1
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
An ordered pair ($$\alpha$$, $$\beta$$) for which the system of linear equations
(1 + $$\alpha$$) x + $$\beta$$y + z = 2
$$\alpha$$x + (1 + $$\beta$$)y + z = 3
$$\alpha$$x + $$\beta$$y + 2z = 2
has a unique solution, is :
A
(–3, 1)
B
(1, –3)
C
(–4, 2)
D
(2, 4)
2
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Let P = $$\left[ {\matrix{ 1 & 0 & 0 \cr 3 & 1 & 0 \cr 9 & 3 & 1 \cr } } \right]$$ and Q = [qij] be two 3 $$\times$$ 3 matrices such that Q – P5 = I3.

Then $${{{q_{21}} + {q_{31}}} \over {{q_{32}}}}$$ is equal to :
A
15
B
9
C
135
D
10
3
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)
4
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Out of Syllabus
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
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