1
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
If $$D = \left| {\matrix{ 1 & 1 & 1 \cr 1 & {1 + x} & 1 \cr 1 & 1 & {1 + y} \cr } } \right|$$ for $$x \ne 0,y \ne 0,$$ then $$D$$ is :
A
divisible by $$x$$ but not $$y$$
B
divisible by $$y$$ but not $$x$$
C
divisible by neither $$x$$ nor $$y$$
D
divisible by both $$x$$ and $$y$$
2
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
If $$A$$ and $$B$$ are square matrices of size $$n\, \times \,n$$ such that
$${A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right),$$ then which of the following will be always true?
A
$$A=B$$
B
$$AB=BA$$
C
either of $$A$$ or $$B$$ is a zero matrix
D
either of $$A$$ or $$B$$ is identity matrix
3
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
Let $$A = \left( {\matrix{ 1 & 2 \cr 3 & 4 \cr } } \right)$$ and $$B = \left( {\matrix{ a & 0 \cr 0 & b \cr } } \right),a,b \in N.$$ Then
A
there cannot exist any $$B$$ such that $$AB=BA$$
B
there exist more then one but finite number of $$B'$$s such that $$AB=BA$$
C
there exists exactly one $$B$$ such that $$AB=BA$$
D
there exist infinitely many $$B'$$s such that $$AB=BA$$
4
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If $${A^2} - A + 1 = 0$$, then the inverse of $$A$$ is :
A
$$A+I$$
B
$$A$$
C
$$A-I$$
D
$$I-A$$
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