1
JEE Main 2015 (Offline)
+4
-1
If $$A = \left[ {\matrix{ 1 & 2 & 2 \cr 2 & 1 & { - 2} \cr a & 2 & b \cr } } \right]$$ is a matrix satisfying the equation

$$A{A^T} = 9\text{I},$$ where $$I$$ is $$3 \times 3$$ identity matrix, then the ordered

pair $$(a, b)$$ is equal to :
A
$$(2, 1)$$
B
$$(-2, -1)$$
C
$$(2, -1)$$
D
$$(-2, 1)$$
2
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 $${1 \over {\alpha \beta }}$$ 3 JEE Main 2014 (Offline) MCQ (Single Correct Answer) +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 $$I$$ 4 JEE Main 2013 (Offline) MCQ (Single Correct Answer) +4 -1 The number of values of $$k$$, for which the system of equations : $$\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \cr {kx + \left( {k + 3} \right)y = 3k - 1} \cr }$$$
has no solution, is
A
infinite
B
1
C
2
D
3
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