1
WB JEE 2020
MCQ (Single Correct Answer)
+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
2
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
If $$\left| {\matrix{ {{a^2}} & {bc} & {{c^2} + ac} \cr {{a^2} + ab} & {{b^2}} & {ca} \cr {ab} & {{b^2} + bc} & {{c^2}} \cr } } \right| = k{a^2}{b^2}{c^2}$$,

then K =
A
2
B
$$-$$ 2
C
$$-$$ 4
D
4
3
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
If f : S $$\to$$ R, where S is the set of all non-singular matrices of order 2 over R and $$f\left[ {\left( {\matrix{ a & b \cr c & d \cr } } \right)} \right] = ad - bc$$, then
A
f is bijective mapping
B
f is one-one but not onto
C
f is onto but not one-one
D
f is neither one-one nor onto
4
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
If the vectors $$\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta = \widehat i + b\widehat j + {b^2}\widehat k$$ and $$\,\gamma = \widehat i + c\widehat j + {c^2}\widehat k$$ are three non-coplanar

vectors and $$\left| {\matrix{ a & {{a^2}} & {1 + {a^3}} \cr b & {{b^2}} & {1 + {b^3}} \cr c & {{c^2}} & {1 + {c^3}} \cr } } \right| = 0$$, then the value of abc is
A
1
B
0
C
$$-$$1
D
2
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