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If f(x) = -f(-x) then show that overset(...

If f(x) = -f(-x) then show that `overset(a)underset(-a)int f(x)dx =0`.

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UNITED BOOK HOUSE-HIGHER SECONDARY EXAMINATION 2020.-EXERCISE
  1. If x>0,y>0 and xy= 100, find the minimum value of (x+y)

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  2. Evaluate: int((cosx+xsinx)/(x(x+cosx)))dx.

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  3. If f(x) = -f(-x) then show that overset(a)underset(-a)int f(x)dx =0.

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  4. Find a vector of magnitude 14 in the direction of the vector -3hat i+6...

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  5. Find the direction cosines of a straight line which is situate on yz-p...

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  6. 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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  7. The mean and variance of a binomial distribution B(n,p|) are 4 and 3.2...

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  8. *' is an operation defined on Z set of all integers as a*b = a+b-2 for...

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  9. *' is an operation defined on Z set of all integers as a*b = a+b-2 for...

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  10. Show that sin^(-1) (12/13)+cos^(-1)(4/5)+tan^(-1)(63/16) = pi.

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  11. If A = [[0,6,7],[-6,0,8],[7,-8,0]],B=[[0,1,1],[1,0,2],[1,2,0]],C=[[2],...

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  12. If A = ([cos theta,sin theta],[-sin theta,cos theta]) show that A= ([c...

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  13. show that |[1,x,x^2],[x^2,1,x],[x,x^2,1]| = (1-x^3)^2

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  14. If (cos x)^y = (cos y)^x then show that (dy)/(dx) = (y tan x+log cos y...

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  15. If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(d...

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  16. Evaluate: int(2dx)/((1-x)(1+x^2))

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  17. Evaluate: int (sqrt(tanx)+sqrtcotx)dx

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  18. Solve: xy (dy)/(dx)=(x+2)(y+2), given x= 1, when y =-1.

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  19. Solve: x^2dy+(xy+y^2)dx=0, given x=1 and y = 1.

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  20. If vec a,vec b, vec c be three vectors such that vec a+vec b+vec c=0 ,...

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