1
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
Let
A = $$\left\{ {\theta \in \left( { - {\pi \over 2},\pi } \right):{{3 + 2i\sin \theta } \over {1 - 2i\sin \theta }}is\,purely\,imaginary} \right\}$$
. Then the sum of the elements in A is :
A
$${5\pi \over 6}$$
B
$$\pi$$
C
$${3\pi \over 4}$$
D
$${{2\pi } \over 3}$$
2
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
If $$A = \left[ {\matrix{ {\cos \theta } & { - \sin \theta } \cr {\sin \theta } & {\cos \theta } \cr } } \right]$$, then the matrix A–50 when $$\theta$$ = $$\pi \over 12$$, is equal to :
A
$$\left[ {\matrix{ { {{\sqrt 3 } \over 2}} & { - {1 \over 2}} \cr {{{ 1} \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right]$$
B
$$\left[ {\matrix{ {{1 \over 2}} & -{{{\sqrt 3 } \over 2}} \cr {{{\sqrt 3 } \over 2}} & {{{ - 1} \over 2}} \cr } } \right]$$
C
$$\left[ {\matrix{ {{{\sqrt 3 } \over 2}} & {{1 \over 2}} \cr -{{1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right]$$
D
$$\left[ {\matrix{ {{1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr {-{{\sqrt 3 } \over 2}} & {{{ 1} \over 2}} \cr } } \right]$$
3
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
If the Boolean expression
(p $$\oplus$$ q) $$\wedge$$ (~ p $$\odot$$ q) is equivalent
to p $$\wedge$$ q, where $$\oplus , \odot \in \left\{ { \wedge , \vee } \right\}$$, then the
ordered pair $$\left( { \oplus , \odot } \right)$$ is :
A
$$\left( { \vee , \wedge } \right)$$
B
$$\left( { \vee , \vee } \right)$$
C
$$\left( { \wedge , \vee } \right)$$
D
$$\left( { \wedge , \wedge } \right)$$
4
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
If y = y(x) is the solution of the differential equation,

x$$dy \over dx$$ + 2y = x2, satisfying y(1) = 1, then y($$1\over2$$) is equal to :
A
$${{7} \over {64}}$$
B
$${{49} \over {16}}$$
C
$${{1} \over {4}}$$
D
$${{13} \over {16}}$$
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