1
JEE Main 2016 (Offline)
+4
-1
If a curve $$y=f(x)$$ passes through the point $$(1,-1)$$ and satisfies the differential equation, $$y(1+xy) dx=x$$ $$dy$$, then $$f\left( { - {1 \over 2}} \right)$$ is equal to :
A
$${2 \over 5}$$
B
$${4 \over 5}$$
C
$$-{2 \over 5}$$
D
$$-{4 \over 5}$$
2
JEE Main 2015 (Offline)
+4
-1
Let $$y(x)$$ be the solution of the differential equation

$$\left( {x\,\log x} \right){{dy} \over {dx}} + y = 2x\,\log x,\left( {x \ge 1} \right).$$ Then $$y(e)$$ is equal to :
A
$$2$$
B
$$2e$$
C
$$e$$
D
$$0$$
3
JEE Main 2014 (Offline)
+4
-1
Let the population of rabbits surviving at time $$t$$ be governed by the differential equation $${{dp\left( t \right)} \over {dt}} = {1 \over 2}p\left( t \right) - 200.$$ If $$p(0)=100,$$ then $$p(t)$$ equals:
A
$$600 - 500\,{e^{t/2}}$$
B
$$400 - 300\,{e^{-t/2}}$$
C
$$400 - 300\,{e^{t/2}}$$
D
$$300 - 200\,{e^{-t/2}}$$
4
JEE Main 2013 (Offline)
+4
-1
At present, a firm is manufacturing $$2000$$ items. It is estimated that the rate of change of production P w.r.t. additional number of workers $$x$$ is given by $${{dp} \over {dx}} = 100 - 12\sqrt x .$$ If the firm employs $$25$$ more workers, then the new level of production of items is
A
$$2500$$
B
$$3000$$
C
$$3500$$
D
$$4500$$
EXAM MAP
Medical
NEET
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12