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 $$\theta \,\, \ne \,\,b\,\,\sin \,\theta$$
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EXAM MAP
Medical
NEET