1
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
If  xloge(logex) $$-$$ x2 + y2 = 4(y > 0), then $${{dy} \over {dx}}$$ at x = e is equal to :
A
$${{\left( {1 + 2e} \right)} \over {2\sqrt {4 + {e^2}} }}$$
B
$${{\left( {1 + 2e} \right)} \over {\sqrt {4 + {e^2}} }}$$
C
$${{\left( {2e - 1} \right)} \over {2\sqrt {4 + {e^2}} }}$$
D
$${e \over {\sqrt {4 + {e^2}} }}$$
2
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
The curve amongst the family of curves represented by the differential equation, (x2 – y2)dx + 2xy dy = 0 which passes through (1, 1) is
A
a circle with centre on the y-axis
B
an ellipse with major axis along the y-axis
C
a circle with centre on the x-axis
D
a hyperbola with transverse axis along the x-axis
3
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Let f be a differentiable function such that f '(x) = 7 - $${3 \over 4}{{f\left( x \right)} \over x},$$ (x > 0) and f(1) $$\ne$$ 4. Then $$\mathop {\lim }\limits_{x \to 0'} \,$$ xf$$\left( {{1 \over x}} \right)$$
A
does not exist
B
exists and equals $${4 \over 7}$$
C
exists and equals 4
D
exists and equals 0
4
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
A helicopter is flying along the curve given by y – x3/2 = 7, (x $$\ge$$ 0). A soldier positioned at the point $$\left( {{1 \over 2},7} \right)$$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is -
A
$${1 \over 6}\sqrt {{7 \over 3}}$$
B
$${{\sqrt 5 } \over 6}$$
C
$${1 \over 2}$$
D
$${1 \over 3}$$$$\sqrt {{7 \over 3}}$$
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination