1
GATE CSE 1998
+2
-0.6
The rank of the matrix given below is: $$\left[ {\matrix{ 1 & 4 & 8 & 7 \cr 0 & 0 & 3 & 0 \cr 4 & 2 & 3 & 1 \cr 3 & {12} & {24} & {2} \cr } } \right]$$$A 3 B 1 C 2 D 4 2 GATE CSE 1998 MCQ (Single Correct Answer) +2 -0.6 Consider the following determinant $$\Delta = \left| {\matrix{ 1 & a & {bc} \cr 1 & a & {ca} \cr 1 & a & {ab} \cr } } \right|$$$

Which of the following is a factor of $$\Delta$$ ?

A
$$a + b$$
B
$$a - b$$
C
$$a + b + c$$
D
$$abc$$
3
GATE CSE 1997
+2
-0.6
Let $$A = ({a_{ij}})$$ be and n-rowed square matrix and $${I_{12}}$$ be the matrix obtained by interchanging the first and second rows of the n-rowed Identity matrix. Then$${AI_{12}}$$ is such that its first
A
row is the same as its second row
B
row is the same as the second row of A
C
column is the same as the second column A
D
row is all zero
4
GATE CSE 1996
+2
-0.6
The matrices$$\left[ {\matrix{ {\cos \,\theta } & { - \sin \,\theta } \cr {\sin \,\,\theta } & {\cos \,\,\theta } \cr } } \right]\,\,and$$
$$\left[ {\matrix{ a & 0 \cr 0 & b \cr } } \right]\,$$ commute under multiplication
A
if a = b or $$\theta = n\,\pi$$, n an integer
B
always
C
never
D
if a cos $$\theta \,\, \ne \,\,b\,\,\sin \,\theta$$
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
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