1
WB JEE 2021
+2
-0.5
The determinant $$\left| {\matrix{ {{a^2} + 10} & {ab} & {ac} \cr {ab} & {{b^2} + 10} & {bc} \cr {ac} & {bc} & {{c^2} + 10} \cr } } \right|$$ is
A
divisible by 10 but not by 100
B
divisible by 100
C
not divisible by 100
D
not divisible by 10
2
WB JEE 2020
+1
-0.25
Let A = $$\left( {\matrix{ {3 - t} \cr { - 1} \cr 0 \cr } \matrix{ {} \cr {} \cr {} \cr } \,\matrix{ 1 \cr {3 - t} \cr { - 1} \cr } \matrix{ {} \cr {} \cr {} \cr } \matrix{ 0 \cr 1 \cr 0 \cr } } \right)$$ and det A = 5, then
A
t = 1
B
t = 2
C
t = $$-$$ 1
D
t = $$-$$ 2
3
WB JEE 2020
+1
-0.25
Let $$A = \left[ {\matrix{ {12} & {24} & 5 \cr x & 6 & 2 \cr { - 1} & { - 2} & 3 \cr } } \right]$$. The value of x for which the matrix A is not invertible is
A
6
B
12
C
3
D
2
4
WB JEE 2020
+1
-0.25
Let $$A = \left( {\matrix{ a & b \cr c & d \cr } } \right)$$ be a 2 $$\times$$ 2 real matrix with det A = 1. If the equation det (A $$-$$ $$\lambda$$I2) = 0 has imaginary roots (I2 be the identity matrix of order 2), then
A
(a + d)2 < 4
B
(a + d)2 = 4
C
(a + d)2 > 4
D
(a + d)2 = 16
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