1
GATE CE 2004
+2
-0.6
The function $$f\left( x \right) = 2{x^3} - 3{x^2} - 36x + 2\,\,\,$$ has its maxima at
A
$$x=-2$$ only
B
$$x=0$$ only
C
$$x=3$$ only
D
both $$x=-2$$ and $$x=3$$
2
GATE CE 2002
+2
-0.6
Limit of the following sequence as $$n \to \infty$$ $$\,\,\,$$ is $$\,\,\,$$ $${x_n} = {n^{{1 \over n}}}$$
A
$$0$$
B
$$1$$
C
$$\infty$$
D
$$- \infty$$
3
GATE CE 2002
+2
-0.6
The value of the following improper integral is $$\,\int\limits_0^1 {x\,\log \,x\,dx} = \_\_\_\_\_.$$
A
$${1 \over 4}$$
B
$$0$$
C
$${{ - 1} \over 4}$$
D
$$1$$
4
GATE CE 2000
+2
-0.6
The Taylor series expansion of sin $$x$$ about $$x = {\pi \over 6}$$ is given by
A
$${1 \over 2} + {{\sqrt 3 } \over 2}\left( {x - {\Pi \over 6}} \right) - {1 \over 4}{\left( {x - {\Pi \over 6}} \right)^2} - {{\sqrt 3 } \over {12}}{\left( {x - {\Pi \over 6}} \right)^3} + - -$$
B
$$x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - - - -$$
C
$${{x - {\Pi \over 6}} \over {1!}} - {{{{\left( {x - {\Pi \over 6}} \right)}^3}} \over {3!}} + {{{{\left( {x - {\Pi \over 6}} \right)}^5}} \over {5!}} - {{{{\left( {x - {\Pi \over 6}} \right)}^7}} \over {7!}} + - - - -$$
D
$${1 \over 2}$$
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