1
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
Let A be a 3 $$\times$$ 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing the operation R2 $$\to$$ 2R2 + 5R3 on 2A, then det(B) is equal to :
A
64
B
16
C
128
D
80
2
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
If for the matrix, $$A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]$$, $$A{A^T} = {I_2}$$, then the value of $${\alpha ^4} + {\beta ^4}$$ is :
A
3
B
2
C
1
D
4
3
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
The following system of linear equations

2x + 3y + 2z = 9

3x + 2y + 2z = 9

x $$-$$ y + 4z = 8
A
does not have any solution
B
has a solution ($$\alpha$$, $$\beta$$, $$\gamma$$) satisfying $$\alpha$$ + $$\beta$$2 + $$\gamma$$3 = 12
C
has a unique solution
D
has infinitely many solutions
4
JEE Main 2021 (Online) 24th February Evening Slot
+4
-1
Let A and B be 3 $$\times$$ 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A2B2 $$-$$ B2A2) X = O, where X is a 3 $$\times$$ 1 column matrix of unknown variables and O is a 3 $$\times$$ 1 null matrix, has :
A
no solution
B
exactly two solutions
C
infinitely many solutions
D
a unique solution
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