1
JEE Main 2018 (Offline)
+4
-1
If $$\left| {\matrix{ {x - 4} & {2x} & {2x} \cr {2x} & {x - 4} & {2x} \cr {2x} & {2x} & {x - 4} \cr } } \right| = \left( {A + Bx} \right){\left( {x - A} \right)^2}$$

then the ordered pair (A, B) is equal to
A
(4, 5)
B
(-4, -5)
C
(-4, 3)
D
(-4, 5)
2
JEE Main 2018 (Offline)
+4
-1
If the system of linear equations

x + ky + 3z = 0
3x + ky - 2z = 0
2x + 4y - 3z = 0

has a non-zero solution (x, y, z), then $${{xz} \over {{y^2}}}$$ is equal to
A
30
B
-10
C
10
D
-30
3
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
Suppose A is any 3$$\times$$ 3 nonsingular matrx and ( A $$-$$ 3I) (A $$-$$ 5I) = O where I = I3 and O = O3. If $$\alpha$$A + $$\beta$$A-1 = 4I, then $$\alpha$$ + $$\beta$$ is equal to :
A
8
B
7
C
13
D
12
4
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
If the system of linear equations
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :
A
a = $$-$$ 1,    b = 9
B
a = $$-$$ 1,    b $$\ne$$ 9
C
a $$\ne$$ $$-$$ 1,    b = 9
D
a = 1,    b $$\ne$$ 9
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