JEE Advanced 2015 Paper 1 Offline | Matrices and Determinants Question 32 | Mathematics

JEE Advanced 2015 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Which of the following values of $$\alpha$$ satisfy the equation

$$\left| {\matrix{ {{{(1 - \alpha )}^2}} & {{{(1 + 2\alpha )}^2}} & {{{(1 + 3\alpha )}^2}} \cr {{{(2 + \alpha )}^2}} & {{{(2 + 2\alpha )}^2}} & {{{(2 + 3\alpha )}^2}} \cr {{{(3 + \alpha )}^2}} & {{{(3 + 2\alpha )}^2}} & {{{(3 + 3\alpha )}^2}} \cr } } \right| = - 648\alpha $$ ?

$$-$$4

$$-$$9

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 = ?

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