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By ........in "Principle of Mathematical Induction" prove that for all n`in`N
`1^2+2^2+3^2+.......+n^2=(n(n+1)(2n+1))/(6)`

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 15-EXERCISE
  1. Show that cot 7(1^@/2)=2+sqrt2+sqrt3+sqrt6

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  2. If a^4+b^4+c^4+a^2b^2=2c^2(a^2+b^2),, then show thatangleC=60^@or120^@

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  3. By ........in "Principle of Mathematical Induction" prove that for all...

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  4. If w be a imaginary cube root of uniyt and a+b+c=0 then show that (a+b...

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  5. How many different numbers of 5 digits each (without repetition of dig...

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  6. Prove that the middle term in the expansion of (1+x)^(2n)is(1.3.5........

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  7. Show that the points (-4, 0). (6, 4), (5, 0)and (0, -2) form a trapezi...

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  8. If p and q are the lengths of perpendiculars from the origin to the li...

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  9. Find the equation to the circle described on the common chord of the g...

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  10. Find the ratio in which the ZX plane divides the line segment joining ...

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  11. Evaluate :lim(xrarr0)(x-sinx)/x^3

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  12. If y=sinx^@.find dy/dx from defination.

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  13. Prove that sqrt2 irrational, (use the method of contradiction).

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  14. If x and y are odd integers, then xy is also an odd integer r examine ...

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  15. The probability of' the solving a problems in mathematics of three stu...

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  16. Scores of a batsman of 5 consecutive inings are 39, 51, 59, 62 and 74....

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  17. If alpha!=betaand atanalpha+b tanbeta=(a+b)tan((alpha+beta)/2),then sh...

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  18. Show that tanalphatanbeta=tan^2gammawhen tan(alpha-beta)/tanalpha+sin^...

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  19. Sum of the square of three different terms, which are in GP is s^2. If...

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  20. Draw the graph and find the common solution region of the . following ...

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