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Evaluate (with the help of definite inte...

Evaluate (with the help of definite integral): `underset(n rarr infty)lim{(1+1/n)(1+2/n)…(1+n/n)}^(1/n)`

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UNITED BOOK HOUSE-SET 15-EXERCISE
  1. Evaluate:int (tan theta d theta)/(1-sin theta)

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  2. Solve:(x+y+1)dx + (2x+2y-1)dy = 0

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  3. solve:(dy)/(dx) + (sin 2y)/(x) = x^3cos^2y.

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  4. If the vectors a hati + hatj + hatk, hati + b hatj + hatk and hati + h...

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  5. If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx ...

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  6. Evaluate (with the help of definite integral): underset(n rarr infty)l...

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  7. find the value of underset(2)overset(3)int a^x dx(a<0).

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  8. Two cards are drawn successively with replacement from a well-shuffled...

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  9. Find the maximum value of f(x)=(1/x)^x

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  10. Solve: xdx+ ydy+ (xdy-ydx)/(x^2+y^2)=0 given y = 1 when x= 1.

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  11. Find the equation of the plane which contains the two parallel line: (...

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  12. A and B are two independent events such that P(AuuB) = 0.8 and P(A) = ...

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  13. vec a,vecb, vec c are three mutually perpendicular unit vectors then |...

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  14. The value of x if tan^(-1)x + 2 cot^(-1)x = (2 pi)/3 is

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  15. The degree of the differential equation(d^3y)/(dx^3) + x((dy)/(dx))^4 ...

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  16. If f(x) = [x] and g(x)=|x| the value of f(g(8/5))-g(f(-8/5)) is

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  17. A random variable x takes values 0,1,2,3…………..wiht probability P(X=x)=...

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  18. The angle between the planes 2x - y +z = 6 and x + y+2z = 7 is

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  19. Statement - 1 : The value of the integral int(pi/6)^(pi/3) dx/(1 + s...

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  20. If A= [[0,2],[3,-4]],kA = [[0,3a],[2b,24]] then find the value of k+a+...

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