1
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
Let a, b, c $$\in$$ R be all non-zero and satisfy
a3 + b3 + c3 = 2. If the matrix

A = $$\left( {\matrix{ a & b & c \cr b & c & a \cr c & a & b \cr } } \right)$$

satisfies ATA = I, then a value of abc can be :
A
3
B
$${1 \over 3}$$
C
-$${1 \over 3}$$
D
$${2 \over 3}$$
2
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
Let A = {X = (x, y, z)T: PX = 0 and

x2 + y2 + z2 = 1} where

$$P = \left[ {\matrix{ 1 & 2 & 1 \cr { - 2} & 3 & { - 4} \cr 1 & 9 & { - 1} \cr } } \right]$$,

then the set A :
A
is an empty set.
B
contains more than two elements.
C
contains exactly two elements.
D
is a singleton.
3
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.
4
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
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