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Evaluate (with the help of definite inte...

Evaluate (with the help of definite integral)
`underset(nrarr infty) It ((1)/(n+1) + (1)/(n+2) + ….. + (1)/(6n))`

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UNITED BOOK HOUSE-SET 17-EXERCISE
  1. Eleminating a and b, find the differential equation of all ellipse of ...

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  2. Evaluate : underset(x rarr 0) Lt (1+3x)^((x+2)/x)

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  3. If vec a, vec b, vec c are unit vectors satisfying the condition veca+...

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  4. Find the value of lambda so that the plane vecr. (veci + 2vecj + 3veck...

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  5. If P(A)=1/4,P(B)=1/3 and P(A-B)=1/6 then verify whether a and B are tw...

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  6. An unbiased coin is tossed 6 times. Find the probability of at least f...

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  7. Given A =[(1,-1,1),(1,-2,-2),(2,1,3)] & B = [(-4,4,4),(-7,1,3),(5 , -3...

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  8. Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|=(a+b+c)(a^2+b^2...

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  9. Show that int(2x+3)/(x^2 - 3x + 2) dx

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  10. If x = sin theta and y = cos ptheta , p is constant, then find the val...

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  11. The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...

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  12. Show that int(2x+3)/(x^2 - 3x + 2) dx

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  13. If theta be the angle between two unit vectors vece1 and vece2 then pr...

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  14. Evaluate (with the help of definite integral) underset(nrarr infty) ...

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  15. Find the value of overset(pi//2)underset(0)int (1 )/((b^2 cos^2 x + a^...

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  16. A mawn takes a step forward with probability 0.4 and backward with pro...

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  17. A card from a pack of 52 cards is lost. From the remaining cards of ...

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  18. If the area of the region {(x , y):0lt=ylt=x^2+1,0lt=ylt=x+1,0lt=xlt=2...

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  19. (b)answer any two questions : (i) a circular ink blot grows at the rat...

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  20. Find the distance of the point (1,-2,3) from the plane x - y +z = 5 me...

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