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If `alpha`and `beta` be two roots of the equation (x-a)(x-b)=c then show that a and b are the roots of `(x-alpha)(x-beta) +c=0`

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UNITED BOOK HOUSE-TANTIA HIGH SCHOOL-EXERCISE
  1. If Snbe the sum of the n consecutive terms of an A.P,find the value of...

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  2. If ^9P5 + 5. ^9P4 = ^I0Pr, find r.

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  3. If alphaand beta be two roots of the equation (x-a)(x-b)=c then show t...

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  4. Find the point on the straight line 3x-4y=25,nearest to the origin .

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  5. Find the centre and the radius of the circle.2x^2+2y^2-4x+8y-4=0

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  6. If theta be a variable parameter find the curve whose parametric equat...

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  7. Find the area of greatest square that can be inscribed given straight ...

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  8. Evaluate :lim(xrarr1)(x+x^2+x^3+...+x^n-n)/(x-1)

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  9. If y=(1-x)(2-x)(3-x)…(n-x),find dy/dx

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  10. show that lim(nrarr0)(root(3)(n+1)-1)/n=1/3

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  11. For any two sets A,B ,prove that (AcapB)'=A'cupB'

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  12. If (cot(alpha-beta))/cotalpha+(cos^2gamma)/(cos^2alpha)=1show that tan...

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  13. If sinx-siny=a and cosx+cosy=b,prove that tan((x+y)/2)=+-sqrt((4-a^2-b...

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  14. Prove that sintheta/(cos3theta)+(sin3theta)/(cos9theta)+(sin9theta)/(c...

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  15. If tan (theta/2)=tan^3 (phi/2)and tanphi=2tanalpha,then prove that the...

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  16. If a,b are real and a^2+b^2=1,then prove that the equation.(1-ix)/(1+i...

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  17. If the roots of the equation x^2+2px+q=0and x^2+2qx+p=0where p!=q.Diff...

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  18. Prove that the product of any r consecutive natural number is always d...

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  19. Find the rank of the word LAKE,when the letters are arranged as in a d...

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  20. The sum of three numbers in G.P is 70.If the two extremes be mulitipli...

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