1
GATE CE 2015 Set 2
+1
-0.3
Given $$i = \sqrt { - 1} ,$$ the value of the definite integral, $$\,{\rm I} = \int\limits_0^{\pi /2} {{{\cos x + \sin x} \over {\cos x - i\,\sin x}}dx\,\,}$$ is :
A
$$1$$
B
$$-1$$
C
$$i$$
D
$$-i$$
2
GATE CE 2014 Set 1
+1
-0.3
With reference to the conventional Cartesian $$(x,y)$$ coordinate system, the vertices of a triangle have the following coordinates: $$\,\left( {{x_1},{y_1}} \right) = \left( {1,0} \right);\,\,\,\left( {{x_2},{y_2}} \right) = \left( {2,2} \right);\,\,\,$$ and $$\,\left( {{x_3},{y_3}} \right) = \left( {4,3} \right).$$ The area of the triangle is equal to
A
$${3 \over 2}$$
B
$${3 \over 4}$$
C
$${4 \over 5}$$
D
$${5 \over 2}$$
3
GATE CE 2014 Set 1
+1
-0.3
$$\,\,\mathop {Lim}\limits_{x \to \infty } \left( {{{x + \sin x} \over x}} \right)\,\,$$ equal to
A
$$- \infty$$
B
$$0$$
C
$$1$$
D
$$\infty$$
4
GATE CE 2013
+1
-0.3
The solution $$\int\limits_0^{\pi /4} {{{\cos }^4}3\theta {{\sin }^3}\,6\theta d\theta \,\,}$$ is :
A
$$0$$
B
$${1 \over {15}}$$
C
$$1$$
D
$${8 \over 3}$$
GATE CE Subjects
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude
EXAM MAP
Joint Entrance Examination