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In a certain culture the rate of increme...

In a certain culture the rate of increment of bactreria at any instant is proportional to the cube root of the number of bacteria present at that instant. If the number of becteria becomes 8 times hours, in how much time that number becomes 64 times?

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The correct Answer is:
15 hours
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In a certain culture the rate of increment of bacterial at any instant is proportional to the cube root of the number of bacteria present at that instant. IF the number of bacteria becomes 8 times in 3 hours, in how much time that number becomes 64 times?

In a certain culture, the number of bacteria at any instant increases at a rate proportional to the cube root of the number present at that instant. If the number becomes 8 times in 3 hours, when the number will be 64 times?

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This year the number of blood donners in a hospital is 24000. If the number of blood donners increases by 5% in every 6 months, then in how much time will the number of blood donners be 27783?

A and B are two separate reservoirs of water. Capacity of reservoir A is double the capacity of reservoir Bdot Both the reservoirs are filled completely with water, their inlets are closed and then the water is released simultaneously from both the reservoirs. The rate of flow of water out of each reservoir at any instant of time is proportional to the quantity of water in the reservoir at the time. One hour after the water is released, the quantity of water is reservoir A is 1 1/2 times the quantity of water in reservoir Bdot After how many hours do both the reservoirs have the same quantity of water?

The rate of decay of a radioactive substance at any time is proportional to its mass at that instant. If m_(0) be the mass of the substance at time t=0, find the law of variation of its mass as a function of time t.

The population of a country doubles in 50 years. Assuming that the rate of increase of population is proportional to the number of inhabitants, in how many years would the population becomes three times ?

A spherical ice ball melts in such a way that the rate of melting is proportional to its volume of ice at that instant. If half the quantity of ice melts in 30 minutes, show that after 90 minutes from the start of melting, the volume of ice that remains is (1)/(8) time of the original volume of the ice ball.

CHHAYA PUBLICATION-QUESTION PAPER 2017-UNIT -3
  1. The value of int(-a)^(a)(xe^(x^4))/(1+x^2)dx is

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  2. The degree of the differential equation (d^3y)/(dx^3)+y=root3(1+(dy)/(...

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  3. If x=sqrt(a^(sin^(-1)t)" and "y=sqrt(a^(cos^(-1)t) show that (dy)/(dx)...

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  4. Varify Rolle's theorem for the function f(x)=x^2-4x+3 in 1lexle3.

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  5. Evalute: int (cosx-cos2x)/(1-cosx)dx.

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  6. A particle starts with the velocity u and moves in a straight line, it...

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  7. Find the interval where f(x)=(1)/(1+x^2) decreases.

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  8. If f(x)=f(a+x), then prove that the value of int(a)^(a+t) f(x)dx is i...

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  9. If f(x)=((a+x)/(b+x))^(a+b+2x), then prove that f'(0)=[2log""(a)/(b)+(...

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  10. [(3,-2),(6,-k)] =A,also detA=0 then find k.

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  11. intcos^(- 1)sqrt(x/(a+x))dx

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  12. Evalute int (xdx)/(x^4-x^2+1)

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  13. Solve: ydx-(x+2y^2)dy=0.

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  14. In a certain culture the rate of increment of bactreria at any instant...

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  15. Evalute: int(0)^((pi)/(4)) log(1+tantheta)d theta.

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  16. From the definition of the definite integral, find the value of int(1...

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  17. Using calculus, find the maximum value of the function ((x)/(a))^x .

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  18. Using integration, prove that the area of the closed region bounded by...

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  19. If the staight line (x)/(h)+(y)/(k)=1touches the curve ((x)/(a))^n+((y...

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  20. Solve: xdy-ydx=sqrt(x^2+y^2)dx.

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