1
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
$${5 \over 2}$$
2
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
$$\infty$$
3
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
$${8 \over 3}$$
4
GATE CE 2012
+1
-0.3
The infinite series $$1 + x + {{{x^2}} \over {2!}} + {{{x^3}} \over {3!}} + {{{x^4}} \over {4!}} + ........$$ corresponds to
A
$$sec\,x$$
B
$${e^x}$$
C
$$cos\,x$$
D
$$1 + si{n^2}x$$
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