1
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
Let $$A = \left( {\matrix{ {\cos \alpha } & { - \sin \alpha } \cr {\sin \alpha } & {\cos \alpha } \cr } } \right)$$, ($$\alpha$$ $$\in$$ R)
such that $${A^{32}} = \left( {\matrix{ 0 & { - 1} \cr 1 & 0 \cr } } \right)$$ then a value of $$\alpha$$ is
A
0
B
$${\pi \over {16}}$$
C
$${\pi \over {32}}$$
D
$${\pi \over {64}}$$
2
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
The greatest value of c $$\in$$ R for which the system of linear equations
x – cy – cz = 0
cx – y + cz = 0
cx + cy – z = 0
has a non-trivial solution, is :
A
-1
B
0
C
1/2
D
2
3
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
$$\left( {1,{5 \over 2}} \right]$$
4
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
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