1
GATE ECE 2014 Set 4
+2
-0.6
For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is
A
$${12^ \circ }$$
B
$${36^ \circ }$$
C
$${60^ \circ }$$
D
$${45^ \circ }$$
2
GATE ECE 2014 Set 3
Numerical
+2
-0
The maximum value of $$f\left( x \right) = 2{x^3} - 9{x^2} + 12x - 3$$
in the interval $$\,0 \le x \le 3$$ is __________.
3
GATE ECE 2014 Set 1
+2
-0.6
The Taylor series expansion of $$3$$ $$sin$$ $$x$$ $$+2cos$$ $$x$$ is
A
$$2 + 3x - {x^2} - {{{x^3}} \over 2} + - - -$$
B
$$2 - 3x + {x^2} - {{{x^3}} \over 2} + - - -$$
C
$$2 + 3x + {x^2} + {{{x^3}} \over 2} + - - -$$
D
$$2 - 3x - {x^2} + {{{x^3}} \over 2} + - - -$$
4
GATE ECE 2014 Set 1
Numerical
+2
-0
The volume under the surface $$z\left( {x,y} \right) = x + y$$ and above the triangle in the $$xy$$ plane defined by $$\left\{ {0 \le y \le x} \right.$$ and $$\,\left. {0 \le x \le 12} \right\}$$ is _________.