1
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
Let M be a 2 $$\times$$ 2 symmetric matrix with integer entries. Then, M is invertible, if
A
the first column of M is the transpose of the second row of M
B
the second row of M is the transpose of the first column of M
C
M is a diagonal matrix with non-zero entries in the main diagonal
D
the product of entries in the main diagonal of M is not the square of an integer
2
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
Let M and N be two 3 $$\times$$ 3 matrices such that MN = NM. Further, if M $$\ne$$ N2 and M2 = N4, then
A
determinant of (M2 + MN2) is 0
B
there is a 3 $$\times$$ 3 non-zero matrix U such that (M2 + MN2) U is zero matrix
C
determinant of (M2 + MN2) $$\ge$$ 1
D
for a 3 $$\times$$ 3 matrix U, if (M2 + MN2) U equals the zero matrix, then U is the zero matrix
3
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

Let $$\omega$$ be a complex cube root of unity with $$\omega$$ $$\ne$$ 1 and P = [pij] be a n $$\times$$ n matrix with pij = $$\omega$$i + j. Then P2 $$\ne$$ 0, when n = ?

A
57
B
55
C
58
D
56
4
JEE Advanced 2013 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-0
For 3 × 3 matrices M and N, which of the following statement(s) is(are) NOT correct?
A
NTMN is symmetric or skew symmetric, according as M is symmetric or skew symmetric.
B
MN – NM is skew symmetric for all symmetric matrices M and N.
C
MN is symmetric for all symmetric matrices M and N.
D
(adj M)·(adj N) = adj(MN) for all invertible matrices M and N.
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