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Show that the coefficient of the middle term in the expansion of `(1+x)^(40)` is equal to the sum of the coefficients of the two middle terms of `(1+x)^(39)` .

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CHHAYA PUBLICATION-BINOMIAL THEOREM -EXERCISE ( short answer Type Questions )
  1. Show that the middle term in the expansion of (x+1)^(2n)" is " (1.3.5....

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  2. Show that the coefficient of the middle term of (1+x)^(2m) is equal to...

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  3. Show that the coefficient of the middle term in the expansion of (1+x...

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  4. If the coefficients of (p +1) th and (p+3)th terms in the expansion of...

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  5. Let n ge 5 b ne0, if in the binomial of (a-b)^(n), the sum of the 5th...

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  6. If the coefficients of x^(2) and x^(11) in the expansion of (1+ax+2x^(...

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  7. If in the expansion of (1+x)^(m)(1-x)^(n) the coefficients of xandx^(...

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  8. Use binomial theorem to show that if nge1 is an integer then , (a) ...

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  9. n(gt1) is a positive integer . Show that 14^(n)-13n-1 is divisible by...

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  10. For every natural number n(gt1) , show that , 4^(n)+15n-1 is divisible...

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  11. If n is a positive integer (gt1) , show that, (4^(2n+2)-15n-16) is a...

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  12. Using binomial theorem find the value : (0.999)^(4) [correct to thr...

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  13. Using binomial theorem find the value : (1.02)^(4) [correct to two ...

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  14. Write down the expansion of (4x-(y)/(4))^(4). By giving suitable valu...

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  15. Prove that , (x^(n))/(n!)+(x^(n-1).a)/((n-1)!1!)+(x^(n-2).a^(2))/((n-2...

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  16. Two successive terms in the expansion of (2+(1)/(2))^9 are equal . ...

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  17. If n be a positive integer and the sums of the odd terms ans even term...

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  18. If n be a positive integer and the sums of the odd terms ans even term...

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  19. Find the value of (1+x)^(n)+^(n)C(1)(1+x)^(n-1).(1-x)+^(n)C(2)(1+x)^...

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  20. If n be positive integer , show that the algebraic sum of the numerica...

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