1
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
Out of Syllabus
If $$A = \left( {\matrix{ 0 & {\sin \alpha } \cr {\sin \alpha } & 0 \cr } } \right)$$ and $$\det \left( {{A^2} - {1 \over 2}I} \right) = 0$$, then a possible value of $$\alpha$$ is :
A
$${\pi \over 4}$$
B
$${\pi \over 6}$$
C
$${\pi \over 2}$$
D
$${\pi \over 3}$$
2
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
Let $$A = \left[ {\matrix{ i & { - i} \cr { - i} & i \cr } } \right],i = \sqrt { - 1}$$. Then, the system of linear equations $${A^8}\left[ {\matrix{ x \cr y \cr } } \right] = \left[ {\matrix{ 8 \cr {64} \cr } } \right]$$ has :
A
Exactly two solutions
B
Infinitely many solutions
C
A unique solution
D
No solution
3
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
Consider the following system of equations :

x + 2y $$-$$ 3z = a

2x + 6y $$-$$ 11z = b

x $$-$$ 2y + 7z = c,

where a, b and c are real constants. Then the system of equations :
A
has no solution for all a, b and c
B
has a unique solution when 5a = 2b + c
C
has infinite number of solutions when 5a = 2b + c
D
has a unique solution for all a, b and c
4
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A2 is 1, then the possible number of such matrices is :
A
6
B
4
C
1
D
12
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