1
JEE Main 2014 (Offline)
+4
-1
If $$\alpha ,\beta \ne 0,$$ and $$f\left( n \right) = {\alpha ^n} + {\beta ^n}$$ and $$\left| {\matrix{ 3 & {1 + f\left( 1 \right)} & {1 + f\left( 2 \right)} \cr {1 + f\left( 1 \right)} & {1 + f\left( 2 \right)} & {1 + f\left( 3 \right)} \cr {1 + f\left( 2 \right)} & {1 + f\left( 3 \right)} & {1 + f\left( 4 \right)} \cr } } \right|$$\$
$$= K{\left( {1 - \alpha } \right)^2}{\left( {1 - \beta } \right)^2}{\left( {\alpha - \beta } \right)^2},$$ then $$K$$ is equal to :
A
$$1$$
B
$$-1$$
C
$$\alpha \beta$$
D
$${1 \over {\alpha \beta }}$$
2
JEE Main 2014 (Offline)
+4
-1
If $$A$$ is a $$3 \times 3$$ non-singular matrix such that $$AA'=A'A$$ and
$$B = {A^{ - 1}}A',$$ then $$BB'$$ equals:
A
$${B^{ - 1}}$$
B
$$\left( {{B^{ - 1}}} \right)'$$
C
$$I+B$$
D
$$I$$
3
JEE Main 2013 (Offline)
+4
-1
If $$P = \left[ {\matrix{ 1 & \alpha & 3 \cr 1 & 3 & 3 \cr 2 & 4 & 4 \cr } } \right]$$ is the adjoint of a $$3 \times 3$$ matrix $$A$$ and
$$\left| A \right| = 4,$$ then $$\alpha$$ is equal to :
A
$$4$$
B
$$11$$
C
$$5$$
D
$$0$$
4
AIEEE 2012
+4
-1
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
$$\left( {\matrix{ 1 \cr -1 \cr -1 \cr } } \right)$$
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