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Q.3 If the coefficients of the rth, (r +...

Q.3 If the coefficients of the `rth, (r + 1)th & (r + 2)th terms in the expansion of (1+x)^14` are in AP,find r:

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The correct Answer is:
`r=5 ` or 9
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MOTION-BINOMIAL THEOREM -Exercise -3 ( Subjective )
  1. Find the coefficients of x^7 in (a x^2+1/(b x))^(11)a n dx^(-7)in(a x^...

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  2. Find the coefficient of x^(7) in the expansion of (ax^(2) + (1)/(bx...

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  3. Q.3 If the coefficients of the rth, (r + 1)th & (r + 2)th terms in the...

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  4. The largest value of x for which the fourth tem in the expansion (5^2/...

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  5. Find the term independent of x in the expansion of (i) [sqrt(x/3)+sqr...

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  6. Find the term independent of x in the expansion of [ x^(1//3)+x^(-1...

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  7. In the expansion of (1+x+(7)/(x))^(11) find the term not containing x.

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  8. Find numerically greatest term in the expansion of (2 + 3 x)^9, when x...

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  9. Find numerically the greatest term in the expansion of (3 - 5x)^(n...

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  10. Prove that : .^(n-1)C(r)+.^(n-2)C(r)+.^(n-3)C(r)+.........+.^(r)C(r)...

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  11. Given s = 1 + q + q^2+. . . . + q^n, Sn = 1 +(q+1 /2)+(q+1 /2)^2+........

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  12. (C(0)+C(1))(C(1)+C(2))(C(2)+C(3))...(C(n-1)+C(n))=(C(0).C(1).C(2)........

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  13. If P(n) denotes the product of all the coefficients in the expansion o...

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  14. Prove that (i) C(1)+2C(2)+3C(3)+……+nC(n)=n.2^(n+1) (ii) C(0)+(C(1)...

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  15. 2.C(0)+(2^(2).C(1))/(2)+(2^(3).C(2))/(3)+(2^(4).C(3))/(4)+......+(2^(n...

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  16. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + C(3) x^(3) + … + C(n) x...

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  17. (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + C(3) x^(3) + … + C(n) x^(n)...

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  18. prove that : C0^2+3C1^@+5C2^2+...+(2n+1)Cn^2=((n+1)2n!)/(n!)^2

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  19. If (1 + x)^(n) = C(0) = C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find...

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  20. Prove that sqrt(C1) +sqrt(C2) +sqrt(C3)+...+sqrt(Cn)le 2^(n-1) +(n-1)/...

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