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Use binomial theorem to show that if nge...

Use binomial theorem to show that if `nge1` is an integer then ,
(a) `11^(n)-10n-1` is divisible by 100

(b)`3^(2n)-8n-1` is divisible by 64.

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CHHAYA PUBLICATION-BINOMIAL THEOREM -EXERCISE ( short answer Type Questions )
  1. If the coefficients of x^(2) and x^(11) in the expansion of (1+ax+2x^(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Show that the sum of the coefficients of the odd terms in the expansio...

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  17. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3)+.....+a(2n)x^(2n)" p...

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  18. If a(r) be the coefficient of x^(r) in the expression of (1+bx^(2)+cx^...

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  19. In a binomial expansion if the coefficients of two successive terms ar...

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  20. Coefficient of x^n in the expansion of (a+x)^(2n)

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