1
GATE CSE 1995
+1
-0.3
The rank of the following (n + 1) x (n + 1) matrix, where a is a real number is $$\left[ {\matrix{ 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr . & . & . & . & . & . & . \cr . & . & . & . & . & . & . \cr . & . & . & . & . & . & . \cr 1 & a & {{a^2}} & . & . & . & {{a^n}} \cr } } \right]$$\$
A
1
B
2
C
n
D
Depends on the value of a
2
GATE CSE 1995
+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
3
GATE CSE 1995
Subjective
+5
-0
Let $${G_1}$$ and $${G_2}$$ be subgroups of a group $$G$$.
(a) Show that $${G_1}\, \cap \,{G_2}$$ is also a subgroup of $$G$$.
(b) $${\rm I}$$s $${G_1}\, \cup \,{G_2}$$ always a subgroup of $$G$$?
4
GATE CSE 1995
Subjective
+2
-0
Prove that in a finite graph, the number of vertices of odd degree is always even.
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