1
GATE ECE 2017 Set 1
+2
-0.6
Let $$\,\,f\left( x \right) = {e^{x + {x^2}}}\,\,$$ for real $$x.$$ From among the following. Choose the Taylor series approximation of $$f$$ $$(x)$$ around $$x=0,$$ which includes all powers of $$x$$ less than or equal to $$3.$$
A
$$1 + x + {x^2} + {x^3}$$
B
$$\,1 + x + {3 \over 2}{x^2} + {x^3}$$
C
$$\,1 + x + {3 \over 2}{x^2} + {7 \over 6}{x^3}$$
D
$$1 + x + 3{x^2} + 7{x^3}$$
2
GATE ECE 2017 Set 1
Numerical
+2
-0
A three dimensional region $$R$$ of finite volume is described by $$\,\,{x^2} + {y^2} \le {z^3},\,\,\,0 \le z \le 1$$
Where $$x, y, z$$ are real. The volume of $$R$$ correct to two decimal places is __________.
3
GATE ECE 2016 Set 3
Numerical
+2
-0
A triangle in the $$xy-$$plane is bounded by the straight lines $$2x=3y, y=0$$ and $$x=3.$$ The volume above the triangle and under the plane $$x+y+z=6Z$$ is ________.
4
GATE ECE 2016 Set 1
Numerical
+2
-0
The integral $$\,\,{1 \over {2\pi }}\int {\int_D {\left( {x + y + 10} \right)dxdy\,\,} }$$ where $$D$$ denotes the disc: $${x^2} + {y^2} \le 4,$$ evaluates to _________.