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Let `a ,b ,c ,d` be four distinct real numbers in A.P. Then half of the smallest positive valueof `k` satisfying `a(a-b)+k(b-c)^2=(c-a)^3=2(a-x)+(b-d)^2+(c-d)^3` is __________.

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VIKAS GUPTA (BLACK BOOK)-SEQUENCE AND SERIES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let a ,b ,c ,d be four distinct real numbers in A.P. Then half of the ...

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  2. The sum of all digits of n for which sum (r =1) ^(n ) r 2 ^(r ) = 2+2^...

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  3. If lim ( x to oo) (r +2)/(2 ^(r+1) r (r+1))=1/k, then k =

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  4. The value of sum (r =1) ^(oo) (8r)/(4r ^(4) +1) is equal to :

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  5. Three non-zero real numbers from an A.P. and the squares of these numb...

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  6. The sum of the fourth and twelfth term of an arithmetic progression is...

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  7. In an increasing sequence of four positive integers, the first 3 terms...

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  8. The limit of (1)/(n ^(4)) sum (k =1) ^(n) k (k +2) (k +4) as n to oo i...

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  9. Which is the last digit of 1+2+3+……+ n if the last digit of 1 ^(3) + ...

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  10. There distinct positive numbers, a,b,c are in G.P. while log (c) a, lo...

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  11. The numbers 1/3, 1/3 log (x) y, 1/3 log (y) z, 1/7 log (x) x are in H...

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  12. If sum ( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relativel...

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  13. The sum of the terms of an infinitely decreassing Geometric Progressio...

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  14. A cricketer has to score 4500 runs. Let a (n) denotes the number of ru...

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  15. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

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  16. Let f (n)=(4n + sqrt(4n ^(2) +1))/( sqrt(2n +1 )+sqrt(2n-1)),n in N th...

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  17. Find the sum of series 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+…… oo, where the...

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  18. Let a (1), a(2), a(3),…….., a(n) be real numbers in arithmatic progres...

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  19. Let the roots of the equation 24 x ^(3) -14x ^(2) + kx +3=0 form a geo...

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  20. How many ordered pair (s) satisfy log (x ^(2) + (1)/(3) y ^(3) + (1)/(...

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