1
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
The number of $$3 \times 3$$ non-singular matrices, with four entries as $$1$$ and all other entries as $$0$$, is :
A
$$5$$
B
$$6$$
C
at least $$7$$
D
less than $$4$$
2
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Let $$A$$ be a $$\,2 \times 2$$ matrix
Statement - 1 : $$adj\left( {adj\,A} \right) = A$$
Statement - 2 :$$\left| {adj\,A} \right| = \left| A \right|$$
A
statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1.
B
statement - 1 is true, statement - 2 is false.
C
statement - 1 is false, statement -2 is true
D
statement -1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1.
3
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
Let $$a, b, c$$ be such that $$b\left( {a + c} \right) \ne 0$$ if

$$\left| {\matrix{ a & {a + 1} & {a - 1} \cr { - b} & {b + 1} & {b - 1} \cr c & {c - 1} & {c + 1} \cr } } \right| + \left| {\matrix{ {a + 1} & {b + 1} & {c - 1} \cr {a - 1} & {b - 1} & {c + 1} \cr {{{\left( { - 1} \right)}^{n + 2}}a} & {{{\left( { - 1} \right)}^{n + 1}}b} & {{{\left( { - 1} \right)}^n}c} \cr } } \right| = 0$$

then the value of $$n$$ :

A
any even integer
B
any odd integer
C
any integer
D
zero
4
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
Let $$A$$ be $$a\,2 \times 2$$ matrix with real entries. Let $$I$$ be the $$2 \times 2$$ identity matrix. Denote by tr$$(A)$$, the sum of diagonal entries of $$a$$. Assume that $${a^2} = I.$$
Statement-1 : If $$A \ne I$$ and $$A \ne - I$$, then det$$(A)=-1$$
Statement- 2 : If $$A \ne I$$ and $$A \ne - I$$, then tr $$(A)$$ $$\ne 0$$.
A
statement - 1 is false, statement -2 is true
B
statement -1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1.
C
statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1.
D
statement - 1 is true, statement - 2 is false.
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