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1^(2)+2^(2)+3^(2)+............+n^(2)=(n(...

`1^(2)+2^(2)+3^(2)+............+n^(2)=(n(n+1)(2n+1))/6 forall n in N.`

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1+2+3+............+n=(n(n+1))/2 forall n in N.

1^(3)+2^(3)+3^(3)+………….+n^(3)=(n^(2)(n+1)^(2))/4 forall n in N.

1*2*3+2*3*4+...+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4 forall n in N.

1^(2) + 1+ 2^(2) + 2 + 3^(2) + 3+"............"+n^(2) + n is equal to :

1/(2*5)+1/(5*8)+1/(8*11)+............1/((3n-1)(3n+2))=n/((6n+4)) forall n in N.

a+ar+ar^(2)+...+ar^(n-1)=(a(1-r^(n)))/(1-r) forall n in N.

For all n ge 1 prove that 1^(2)+2^(2)+ 3^(2)+4^(2)+….+n^(2)= (n(n+1)(2n+1))/(6)

1.2+2.3+3.4+…………..+n(n+1)=n/3(n+1)(n+2) forall n in N.

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OSWAAL PUBLICATION-SOLVED PAPER 2017-1-EXERCISE
  1. How many terms of AP - 6 -11//2,-5 . . . are needed to give the s...

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  2. In an A.P if m^(th) term is n and n^(th) term is m, where mnen, find t...

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  3. Compute the derivative of sinx using first principal method ?

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  4. Verify by the method of contradiction that sqrt(2) is irrational .

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  5. A committee of two persons is selected from two men and two women.What...

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  6. A committee of two persons is selected from two men and two women.What...

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  7. If E and F are two events such that P(E)=1/4, P(E)=1/2 and P(E and F)=...

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  8. Prove that underset(xrarr0)lim(sinx/x=1) ?

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  9. 1^(2)+2^(2)+3^(2)+............+n^(2)=(n(n+1)(2n+1))/6 forall n in N.

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  10. Define a modulus function . Draw its graph. Also write down its domai...

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  11. A group consists of 7 boys and 5 girls . Find the number of ways in wh...

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  12. State and prove Bionomial theorem for any positive integer n.

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  13. If p is the length of perpendicular from origin to the line whose int...

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  14. (cos 4x+cos3x+cos2x)/(sin 4x+sin3x+sin2x)=cot3x

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  15. Solve the following system of inequalities graphivally 2x+y>+4,x+yle3,...

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  16. Find the mean deviation about median for the following data:

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  17. To cos(A+B)=cosx.cosy - sin x sin "and hence find "cos75^(@)

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  18. Find the sum to n terms of the series 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)...

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  19. Derive the equation of the ellipse in the form (x^(2))/(a^(2))+(y^(2))...

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  20. (b) Find the derivative of (x^(5) - cos x)/(sin x) with respect to x.

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