1
GATE EE 1995
MCQ (Single Correct Answer)
+1
-0.3
The rank of the following $$(n+1)$$ $$x$$ $$(n+1)$$ matrix, where $$'a'$$ is a real number is $$$\left[ {\matrix{ 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr . & {} & {} & {} & {} & {} & {} \cr . & {} & {} & {} & {} & {} & {} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr } } \right]$$$
A
$$1$$
B
$$2$$
C
$$n$$
D
depends on the value of a
2
GATE EE 1995
MCQ (Single Correct Answer)
+1
-0.3
$$\mathop {Lim}\limits_{x \to \infty } \,x\sin {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle x$}} = \_\_\_\_\_.$$
A
$$ \propto $$
B
$$0$$
C
$$1$$
D
Does not exist
3
GATE EE 1995
MCQ (Single Correct Answer)
+1
-0.3
If $$f(0)=2$$ and $$f'\left( x \right) = {1 \over {5 - {x^2}}},$$ then the lower and upper bounds of $$f(1)$$ estimated by the mean value theorem are ______.
A
$$1.9,2.2$$
B
$$2.2, 2.25$$
C
$$2.25, 2.5$$
D
None of the above
4
GATE EE 1995
MCQ (Single Correct Answer)
+1
-0.3
If at every point of a certain curve , the slope of the tangent equals $${{ - 2x} \over y},$$ the curve is _______.
A
A straight line
B
A parabola
C
A circle
D
An Ellipse
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