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Prove that the product of any r consecut...

Prove that the product of any r consecutive natural number is always divisible by r!.

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UNITED BOOK HOUSE-TANTIA HIGH SCHOOL-EXERCISE
  1. If a,b are real and a^2+b^2=1,then prove that the equation.(1-ix)/(1+i...

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

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

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

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

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  6. A ray of light comming from (1, 2) to the x axis at A and reflecting w...

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  7. The equation of a side of a rectangle is 4x+7y+5=0 and the two vertice...

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  8. Find the equation of the circle described on the common chord of the c...

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  9. Find the equation of the parabola whose focus is at the origin and the...

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  10. Evaluate :lim(xrarr0)(sqrtcosx-root(3)(cosx))/(sin^2x)

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  11. Find from first principle,the derivative of sqrttanx

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  12. If y=sqrt(x/m)+sqrt(m/x),Prove that 2xydy/dx=x/m-m/x

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  13. Show that,tan7 (1^@/2)=sqrt6-sqrt3+sqrt2-2

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  14. Solve theta for 4sinthetacostheta=1+2costheta-2sintheta (0<theta<pi)

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  15. Exhibit graphically the solution sets of the following system of linea...

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  16. state the fundamental theorm of algebra and solve the equation 3x^2-5i...

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  17. Find the number of selection that can be done from the letters of the ...

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  18. Find the sum of the series upto a n terms 2+3.3+4.3^2+5.3^3+...+to n t...

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  19. Show that the straight line (a + 2b) x + (a -3b)y + b -a = 0 always p...

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  20. Show that for all values p.the circle x^2+y^2-x(3p+4)-y(p-2)+10p=0pass...

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