1
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
Let $$A + 2B = \left[ {\matrix{ 1 & 2 & 0 \cr 6 & { - 3} & 3 \cr { - 5} & 3 & 1 \cr } } \right]$$ and $$2A - B = \left[ {\matrix{ 2 & { - 1} & 5 \cr 2 & { - 1} & 6 \cr 0 & 1 & 2 \cr } } \right]$$. If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A) $$-$$ Tr(B) has value equal to
A
1
B
2
C
0
D
3
2
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
3
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
4
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
$${\pi \over 3}$$
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