1
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
If a + x = b + y = c + z + 1, where a, b, c, x, y, z
are non-zero distinct real numbers, then
$$\left| {\matrix{ x & {a + y} & {x + a} \cr y & {b + y} & {y + b} \cr z & {c + y} & {z + c} \cr } } \right|$$ is equal to :
A
y(b – a)
B
y(a – b)
C
y(a – c)
D
0
2
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
If the system of linear equations
x + y + 3z = 0
x + 3y + k2z = 0
3x + y + 3z = 0
has a non-zero solution (x, y, z) for some k $$\in$$ R, then x + $$\left( {{y \over z}} \right)$$ is equal to :
A
9
B
3
C
-9
D
-3
3
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
Let $$\lambda \in$$ R . The system of linear equations
2x1 - 4x2 + $$\lambda$$x3 = 1
x1 - 6x2 + x3 = 2
$$\lambda$$x1 - 10x2 + 4x3 = 3
is inconsistent for:
A
exactly one positive value of $$\lambda$$
B
exactly one negative value of $$\lambda$$
C
exactly two values of $$\lambda$$
D
every value of $$\lambda$$
4
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
Suppose the vectors x1, x2 and x3 are the
solutions of the system of linear equations,
Ax = b when the vector b on the right side is equal to b1, b2 and b3 respectively. if

$${x_1} = \left[ {\matrix{ 1 \cr 1 \cr 1 \cr } } \right]$$, $${x_2} = \left[ {\matrix{ 0 \cr 2 \cr 1 \cr } } \right]$$, $${x_3} = \left[ {\matrix{ 0 \cr 0 \cr 1 \cr } } \right]$$

$${b_1} = \left[ {\matrix{ 1 \cr 0 \cr 0 \cr } } \right]$$, $${b_2} = \left[ {\matrix{ 0 \cr 2 \cr 0 \cr } } \right]$$ and $${b_3} = \left[ {\matrix{ 0 \cr 0 \cr 2 \cr } } \right]$$,
then the determinant of A is equal to :
A
$${3 \over 2}$$
B
4
C
2
D
$${1 \over 2}$$
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