1
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
If   A = $$\left[ {\matrix{ 1 & {\sin \theta } & 1 \cr { - \sin \theta } & 1 & {\sin \theta } \cr { - 1} & { - \sin \theta } & 1 \cr } } \right]$$;

then for all $$\theta$$ $$\in$$ $$\left( {{{3\pi } \over 4},{{5\pi } \over 4}} \right)$$, det (A) lies in the interval :
A
$$\left( {{3 \over 2},3} \right]$$
B
$$\left( {0,{3 \over 2}} \right]$$
C
$$\left[ {{5 \over 2},4} \right)$$
D
$$\left( {1,{5 \over 2}} \right]$$
2
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
The set of all values of $$\lambda$$ for which the system of linear equations
x – 2y – 2z = $$\lambda$$x
x + 2y + z = $$\lambda$$y
– x – y = $$\lambda$$z
has a non-trivial solutions :
A
is an empty set
B
contains more than two elements
C
is a singleton
D
contains exactly two elements
3
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
An ordered pair ($$\alpha$$, $$\beta$$) for which the system of linear equations
(1 + $$\alpha$$) x + $$\beta$$y + z = 2
$$\alpha$$x + (1 + $$\beta$$)y + z = 3
$$\alpha$$x + $$\beta$$y + 2z = 2
has a unique solution, is :
A
(–3, 1)
B
(1, –3)
C
(–4, 2)
D
(2, 4)
4
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Let P = $$\left[ {\matrix{ 1 & 0 & 0 \cr 3 & 1 & 0 \cr 9 & 3 & 1 \cr } } \right]$$ and Q = [qij] be two 3 $$\times$$ 3 matrices such that Q – P5 = I3.

Then $${{{q_{21}} + {q_{31}}} \over {{q_{32}}}}$$ is equal to :
A
15
B
9
C
135
D
10
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