1
JEE Main 2019 (Online) 11th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If y(x) is the solution of the differential equation $${{dy} \over {dx}} + \left( {{{2x + 1} \over x}} \right)y = {e^{ - 2x}},\,\,x > 0,\,$$ where $$y\left( 1 \right) = {1 \over 2}{e^{ - 2}},$$ then
A
y(loge2) = loge4
B
y(x) is decreasing in (0, 1)
C
y(loge2) = $${{{{\log }_e}2} \over 4}$$
D
y(x) is decreasing in $$\left( {{1 \over 2},1} \right)$$
2
JEE Main 2019 (Online) 11th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let A = $$\left( {\matrix{ 0 & {2q} & r \cr p & q & { - r} \cr p & { - q} & r \cr } } \right).$$   If  AAT = I3,   then   $$\left| p \right|$$ is :
A
$${1 \over {\sqrt 2 }}$$
B
$${1 \over {\sqrt 5 }}$$
C
$${1 \over {\sqrt 6 }}$$
D
$${1 \over {\sqrt 3 }}$$
3
JEE Main 2019 (Online) 11th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let [x] denote the greatest integer less than or equal to x. Then $$\mathop {\lim }\limits_{x \to 0} {{\tan \left( {\pi {{\sin }^2}x} \right) + {{\left( {\left| x \right| - \sin \left( {x\left[ x \right]} \right)} \right)}^2}} \over {{x^2}}}$$
A
equals $$\pi $$ + 1
B
equals 0
C
does not exist
D
equals $$\pi $$
4
JEE Main 2019 (Online) 11th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) and making an angle $${\pi \over 4}$$ with the plane y $$-$$ z + 5 = 0 are :
A
2, $$-$$1, 1
B
$$2\sqrt 3 ,1, - 1$$
C
$$\sqrt 2 ,1, - 1$$
D
$$\sqrt 2 , - \sqrt 2 $$
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