1
GATE ECE 2022
Numerical
+1
-0.33

The value of the integral

$$\int\!\!\!\int\limits_D {3({x^2} + {y^2})dx\,dy}$$,

where D is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest integer).

2
GATE ECE 2019
+1
-0.33
The families of curves represented by the solution of the equation

$${{dy} \over {dx}} = - {\left( {{x \over y}} \right)^n}$$

for n = –1 and n = 1 respectively, are
A
Circles and Hyperbolas
B
Hyperbolas and Circles
C
Parabolas and Circles
D
Hyperbolas and Parabolas
3
GATE ECE 2018
+1
-0.33
Let $$f\left( {x,y} \right) = {{a{x^2} + b{y^2}} \over {xy}}$$, where $$a$$ and $$b$$ are constants. If $${{\partial f} \over {\partial x}} = {{\partial f} \over {\partial y}}$$ at x = 1 and y = 2, then the relation between $$a$$ and $$b$$ is
A
$$a = {b \over 4}$$
B
$$a = {b \over 2}$$
C
$$a = 2b$$
D
$$a = 4b$$
4
GATE ECE 2018
Numerical
+1
-0.33
Taylor series expansion of $$f\left( x \right) = \int\limits_0^x {{e^{ - \left( {{{{t^2}} \over 2}} \right)}}} dt$$ around 𝑥 = 0 has the form

f(x) = $${a_0} + {a_1}x + {a_2}{x^2} + ...$$

The coefficient $${a_2}$$ (correct to two decimal places) is equal to _______.