1
GATE CSE 2009
+2
-0.6
$$\int\limits_0^{\pi /4} {\left( {1 - \tan x} \right)/\left( {1 + \tan x} \right)dx}$$ $$\,\,\,\,\,\,$$ evaluates to
A
$$0$$
B
$$1$$
C
In $$2$$
D
$${1 \over 2}$$ in $$2$$
2
GATE CSE 2008
+2
-0.6
If $$\,\,\,\,f\,\,\,\,\left( x \right)$$ is defined as follows, what is the minimum value of $$f\,\left( x \right)$$ for $$x \in \left( {0,2} \right)$$ ? $$f\left( x \right) = \left\{ {\matrix{ {{{25} \over {8x}}\,\,when\,\,x \le {3 \over 2}} \cr {x + {1 \over x}other\,wise} \cr } } \right.$$\$
A
$$2$$
B
$$2{1 \over {12}}$$
C
$$2{1 \over {6}}$$
D
$$2{1 \over {2}}$$
3
GATE CSE 2008
+2
-0.6
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $$3{x^4} - 16{x^3} + 24{x^2} + 37$$ is
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
4
GATE CSE 2005
+2
-0.6
What is the value of $$\int\limits_0^{2\pi } {{{\left( {x - \pi } \right)}^3}\left( {\sin x} \right)dx}$$
A
$$-1$$
B
$$0$$
C
$$1$$
D
$$\pi$$
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