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Let n in N . If (1 + x)^n = a0 + a1 x + ...

Let `n in N` . If `(1 + x)^n = a_0 + a_1 x + a_2x^2+…. + a_nx^n` and `a_(n-3), a_(n-2) , a_(n-1) `are in A.P then
Statement - I ` : a_1, a_2, a_3` are in A.P.
Statement -II : n = 7
The true statements are :

A

only I

B

only II

C

both I, II

D

neither I nor II

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
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  2. The coefficient of x^53 in sum(r = 0)^(100) ""^100Cr (x - 3)^(100 - r)...

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  3. Let n in N . If (1 + x)^n = a0 + a1 x + a2x^2+…. + anx^n and a(n-3), a...

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  4. If the coefficient of rth term and (r+1)th term in the expansion of (...

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  5. If the coefficients of r^(th) , (r + 1)^(th) and (r + 2)^(th) terms i...

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  6. If the coefficients of three consecutive terms in the expansion of (1+...

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

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  8. The coefficient of x^11 in the expansion of (1- 2x + 3x^2) (1 + x)^11 ...

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  9. The coefficient of x^5 in the expansion of (x^2 - x - 2)^5 is

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  10. The coefficient of x^4 in (1+x+x^2+x^3)^11 is

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  11. Coefficient of x^5 in ( 1+ x)^21 + (1 + x)^22 + …….+ (1 + x)^30 is

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  12. Coefficient of a^8b^6c^4 in (a+b+c)^18 is

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  13. The coefficient of x^9 in (x - 1)(x - 4) ( x- 9) ……. ( x -100) is

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  14. The term in (x + y)^50 which is greatest in absolute value if |x| = sq...

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  15. The greatest integer which divides the number 101^100 - 1 is

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  16. 9^7 + 7^9 is divisible by

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  17. Larger of 99^50+100^50 and 101^50

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  18. The remainder left out when 8^(2n) - 6(2)^( 2n+1) is divided by 9 is

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  19. Integral part of 7 + 4sqrt3)^n is (n in N)

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  20. Integral part of (7 + 5sqrt2)^(2n+1) is (n in N)

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