1
GATE CE 2004
MCQ (Single Correct Answer)
+1
-0.3
Real matrices $$\,\,{\left[ A \right]_{3x1,}}$$ $$\,\,{\left[ B \right]_{3x3,}}$$ $$\,\,{\left[ C \right]_{3x5,}}$$ $$\,\,{\left[ D \right]_{5x3,}}$$ $$\,\,{\left[ E \right]_{5x5,}}$$ $$\,\,{\left[ F \right]_{5x1,}}$$ are given. Matrices $$\left[ B \right]$$ and $$\left[ E \right]$$ are symmetric. Following statements are made with respect to their matrices.
$$(I)$$ Matrix product $$\,\,{\left[ F \right]^T}\,\,$$ $$\,\,{\left[ C \right]^T}\,\,$$ $$\,\,\left[ B \right]\,\,$$ $$\,\,\left[ C \right]\,\,$$ $$\,\,\left[ F \right]\,\,$$ is a scalar.
$$(II)$$ Matrix product $$\,\,{\left[ D \right]^T}\,\,$$ $$\,\left[ F \right]\,\,$$ $$\,\left[ D \right]\,\,$$ is always symmetric.
With reference to above statements which of the following applies?
A
statement $$(I)$$ is true but $$(II)$$ is false
B
statement $$(I)$$ is false but $$(II)$$ is true
C
both the statements are true
D
both the statements are false
2
GATE CE 2004
MCQ (Single Correct Answer)
+1
-0.3
The eigen values of the matrix $$\left[ {\matrix{ 4 & { - 2} \cr { - 2} & 1 \cr } } \right]$$ are
A
$$1,4$$
B
$$-1,2$$
C
$$0.5$$
D
can not be determined
3
GATE CE 2004
MCQ (Single Correct Answer)
+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 $$x=3$$
4
GATE CE 2004
MCQ (Single Correct Answer)
+1
-0.3
The value of the function, $$f\left( x \right) = \mathop {Lim}\limits_{x \to 0} {{{x^3} + {x^2}} \over {2{x^3} - 7{x^2}}}\,\,\,$$ is
A
$$0$$
B
$${-1 \over 7}$$
C
$${1 \over 7}$$
D
$$\infty $$
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