1
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
Let S be the set of all $$\lambda$$ $$\in$$ R for which the system of linear equations

2x – y + 2z = 2
x – 2y + $$\lambda$$z = –4
x + $$\lambda$$y + z = 4

has no solution. Then the set S :
A
contains more than two elements.
B
contains exactly two elements.
C
is a singleton.
D
is an empty set.
2
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
Let A be a 2 $$\times$$ 2 real matrix with entries from {0, 1} and |A| $$\ne$$ 0. Consider the following two statements :

(P) If A $$\ne$$ I2 , then |A| = –1
(Q) If |A| = 1, then tr(A) = 2,

where I2 denotes 2 $$\times$$ 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then :
A
(P) is true and (Q) is false
B
Both (P) and (Q) are false
C
Both (P) and (Q) are true
D
(P) is false and (Q) is true
3
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
The following system of linear equations
7x + 6y – 2z = 0
3x + 4y + 2z = 0
x – 2y – 6z = 0, has
A
no solution
B
infinitely many solutions, (x, y, z) satisfying y = 2z
C
infinitely many solutions, (x, y, z) satisfying x = 2z
D
only the trivial solution
4
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
Out of Syllabus
If the matrices A = $$\left[ {\matrix{ 1 & 1 & 2 \cr 1 & 3 & 4 \cr 1 & { - 1} & 3 \cr } } \right]$$,

B = adjA and C = 3A, then $${{\left| {adjB} \right|} \over {\left| C \right|}}$$ is equal to :
A
8
B
2
C
72
D
16
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