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If n is a positive integer then 2^(4n) -...

If n is a positive integer then `2^(4n) - 15n - 1` is divisible by

A

64

B

196

C

225

D

256

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. If the sum of all the binomial coefficients in (x+y)^n is 512 , then t...

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  2. The coefficient of x^(-n) in (1+x)^n (1+(1)/(x))^n is

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  3. If n is a positive integer then 2^(4n) - 15n - 1 is divisible by

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  4. Smaller of (19^10 + 20^10) and 21^10 is

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  5. 9^11 + 11^9 is divisible by

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  6. Integral part of (8 + 3sqrt7)^n is

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  7. If n = (sqrt2 +1)^6. Then the integer just greater than n is

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  8. 1.C0 + 3.C1+ 3^2.C2+….+3^n.Cn =

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  9. C0 + (C1)/(2) + (C2)/(2^2) + (C3)/(2^3)+…..+(Cn)/(2^n)=

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  10. ""^11C0 + ""^11C1 + ""^11C2 + ……+ ""^11C5 =

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  11. C0^2 + C1^2 + C2^2 - ………-C15^2 =

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  12. 1/2.""^10C0 -""^10C1 +2.""^10C2 - 2^2.""^10C3+…..+2^9. ""^10C10 =

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  13. ""^(2n +1)C0^2 -""^(2n+1)C1^2 + ""^(2n+1)C2^2 -…….- ""^(2n+1)C(2n+1)^2...

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  14. Prove that following i) 2.C(0)+5.C(1)+8.C(2)+…..+(3n+2)C(n)=(3n+4).2...

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  15. ""^20C0 + ""^20C1 + ""^20C2+…….+""^20C10 =

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  16. C1 + 2. C2 + 3. C3 + …... + n. Cn=

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  17. If ar is the coefficient of x^r in the expansion of (1+x)^n then a1/a0...

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  18. If (1+x)^n = C0 + C1 x+ C2 x^2 + ….....+ Cn x^n, then C0+2. C1 +3. C...

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  19. 1.""^20C1 - 2.""^20C2 + 3.""^20C3 - …..-20.""^20C20 =

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  20. (1+x+x^2 + ……+x^p)^n = a0 + a1x + a2 x^2 + ….+a(np) x^(np) rArr a1 + 2...

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