1

GATE CSE 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
$$$\left[ {\matrix{
1 & a & {{a^2}} & . & . & . & {{a^n}} \cr
1 & a & {{a^2}} & . & . & . & {{a^n}} \cr
. & . & . & . & . & . & . \cr
. & . & . & . & . & . & . \cr
. & . & . & . & . & . & . \cr
1 & a & {{a^2}} & . & . & . & {{a^n}} \cr
} } \right]$$$

2

GATE CSE 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
$$$\left[ {\matrix{
1 & a & {{a^2}} & . & . & . & {{a^n}} \cr
1 & a & {{a^2}} & . & . & . & {{a^n}} \cr
. & . & . & . & . & . & . \cr
. & . & . & . & . & . & . \cr
. & . & . & . & . & . & . \cr
1 & a & {{a^2}} & . & . & . & {{a^n}} \cr
} } \right]$$$

3

GATE CSE 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

4

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 $$G$$?

(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 $$G$$?

Paper analysis

Total Questions

Algorithms

3

Compiler Design

4

Computer Organization

4

Data Structures

2

Database Management System

1

Discrete Mathematics

13

Operating Systems

12

Programming Languages

2

Theory of Computation

3

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