1
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Let X and Y be two arbitrary, 3 $$\times$$ 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 $$\times$$ 3, non-zero, symmetric matrix. Then which of the following matrices is(are) skew symmetric?

A
Y3Z4 $$-$$ Z4Y3
B
X44 + Y44
C
X4Z3 $$-$$ Z3X4
D
X23 + Y23
2
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

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

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

A
$$-$$4
B
9
C
$$-$$9
D
4
3
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
4
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
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