1
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Let the system of linear equations

x + y + $$\alpha$$z = 2

3x + y + z = 4

x + 2z = 1

have a unique solution (x$$^ *$$, y$$^ *$$, z$$^ *$$). If ($$\alpha$$, x$$^ *$$), (y$$^ *$$, $$\alpha$$) and (x$$^ *$$, $$-$$y$$^ *$$) are collinear points, then the sum of absolute values of all possible values of $$\alpha$$ is

A
4
B
3
C
2
D
1
2
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

The number of values of $$\alpha$$ for which the system of equations :

x + y + z = $$\alpha$$

$$\alpha$$x + 2$$\alpha$$y + 3z = $$-$$1

x + 3$$\alpha$$y + 5z = 4

is inconsistent, is

A
0
B
1
C
2
D
3
3
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

Let S = {$$\sqrt{n}$$ : 1 $$\le$$ n $$\le$$ 50 and n is odd}.

Let a $$\in$$ S and $$A = \left[ {\matrix{ 1 & 0 & a \cr { - 1} & 1 & 0 \cr { - a} & 0 & 1 \cr } } \right]$$.

If $$\sum\limits_{a\, \in \,S}^{} {\det (adj\,A) = 100\lambda }$$, then $$\lambda$$ is equal to :

A
218
B
221
C
663
D
1717
4
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Consider the system of linear equations

$$-$$x + y + 2z = 0

3x $$-$$ ay + 5z = 1

2x $$-$$ 2y $$-$$ az = 7

Let S1 be the set of all a$$\in$$R for which the system is inconsistent and S2 be the set of all a$$\in$$R for which the system has infinitely many solutions. If n(S1) and n(S2) denote the number of elements in S1 and S2 respectively, then
A
n(S1) = 2, n(S2) = 2
B
n(S1) = 1, n(S2) = 0
C
n(S1) = 2, n(S2) = 0
D
n(S1) = 0, n(S2) = 2
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