1
GATE CE 2000
MCQ (Single Correct Answer)
+1
-0.3
Consider the following two statements.

$$(I)$$ The maximum number of linearly independent column vectors of a matrix $$A$$ is called the rank of $$A.$$

$$(II)$$ If $$A$$ is $$nxn$$ square matrix then it will be non-singular if rank of $$A=n$$

A
Both the statements are false
B
Both the statements are true
C
$$(I)$$ is true but $$(II)$$ is false
D
$$(I)$$ is false but $$(II)$$ is true
2
GATE CE 2000
MCQ (Single Correct Answer)
+1
-0.3
If $$A,B,C$$ are square matrices of the same order then $${\left( {ABC} \right)^{ - 1}}$$ is equal be
A
$${C^{ - 1}}\,{A^{ - 1}}\,{B^{ - 1}}$$
B
$${C^{ - 1}}\,{B^{ - 1}}\,{A^{ - 1}}$$
C
$${A^{ - 1}}\,{B^{ - 1}}\,{C^{ - 1}}$$
D
$${A^{ - 1}}\,{C^{ - 1}}\,{B^{ - 1}}$$
3
GATE CE 2000
MCQ (Single Correct Answer)
+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
$${1 \over 2}$$
4
GATE CE 2000
MCQ (Single Correct Answer)
+2
-0.6
Limit of the function
$$f\left( x \right) = {{1 - {a^4}} \over {{x^4}}}\,\,as\,\,x \to \infty $$ is given by
A
$$1$$
B
$${e^{ - {a^4}}}$$
C
$$\infty $$
D
$$0$$
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