1
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
If x, y, z are in arithmetic progression with common difference d, x $$\ne$$ 3d, and the determinant of the matrix $$\left[ {\matrix{ 3 & {4\sqrt 2 } & x \cr 4 & {5\sqrt 2 } & y \cr 5 & k & z \cr } } \right]$$ is zero, then the value of k2 is :
A
72
B
12
C
36
D
6
2
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k2 has no solution if k is equal to :
A
0
B
$$-$$1
C
$$-$$2
D
1
3
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
$${\pi \over 3}$$
4
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
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