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1
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
The solutions of the equation $$\left| {\matrix{ {1 + {{\sin }^2}x} & {{{\sin }^2}x} & {{{\sin }^2}x} \cr {{{\cos }^2}x} & {1 + {{\cos }^2}x} & {{{\cos }^2}x} \cr {4\sin 2x} & {4\sin 2x} & {1 + 4\sin 2x} \cr } } \right| = 0,(0 < x < \pi )$$, are
A
$${\pi \over {12}},{\pi \over 6}$$
B
$${\pi \over 6},{{5\pi } \over 6}$$
C
$${{5\pi } \over {12}},{{7\pi } \over {12}}$$
D
$${{7\pi } \over {12}},{{11\pi } \over {12}}$$
2
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
3
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
4
JEE Main 2021 (Online) 17th March Morning Shift
$$-$$1
$$-$$2