1
GATE ECE 2016 Set 2
Numerical
+2
-0
The matrix $$A = \left[ {\matrix{ a & 0 & 3 & 7 \cr 2 & 5 & 1 & 3 \cr 0 & 0 & 2 & 4 \cr 0 & 0 & 0 & b \cr } } \right]$$ has det
$$(A)=100$$ and trace $$(A)=14.$$ The value of $$\left| {a - b} \right|$$ is ___________.
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2
GATE ECE 2016 Set 2
Numerical
+1
-0
The value of $$x$$ for which the matrix $$A = \left[ {\matrix{ 3 & 2 & 4 \cr 9 & 7 & {13} \cr { - 6} & { - 4} & { - 9 + x} \cr } } \right]$$ has zero as an eigen value is __________.
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3
GATE ECE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
As $$x$$ varies from $$- 1$$ to $$3,$$ which of the following describes the behavior of the function $$f\left( x \right) = {x^3} - 3{x^2} + 1?$$
A
$$f(x)$$ increases monotonically
B
$$f(x)$$ increases, then decreases and increases again
C
$$f(x)$$ decreases, then increases and decreases again
D
$$f(x)$$ increases and then decreases
4
GATE ECE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
How many distinct values of $$x$$ satisfy the equation $$sin(x)=x/2,$$ where $$x$$ is in radians ?
A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$ or more
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