1
GATE ME 2024
Numerical
+2
-1.33

If the value of the double integral

$\int_{x=3}^{4} \int_{y=1}^{2} \frac{dydx}{(x + y)^2}$

is $\log_e(\frac{a}{24})$, then $a$ is __________ (answer in integer).

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2
GATE ME 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
A parametric curve defined by $$x = \cos \left( {{{\pi u} \over 2}} \right),y = \sin \left( {{{\pi u} \over 2}} \right)\,\,$$ in the range $$0 \le u \le 1$$ is rotated about the $$x-$$axis by $$360$$ degrees. Area of the surface generated is
A
$${\pi \over 2}$$
B
$$\pi $$
C
$${2\pi }$$
D
$${4\pi }$$
3
GATE ME 2016 Set 3
MCQ (Single Correct Answer)
+2
-0.6
$$\mathop {Lt}\limits_{x \to \infty } \left( {\sqrt {{x^2} + x - 1} - x} \right)$$ is
A
$$0$$
B
$$\infty $$
C
$$1/2$$
D
$$ - \infty $$
4
GATE ME 2016 Set 1
Numerical
+2
-0
Consider the function $$f\left( x \right) = 2{x^3} - 3{x^2}\,\,$$ in the domain $$\,\left[ { - 1,2} \right].$$ The global minimum of $$f(x)$$ is _________.
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