1
JEE Main 2021 (Online) 25th February Morning Shift
+4
-1
If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is $${{{x^2} - 4x + y + 8} \over {x - 2}}$$, then this curve also passes through the point :
A
(4, 4)
B
(5, 5)
C
(5, 4)
D
(4, 5)
2
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
The population P = P(t) at time 't' of a certain species follows the differential equation
$${{dP} \over {dt}}$$ = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is :
A
$${\log _e}18$$
B
$${1 \over 2}{\log _e}18$$
C
2$${\log _e}18$$
D
$${\log _e}9$$
3
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
If $$y = \left( {{2 \over \pi }x - 1} \right) cosec\,x$$ is the solution

of the differential equation,
$${{dy} \over {dx}} + p\left( x \right)y = {2 \over \pi } cosec\,x$$,

$$0 < x < {\pi \over 2}$$, then the function p(x) is equal to :
A
cot x
B
sec x
C
tan x
D
cosec x
4
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
The general solution of the differential equation
$$\sqrt {1 + {x^2} + {y^2} + {x^2}{y^2}}$$ + xy$${{dy} \over {dx}}$$ = 0 is :

(where C is a constant of integration)
A
$$\sqrt {1 + {y^2}} + \sqrt {1 + {x^2}} = {1 \over 2}{\log _e}\left( {{{\sqrt {1 + {x^2}} - 1} \over {\sqrt {1 + {x^2}} + 1}}} \right) + C$$
B
$$\sqrt {1 + {y^2}} - \sqrt {1 + {x^2}} = {1 \over 2}{\log _e}\left( {{{\sqrt {1 + {x^2}} - 1} \over {\sqrt {1 + {x^2}} + 1}}} \right) + C$$
C
$$\sqrt {1 + {y^2}} + \sqrt {1 + {x^2}} = {1 \over 2}{\log _e}\left( {{{\sqrt {1 + {x^2}} + 1} \over {\sqrt {1 + {x^2}} - 1}}} \right) + C$$
D
$$\sqrt {1 + {y^2}} - \sqrt {1 + {x^2}} = {1 \over 2}{\log _e}\left( {{{\sqrt {1 + {x^2}} + 1} \over {\sqrt {1 + {x^2}} - 1}}} \right) + C$$
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