New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2021 · 26 Feb · Shift 1 · Q35

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Differential Equations
2021 · 26 Feb · Shift 1 · Q35

Differential Equations question

2021 · 26 Feb · Shift 1 · Q35

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time t = 0. The number of bacteria is increased by 20% in 2 hours. If the population of bacteria is 2000 after

{k \over {{{\log }_e}\left( {{6 \over 5}} \right)}}

hours, then

{\left( {{k \over {{{\log }_e}2}}} \right)^2}

is equal to :

A
16
B
8
C
2
D
4

More from Differential Equations

The difference between degree and order of a differential equation that represents the family of curves given by $y^{2} = a (x + \frac{a}{2})$ , a > 0 is .2021 · Numerical
If y = y(x) is the solution of the equation $e^{s i n y} cos y \frac{d y}{d x} + e^{s i n y} cos x = cos x$ , y(0) = 0; then $1 + y (\frac{π}{6}) + \frac{3}{2} y (\frac{π}{3}) + \frac{1}{2} y (\frac{π}{4})$ …2021 · Numerical
Let y = y(x) be the solution of the differential equation $\frac{d y}{d x} = 2 (y + 2 sin x - 5) x - 2 cos x$ such that y(0) = 7. Then y( $π$ ) is equal to :2021 · MCQ
Let us consider a curve, y = f(x) passing through the point ( $-$ 2, 2) and the slope of the tangent to the curve at any point (x, f(x)) is given by f(x) + xf'(x) = x2. Then :2021 · MCQ
If the solution curve of the differential equation (2x $-$ 10y3)dy + ydx = 0, passes through the points (0, 1) and (2, $β$ ), then $β$ is a root of the equation :2021 · MCQ
Let y = y(x) be solution of the differential equation $lo g (\frac{d y}{d x}) = 3 x + 4 y$ , with y(0) = 0. If $y (- \frac{2}{3} lo g_{e} 2) = α lo g_{e} 2$ , then the value of $α$ is equal…2021 · MCQ
If $y = y (x), y \in [0, \frac{π}{2})$ is the solution of the differential equation $sec y \frac{d y}{d x} - sin (x + y) - sin (x - y) = 0$ , with y(0) = 0, then $5 y^{'} (\frac{π}{2})$ is equal to …2021 · Numerical
Let y = y(x) be the solution of the differential equation (x $-$ x3)dy = (y + yx2 $-$ 3x4)dx, x > 2. If y(3) = 3, then y(4) is equal to :2021 · MCQ