1
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
If  $$\left| {\matrix{ {a - b - c} & {2a} & {2a} \cr {2b} & {b - c - a} & {2b} \cr {2c} & {2c} & {c - a - b} \cr } } \right|$$

= (a + b + c) (x + a + b + c)2, x $$\ne$$ 0,

then x is equal to :
A
–2(a + b + c)
B
2(a + b + c)
C
abc
D
–(a + b + c)
2
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Let A and B be two invertible matrices of order 3 $$\times$$ 3. If det(ABAT) = 8 and det(AB–1) = 8,
then det (BA–1 BT) is equal to :
A
$${1 \over 4}$$
B
16
C
$${1 \over {16}}$$
D
1
3
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
If the system of linear equations
2x + 2y + 3z = a
3x – y + 5z = b
x – 3y + 2z = c
where a, b, c are non zero real numbers, has more one solution, then :
A
b – c – a = 0
B
a + b + c = 0
C
b – c + a = 0
D
b + c – a = 0
4
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
Let A = $$\left( {\matrix{ 0 & {2q} & r \cr p & q & { - r} \cr p & { - q} & r \cr } } \right).$$   If  AAT = I3,   then   $$\left| p \right|$$ is
A
$${1 \over {\sqrt 2 }}$$
B
$${1 \over {\sqrt 5 }}$$
C
$${1 \over {\sqrt 6 }}$$
D
$${1 \over {\sqrt 3 }}$$
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