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

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Coefficient of x^n in the expansion of (1+x)^(2n) is

If A and B are coefficients of x^n in the expansions of (1+x)^(2n) and (1+x)^(2n-1) respectively, then A/B is equal to

If a_1, a_2 are the coefficients of x^n in the expansion of (1+x)^(2n) & (1+x)^(2n-1) respectively then a_1:a_2 will be

Prove that the coefficents of x^(n) in the expansion of (1+x)^(2n) is twice the coefficent of x^(n) in the expansion of (1+x)^(2n-1) .

'Prove that the co-efficient of x^n of the expansion of (1+x)^(2n) is the double of the coefficient of x^n of the expansion of '(1+x)^(2n-1)'

If n is a positive integer then the coefficient of x ^(-1) in the expansion of (1+x) ^(n) (1+ (1)/(x)) ^(n) is-

The coefficient of x^(m) in the expansion of (1+x)^(m+n) is -

If a _(r) is the coefficient of x^r in the expansion of (1+ x+x^(2)) ^(n), then the value of a_(1)- 2a_(2) +3a_(3)-4a_(4)+…-2na_(2n) is -

The coefficient of x^n in the expansion of (1+x)(1-x)^n is

Find the coefficient of x^(r) in the expansion of (x+4)^(n)+(x+4)^(n-1)(x+3)+(x+4)^(n-2)(x+3)^(2)+.....+(x+3)^(n)

CHHAYA PUBLICATION-BINOMIAL THEOREM -EXERCISE ( short answer Type Questions )
  1. If in the expansion of (1+x)^(m)(1-x)^(n) the coefficients of xandx^(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. If the coefficients of three successive terms in the expansion of (1+...

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