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Prove the following by the method of mat...

Prove the following by the method of mathematical induction. :`n^3+(n+1)^3+(n+2)^3` is divisible by 9, when n is a positive integer.

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 9-EXERCISE
  1. If acosphi=b costheta,show that a tantheta+b tanphi=(a+b)tan((theta+ph...

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  2. Show that tan20^@tan40^@tan80^@=sqrt3

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  3. Prove the following by the method of mathematical induction. :n^3+(n+1...

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  4. If the sum of 1+2r+3r^2+4r^3+...oo9/16,find the value of r.

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  5. In how many ways can the crew of an 8-oared boat be arranged if 2 of t...

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  6. Express(sqrt3-i)/(1-sqrt3i)in modulus amplitude form

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  7. In /\XYZthe equation of the perpendicularbisector of XY and XZ arc x-y...

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  8. Find the co-ordinate of the image of the point (-3, -1), with respect ...

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  9. Show that the circle with the portion of the line 3x + 4y = 12 interce...

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  10. Find the equation to the locus of a point whose distance from YZ plane...

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  11. Evaluate the following limits :lim(xrarr0)(xtan2x-2xtanx)/((1-cos2x)^2...

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  12. If f(x)=|x-1|1+x^2.Is f'(x) exist?examine it.

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  13. Using contrapositive method show tha the compund statement .is true or...

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  14. Show that sqrt3is irrational. (Use the method of contradiction).

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  15. If the letters of the word PROBABILITY be arranged at random, find the...

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  16. AM and SD of 7- observations are 8 and 4. If 5.of the 7 observations a...

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  17. Find the maximum and minimum value of 5costheta+12sintheta+12

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  18. Show that the equations,sin^2theta=sin^2alpha,cos^2theta=cos^2alphaand...

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  19. Solve :barz=iz^2(z being a complex number)

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  20. Find the sum of the numbers from 1 to 100 which are not divisible by 3...

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