1
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
Out of Syllabus
Let A = [aij] and B = [bij] be two 3 × 3 real matrices such that bij = (3)(i+j-2)aji, where i, j = 1, 2, 3. If the determinant of B is 81, then the determinant of A is:
A
3
B
$${1 \over 3}$$
C
$${1 \over 9}$$
D
$${1 \over {81}}$$
2
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
3
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.
4
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
$${{7\pi } \over {36}}$$
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