1
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$M = \left[ {\matrix{ 0 & 1 & a \cr 1 & 2 & 3 \cr 3 & b & 1 \cr } } \right]$$ and

adj $$M = \left[ {\matrix{ { - 1} & 1 & { - 1} \cr 8 & { - 6} & 2 \cr { - 5} & 3 & { - 1} \cr } } \right]$$

where a and b are real numbers. Which of the following options is/are correct?
A
B
If $$M\left[ {\matrix{ \alpha \cr \beta \cr \gamma \cr } } \right] = \left[ {\matrix{ 1 \cr 2 \cr 3 \cr } } \right]$$, then $$\alpha - \beta + \gamma = 3$$
C
$${(adj\,M)^{ - 1}} + adj\,{M^{ - 1}} = - M$$
D
a + b = 3
2
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let S be the set of all column matrices $$\left[ {\matrix{ {{b_1}} \cr {{b_2}} \cr {{b_3}} \cr } } \right]$$ such that $${b_1},{b_2},{b_3} \in R$$ and the system of equations (in real variables)

\eqalign{ & - x + 2y + 5z = {b_1} \cr & 2x - 4y + 3z = {b_2} \cr & x - 2y + 2z = {b_3} \cr}

has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each $$\left[ {\matrix{ {{b_1}} \cr {{b_2}} \cr {{b_3}} \cr } } \right]$$$$\in$$S?
A
$$x + 2y + 3z = {b_1}$$, $$\,4y + 5z = {b_2}$$ and $$x + 2y + 6z = {b_3}$$
B
$$x + y + 3z = {b_1}$$, $$5x + 2y + 6z = {b_2}$$ and $$- 2x - y - 3z = {b_3}$$
C
$$- x + 2y - 5z = {b_1}$$, $$\,2x - 4y + 10z = {b_2}$$ and $$x - 2y + 5z = {b_3}$$
D
$$x + 2y + 5z = {b_1}$$, $$2x + 3z = {b_2}$$ and $$x + 4y - 5z = {b_3}$$
3
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
$$\left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right]$$
4
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.
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