1
WB JEE 2022
+1
-0.25

Under which of the following condition(s) does(do) the system of equations $$\left( {\matrix{ 1 & 2 & 4 \cr 2 & 1 & 2 \cr 1 & 2 & {(a - 4)} \cr } } \right)\left( {\matrix{ x \cr y \cr z \cr } } \right) = \left( {\matrix{ 6 \cr 4 \cr a \cr } } \right)$$ possesses(possess) unique solution ?

A
$$\forall$$ a $$\in$$ R
B
a = 8
C
for all integral values of a
D
a $$\ne$$ 8
2
WB JEE 2022
+1
-0.25

If $$\Delta (x) = \left| {\matrix{ {x - 2} & {{{(x - 1)}^2}} & {{x^3}} \cr {x - 1} & {{x^2}} & {{{(x + 1)}^3}} \cr x & {{{(x + 1)}^2}} & {{{(x + 2)}^3}} \cr } } \right|$$, then coefficient of x in $$\Delta$$x is

A
2
B
$$-$$2
C
3
D
$$-$$4
3
WB JEE 2022
+1
-0.25

If $$p = \left[ {\matrix{ 1 & \alpha & 3 \cr 1 & 3 & 3 \cr 2 & 4 & 4 \cr } } \right]$$ is the adjoint of the $$3 \times 3$$ matrix A and det A = 4, then $$\alpha$$ is equal to

A
4
B
11
C
5
D
0
4
WB JEE 2022
+1
-0.25

If $$A = \left( {\matrix{ 1 & 1 \cr 0 & i \cr } } \right)$$ and $${A^{2018}} = \left( {\matrix{ a & b \cr c & d \cr } } \right)$$, then $$(a + d)$$ equals

A
1 + i
B
0
C
2
D
2018
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