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In a certain culture the rate of increme...

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?

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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?

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?

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?

In a certain culture, the number of bacteria at any instant increases at a rate proportional to the square root of the number present at that instant. If the number becomes 16 times in 5 hours, when the number will be 49 times?

In a certain culture of bacteria, the rate of increase of its number is equal to half of the number present at that moment. When the number of bacteria will be double of its initial number? (Given log_(e)2=0.693 )

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.

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?

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.

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2^("nd") hour, 4^("th") hour and n^("th") hour ?

UNITED BOOK HOUSE-QUESTION PAPER 2017-EXERCISE
  1. Solve: tan^(-1)(x+1)+tan^(-1)(x-1)=tan^(-1)(8/31).

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  2. If A=([2,-1],[1,3]) then show that A^2-5A+7I2=0 hence find A^(-1)

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  3. Solve by Cramer's rule: x+3y= 4,y+3z = 7, 4x+z= 6.

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  4. Prove that |[2ab,a^2,b^2],[a^2,b^2,2ab],[b^2,2ab,a^2]|=-(a^3+b^3)^2.

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

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  6. Evaluate: int (xdx)/(x^4-x^2+1)

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

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  8. In a certain culture the rate of increment of bacterial at any instant...

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  9. The position vectors of four points A,B,C and D are 4hati+8 hat j+12ha...

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  10. If a vector 2 i ^ +3 j ^ ​ +8 k ^ is perpendicular to the vecto...

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  11. Evaluate: overset(pi/4)underset(0)intlog(1+tan theta)d theta.

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  12. find the value of overset(2)underset(1)int 5x^2dx.

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  13. A man is known to speak the truth 3 out of 4 times. HE throws an unbia...

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  14. If the sum of the mean and variance of a binomial distribution for 5 r...

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  15. Solve the following linear programming problem by graphical method and...

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  16. Using calculus, show that the maximum value of the function (1/x)^x is...

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

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

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  19. Find the shortest distance between the straight lines vecr = -4hati+...

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  20. A variable plane is at a constant distance p from the origin and meets...

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