1
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Which of the following is(are) NOT the square of a 3 $$ \times $$ 3 matrix with real entries?
A
$$\left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & { - 1} \cr } } \right]$$
B
$$\left[ {\matrix{ 1 & 0 & 0 \cr 0 & { - 1} & 0 \cr 0 & 0 & { - 1} \cr } } \right]$$
C
$$\left[ {\matrix{ { - 1} & 0 & 0 \cr 0 & { - 1} & 0 \cr 0 & 0 & { - 1} \cr } } \right]$$
D
$$\left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right]$$
2
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

Let a, $$\lambda$$, m $$\in$$ R. Consider the system of linear equations

ax + 2y = $$\lambda$$

3x $$-$$ 2y = $$\mu$$

Which of the following statements is(are) correct?

A
If a = $$-$$3, then the system has infinitely many solutions for all values of $$\lambda$$ and $$\mu$$.
B
If a $$\ne$$ $$-$$3, then the system has a unique solution for all values of $$\lambda$$ and $$\mu$$.
C
If $$\lambda$$ + $$\mu$$ = 0, then the system has infinitely many solutions for a = $$-$$3.
D
If $$\lambda$$ + $$\mu$$ $$\ne$$ 0, then the system has no solution for a = 3.
3
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Let $$P = \left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]$$, where $$\alpha$$ $$\in$$ R. Suppose $$Q = [{q_{ij}}]$$ is a matrix such that PQ = kl, where k $$\in$$ R, k $$\ne$$ 0 and I is the identity matrix of order 3. If $${q_{23}} = - {k \over 8}$$ and $$\det (Q) = {{{k^2}} \over 2}$$, then

A
$$\alpha$$ = 0, k = 8
B
$$4\alpha - k + 8 = 0$$
C
$$\det (Padj(Q)) = {2^9}$$
D
$$\det (Qadj(P)) = {2^{13}}$$
4
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
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