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Prove the following by using the princip...

Prove the following by using the principle of mathematical induction for all `n in N` :- `1^3 + 2^3 + 3^3 + ... +n^3 =((n(n+1))/2)^2`.

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JBD PUBLICATION-MODEL PAPER (4)-EXERCISE
  1. Prove that:(1+sin2x-cos2x)/(1+sin2x+cos2x)=tanx

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  2. Find the general solution of the following equations: sin x + sin 3x +...

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  3. Find the general solution of the following equations: cos 3x + cosx- c...

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  4. Using principle of mathematical induction of prove that: 1+2+3+……….+n<...

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  5. Use principle of mathematical induction to prove that:1+2+3+……….+n=(n(...

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  6. Prove the following by using the principle of mathematical induction f...

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  7. Find n if "^(n-1)P3 : "^nP4 =1:9.

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  8. If m times the mth term is equal to n times the nth term of an A.P. pr...

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  9. Without using the pythagorus, show that the points (4, 4), (3, 5) and ...

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  10. Find the equation of a hyperbola whose vertices lie on y-axis, centre ...

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  11. Find the derivative of 2/(x+1)-x^2/(3x-1).

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  12. An integer is chosen from the first 200 integers. Find the probability...

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  13. Find the squre root of 1+2sqrt(6)i.

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  14. Convert the complex number -sqrt3-i in the polar form. Also find their...

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  15. Solve the following system of unequalities graphically: 3x+2y le 12, x...

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  16. How many litres of water will have to be added to 1125 litres of the 4...

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  17. Find the derivative of xsinx

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  18. Find the derivative of (secx - 1)/(secx + 1)

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  19. Find the mean and variance of the first n natural numbers.

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  20. Find the mean and variance of the following frequency distribution:

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