JEE Advanced 2014 Paper 1 Offline | Matrices and Determinants Question 33 | Mathematics

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JEE Advanced 2014 Paper 1 Offline

MCQ (More than One Correct Answer)

-0

Let M be a 2 $$\times$$ 2 symmetric matrix with integer entries. Then, M is invertible, if

the first column of M is the transpose of the second row of M

the second row of M is the transpose of the first column of M

M is a diagonal matrix with non-zero entries in the main diagonal

the product of entries in the main diagonal of M is not the square of an integer

JEE Advanced 2014 Paper 1 Offline

MCQ (More than One Correct Answer)

-0

Let M and N be two 3 $$\times$$ 3 matrices such that MN = NM. Further, if M $$\ne$$ N² and M² = N⁴, then

determinant of (M² + MN²) is 0

there is a 3 $$\times$$ 3 non-zero matrix U such that (M² + MN²) U is zero matrix

determinant of (M² + MN²) $$\ge$$ 1

for a 3 $$\times$$ 3 matrix U, if (M² + MN²) U equals the zero matrix, then U is the zero matrix

JEE Advanced 2013 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

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

JEE Advanced 2013 Paper 1 Offline

MCQ (More than One Correct Answer)

-0

For 3 × 3 matrices M and N, which of the following statement(s) is(are) NOT correct?

N^TMN is symmetric or skew symmetric, according as M is symmetric or skew symmetric.

MN – NM is skew symmetric for all symmetric matrices M and N.

MN is symmetric for all symmetric matrices M and N.

(adj M)·(adj N) = adj(MN) for all invertible matrices M and N.

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