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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 (10)-EXERCISE
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  2. Let A, B, and C be the sets such that A uu B = A uu C and A nn B = A n...

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  3. If f (x) = loge ((1+x)/(1-x)), prove that: f (x) +f (y)= f ((x+y)/(1+x...

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

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  5. If ""^(n)C(r ): ""^(n)C(r+1)=1:2 and ""^(n)C(r+1): ""^(n)C(r+2)=2:3, ...

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  6. Find the number of different signals that can be generated by arrangin...

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  7. Find the sum of all natural numbers lying between 100 and 1000, which ...

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  8. Find the three number is G.P. such that their sum is 19 and sum of the...

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  9. P(a,b) is the mid-point of a line segment between axes. Show that the ...

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  10. Find the equations of the ellipse whose length of the major axis is 20...

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  11. Evaluate: underset(xrarr5)lim (1-sqrt(x-4))/5.

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  12. If siny = xsin(a+y), prove that dy/dx=sin^2(a+y)/sina

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

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  14. Find the square root of -15 - 8i.

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  15. If (a+ib)(c+id)(e+if)(g+ih)=A+iB, then show that: (a^2+b^2)(c^2+d^2)(e...

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  16. Ravi obtained 70 and 75 marks in first two unit test. Find the minimum...

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  17. If x sin (a+y) + sin a cos (a+y) = 0, then prove that : dy/dx = (sin^...

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  18. Find the derivative of (px^2+qx+r)/(ax+b).

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  19. Find the median of the data:

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

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