1
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+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
2
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
If $$\alpha$$ + $$\beta$$ + $$\gamma$$ = 2$$\pi$$, then the system of equations

x + (cos $$\gamma$$)y + (cos $$\beta$$)z = 0

(cos $$\gamma$$)x + y + (cos $$\alpha$$)z = 0

(cos $$\beta$$)x + (cos $$\alpha$$)y + z = 0

has :
A
no solution
B
infinitely many solution
C
exactly two solutions
D
a unique solution
3
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
If the following system of linear equations

2x + y + z = 5

x $$-$$ y + z = 3

x + y + az = b

has no solution, then :
A
$$a = - {1 \over 3},b \ne {7 \over 3}$$
B
$$a \ne {1 \over 3},b = {7 \over 3}$$
C
$$a \ne - {1 \over 3},b = {7 \over 3}$$
D
$$a = {1 \over 3},b \ne {7 \over 3}$$
4
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
If $${a_r} = \cos {{2r\pi } \over 9} + i\sin {{2r\pi } \over 9}$$, r = 1, 2, 3, ....., i = $$\sqrt { - 1}$$, then
the determinant $$\left| {\matrix{ {{a_1}} & {{a_2}} & {{a_3}} \cr {{a_4}} & {{a_5}} & {{a_6}} \cr {{a_7}} & {{a_8}} & {{a_9}} \cr } } \right|$$ is equal to :
A
a2a6 $$-$$ a4a8
B
a9
C
a1a9 $$-$$ a3a7
D
a5
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