1
JEE Main 2021 (Online) 24th February Evening Shift
+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
2
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
For the system of linear equations:

$$x - 2y = 1,x - y + kz = - 2,ky + 4z = 6,k \in R$$,

consider the following statements :

(A) The system has unique solution if $$k \ne 2,k \ne - 2$$.

(B) The system has unique solution if k = $$-$$2

(C) The system has unique solution if k = 2

(D) The system has no solution if k = 2

(E) The system has infinite number of solutions if k $$\ne$$ $$-$$2.

Which of the following statements are correct?
A
(B) and (E) only
B
(C) and (D) only
C
(A) and (E) only
D
(A) and (D) only
3
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
The system of linear equations
3x - 2y - kz = 10
2x - 4y - 2z = 6
x+2y - z = 5m
is inconsistent if :
A
k $$\ne$$ 3, m $$\in$$ R
B
k = 3, m $$\ne$$ $${4 \over 5}$$
C
k = 3, m $$=$$ $${4 \over 5}$$
D
k $$\ne$$ 3, m $$\ne$$ $${4 \over 5}$$
4
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
Let $$\theta = {\pi \over 5}$$ and $$A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$.

If B = A + A4 , then det (B) :
A
lies in (1, 2)
B
lies in (2, 3).
C
is zero.
D
is one.
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