}{8 \sqrt{2}}$

2
GATE ECE 2023
MCQ (Single Correct Answer)
+2
-0.67

The value of the line integral $$\int_P^Q {({z^2}dx + 3{y^2}dy + 2xz\,dz)} $$ along the straight line joining the points $$P(1,1,2)$$ and $$Q(2,3,1)$$ is

A
20
B
24
C
29
D
$$-$$5
3
GATE ECE 2023
Numerical
+2
-0

The value of the integral $$\int\limits\!\!\!\int_R {xy\,dx\,dy} $$ over the regioin R, given in the figure, is _________ (rounded off to the nearest integer).

GATE ECE 2023 Engineering Mathematics - Calculus Question 3 English

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4
GATE ECE 2022
MCQ (Single Correct Answer)
+2
-0.67

The function f(x) = 8loge x $$-$$ x2 + 3 attains its minimum over the interval [1, e] at x = __________.

(Here loge x is the natural logarithm of x.)

A
2
B
1
C
e
D
$${{1 + e} \over 2}$$
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