1
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
Let $$\alpha$$ be a root of the equation x2 + x + 1 = 0 and the
matrix A = $${1 \over {\sqrt 3 }}\left[ {\matrix{ 1 & 1 & 1 \cr 1 & \alpha & {{\alpha ^2}} \cr 1 & {{\alpha ^2}} & {{\alpha ^4}} \cr } } \right]$$

then the matrix A31 is equal to
A
A2
B
A
C
I3
D
A3
2
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
If the system of linear equations
2x + 2ay + az = 0
2x + 3by + bz = 0
2x + 4cy + cz = 0,
where a, b, c $$\in$$ R are non-zero distinct; has a non-zero solution, then:
A
$${1 \over a},{1 \over b},{1 \over c}$$ are in A.P.
B
a + b + c = 0
C
a, b, c are in G.P.
D
a,b,c are in A.P.
3
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
A value of $$\theta \in \left( {0,{\pi \over 3}} \right)$$, for which
$$\left| {\matrix{ {1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {{{\sin }^2}\theta } & {1 + 4\cos 6\theta } \cr } } \right| = 0$$, is :
A
$${\pi \over {18}}$$
B
$${\pi \over {9}}$$
C
$${{7\pi } \over {24}}$$
D
$${{7\pi } \over {36}}$$
4
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = $$\left[ {\matrix{ 2 & 3 \cr 5 & { - 1} \cr } } \right]$$, then AB is equal to :
A
$$\left[ {\matrix{ 4 & { - 2} \cr 1 & { - 4} \cr } } \right]$$
B
$$\left[ {\matrix{ { - 4} & { - 2} \cr { - 1} & 4 \cr } } \right]$$
C
$$\left[ {\matrix{ { - 4} & 2 \cr 1 & 4 \cr } } \right]$$
D
$$\left[ {\matrix{ 4 & { - 2} \cr { - 1} & { - 4} \cr } } \right]$$
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