1
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 $$\lambda$$
2
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
$${1 \over 2}$$
3
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
If the system of equations
x+y+z=2
2x+4y–z=6
3x+2y+$$\lambda$$z=$$\mu$$
has infinitely many solutions, then
A
2$$\lambda$$ - $$\mu$$ = 5
B
$$\lambda$$ - 2$$\mu$$ = -5
C
2$$\lambda$$ + $$\mu$$ = 14
D
$$\lambda$$ + 2$$\mu$$ = 14
4
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
If $$A = \left[ {\matrix{ {\cos \theta } & {i\sin \theta } \cr {i\sin \theta } & {\cos \theta } \cr } } \right]$$, $$\left( {\theta = {\pi \over {24}}} \right)$$

and $${A^5} = \left[ {\matrix{ a & b \cr c & d \cr } } \right]$$, where $$i = \sqrt { - 1}$$ then which one of the following is not true?
A
$$a$$2 - $$c$$2 = 1
B
$$0 \le {a^2} + {b^2} \le 1$$
C
$$a$$2 - $$d$$2 = 0
D
$${a^2} - {b^2} = {1 \over 2}$$
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