1
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
Let m and M be respectively the minimum and maximum values of

$$\left| {\matrix{ {{{\cos }^2}x} & {1 + {{\sin }^2}x} & {\sin 2x} \cr {1 + {{\cos }^2}x} & {{{\sin }^2}x} & {\sin 2x} \cr {{{\cos }^2}x} & {{{\sin }^2}x} & {1 + \sin 2x} \cr } } \right|$$

Then the ordered pair (m, M) is equal to :
A
(–3, –1)
B
(–4, –1)
C
(1, 3)
D
(–3, 3)
2
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
The values of $$\lambda$$ and $$\mu$$ for which the system of linear equations
x + y + z = 2
x + 2y + 3z = 5
x + 3y + $$\lambda$$z = $$\mu$$
has infinitely many solutions are, respectively:
A
6 and 8
B
5 and 8
C
5 and 7
D
4 and 9
3
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
4
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
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