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Prove that underset(r = 0) overset (n)(s...

Prove that `underset(r = 0) overset (n)(sum) 3^(r) ""^(n)C_(r) = 4^(n)`

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`4^(n)`
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NEW JOYTHI PUBLICATION-BINOMIAL THEOREM-QUESTIONS FROM COMPETITIVE EXAMS
  1. Prove that underset(r = 0) overset (n)(sum) 3^(r) ""^(n)C(r) = 4^(n)

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  2. If T, denotes the r^(th) term in the expansion of [x + 1/x]^(23), then

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  3. If the coefficient of the 2^(nd),3^(rd) and 4^(th) terms in the expans...

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  4. The number of terms in the expansion of (1 + 5sqrt(2)x)^(9) + (1 - 5sq...

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  5. The term independent of x in the expansion of (x + 1/x^())^(6) is

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  6. The coefficient of x^(-9) in the expansion of (x^(2)/2 - 2/x)^(9) is

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  7. If the coefficients of the r^(th) term and the (r + 1)^(th) term in th...

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  8. If (1 + ax)^(n) = 1 + 6x + 27/2 x^(2) + ...... + a^(n)x^(n), then the ...

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  9. If x = (729 + 6(2)(243) + 15(4)(81) + 20(8)(27) + 15(16)(9) + 6(32)3 +...

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  10. The number of terms in the expansion of (a + b + c)^(10) is

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  11. If |x| lt 1, then the coefficient of x^(n) in (1 + 2x + 3x^(2) + 4x^(3...

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  12. The sum of the rational terms in the expansion of (sqrt(2) + 3^(1/5))^...

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  13. if (1 + C(1)/C(0))(1 + C(2)/C(1)) (1 + C(3)/C(2)) ...... (1 + C(n)/C(n...

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  14. In the expansion of (1 + 3x + 2x^(2))^(6) the coefficient of x^(n) is

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  15. If (2x^(2) - x - 1)^(5) = a(0) + a(1)x + a(2)x^(2) + ....... + a(10)x^...

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  16. If (1 + x - 3x^(2))^(10) = a(0) + a(1)x + a(2)x^(2) + ....... + a(20)x...

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  17. (i) What is the second term in the expansion of (1 + x)^(n)? (ii) Wr...

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  18. The coefficient of a^(5)b^(6)c^(7) in the expansion of (bc + ca + ab)^...

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  19. If the expansion of (3sqrt(x)/7 - 5/(2xsqrt(x)))^(13n) contains a term...

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  20. Prove that ""^(10)C(2)+2xx^(10)C(3)+^(10)C(4)=^(12)C(4)

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  21. Let f (x) = [x] , where [x] denotes the greater integer less t...

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