1
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
$$0$$
2
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
$$300 - 200\,{e^{-t/2}}$$
3
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
$$4500$$
4
AIEEE 2012
+4
-1
The population $$p$$ $$(t)$$ at time $$t$$ of a certain mouse species satisfies the differential equation $${{dp\left( t \right)} \over {dt}} = 0.5\,p\left( t \right) - 450.\,\,$$ If $$p(0)=850,$$ then the time at which the population becomes zero is :
A
$$2ln$$ $$18$$
B
$$ln$$ $$9$$
C
$${1 \over 2}$$$$ln$$ $$18$$
D
$$ln$$ $$18$$
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