1
JEE Main 2022 (Online) 26th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The ordered pair (a, b), for which the system of linear equations

3x $$-$$ 2y + z = b

5x $$-$$ 8y + 9z = 3

2x + y + az = $$-$$1

has no solution, is :

A
$$\left( {3,{1 \over 3}} \right)$$
B
$$\left( { - 3,{1 \over 3}} \right)$$
C
$$\left( { - 3, - {1 \over 3}} \right)$$
D
$$\left( {3, - {1 \over 3}} \right)$$
2
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The system of equations

$$ - kx + 3y - 14z = 25$$

$$ - 15x + 4y - kz = 3$$

$$ - 4x + y + 3z = 4$$

is consistent for all k in the set

A
R
B
R $$-$$ {$$-$$11, 13}
C
R $$-$$ {13}
D
R $$-$$ {$$-$$11, 11}
3
JEE Main 2022 (Online) 25th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let A be a 3 $$\times$$ 3 real matrix such that

$$A\left( {\matrix{ 1 \cr 1 \cr 0 \cr } } \right) = \left( {\matrix{ 1 \cr 1 \cr 0 \cr } } \right);A\left( {\matrix{ 1 \cr 0 \cr 1 \cr } } \right) = \left( {\matrix{ { - 1} \cr 0 \cr 1 \cr } } \right)$$ and $$A\left( {\matrix{ 0 \cr 0 \cr 1 \cr } } \right) = \left( {\matrix{ 1 \cr 1 \cr 2 \cr } } \right)$$.

If $$X = {({x_1},{x_2},{x_3})^T}$$ and I is an identity matrix of order 3, then the system $$(A - 2I)X = \left( {\matrix{ 4 \cr 1 \cr 1 \cr } } \right)$$ has :

A
no solution
B
infinitely many solutions
C
unique solution
D
exactly two solutions
4
JEE Main 2022 (Online) 25th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$A = \left[ {\matrix{ 0 & { - 2} \cr 2 & 0 \cr } } \right]$$. If M and N are two matrices given by $$M = \sum\limits_{k = 1}^{10} {{A^{2k}}} $$ and $$N = \sum\limits_{k = 1}^{10} {{A^{2k - 1}}} $$ then MN2 is :

A
a non-identity symmetric matrix
B
a skew-symmetric matrix
C
neither symmetric nor skew-symmetric matrix
D
an identity matrix
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