1
AIEEE 2012
+4
-1
Out of Syllabus
Let $$P$$ and $$Q$$ be $$3 \times 3$$ matrices $$P \ne Q.$$ If $${P^3} = {Q^3}$$ and
$${P^2}Q = {Q^2}P$$ then determinant of $$\left( {{P^2} + {Q^2}} \right)$$ is equal to :
A
$$-2$$
B
$$1$$
C
$$0$$
D
$$-1$$
2
AIEEE 2012
+4
-1
Out of Syllabus
Let $$A = \left( {\matrix{ 1 & 0 & 0 \cr 2 & 1 & 0 \cr 3 & 2 & 1 \cr } } \right)$$. If $${u_1}$$ and $${u_2}$$ are column matrices such
that $$A{u_1} = \left( {\matrix{ 1 \cr 0 \cr 0 \cr } } \right)$$ and $$A{u_2} = \left( {\matrix{ 0 \cr 1 \cr 0 \cr } } \right),$$ then $${u_1} + {u_2}$$ is equal to :
A
$$\left( {\matrix{ -1 \cr 1 \cr 0 \cr } } \right)$$
B
$$\left( {\matrix{ -1 \cr 1 \cr -1 \cr } } \right)$$
C
$$\left( {\matrix{ -1 \cr -1 \cr 0 \cr } } \right)$$
D
$$\left( {\matrix{ 1 \cr -1 \cr -1 \cr } } \right)$$
3
AIEEE 2011
+4
-1
Let $$A$$ and $$B$$ be two symmetric matrices of order $$3$$.

Statement - 1 : $$A(BA)$$ and $$(AB)$$$$A$$ are symmetric matrices.

Statement - 2 : $$AB$$ is symmetric matrix if matrix multiplication of $$A$$ with $$B$$ is commutative.
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.
4
AIEEE 2011
+4
-1
The number of values of $$k$$ for which the linear equations
$$4x + ky + 2z = 0,kx + 4y + z = 0$$ and $$2x+2y+z=0$$ possess a non-zero solution is :
A
$$2$$
B
$$1$$
C
zero
D
$$3$$
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