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If x^2 = a^(sin^(-1)t) and y^2= a^(cos^(...

If `x^2 = a^(sin^(-1)t)` and `y^2= a^(cos^(-1)t)` then show that `(dy)/(dx)=-y/x`.

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UNITED BOOK HOUSE-HIGHER SECONDARY EXAMINATION 2020.-EXERCISE
  1. Show that |[1,logab,logac],[logba,1,logbc],[logca,logcb,1]|=0,(a>0,b>0...

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  2. Find the deferential equation of xy= Ae^x+Be^(-x)+x^2 by eleminating A...

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  3. If x^2 = a^(sin^(-1)t) and y^2= a^(cos^(-1)t) then show that (dy)/(dx)...

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  4. If f(x) = (sin 5x)/(2x) (when x!=0) = (5k)/4(when x= 0), and f(x) is...

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  5. If x>0,y>0 and xy= 100, find the minimum value of (x+y)

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

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

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

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

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

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

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

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

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

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

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

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

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