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The coefficient of the quadratic equatio...

The coefficient of the quadratic equation `a x^2+(a+d)x+(a+2d)=0` are consecutive terms of a positively valued, increasing arithmetic sequence. Then the least integral value of `d//a` such that the equation has real solutions is __________.

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RESONANCE-SEQUENCE & SERIES -EXERCISE -1 PART -I RMO
  1. In a G.P. of real numbers, the sum of the first two terms is 7. The su...

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  2. In a potato race, a bucket is placed at the starting point, which is 7...

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  3. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

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  4. Find the sum of integers from 1 to 100 that are divisible by 2 or 5...

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  5. The sum of three numbers in A.P. is 27, and their product is 504, find...

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  6. The friends whose ages from a G.P. divide a certain sum of money in pr...

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  7. The roots of the equation x^(5)-40x^(4)+ax^

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  8. Let T(n) denotes the n ^(th) term of a G.P. with common ratio 2 and (l...

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  9. If a,b,c are in A.P. and if (b-c) x^(2)+(c-a) x+(a-b)=0 and 2 (c+a) x^...

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  10. Along a road lies an odd number of stones placed at intervals of 10m. ...

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  11. Determine all pairs (a,b) of real numbers such that 10, a,b,ab are in ...

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  12. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

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  13. If n is any positive integer, then find the number whose square is und...

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  14. Find the sum of infinite terms of the series : (3)/(2.4) + (5)/(2.4.6)...

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  15. If S(1),S(2),S(3),"…….",S(2n) are the same of infinite geometric serie...

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  16. Find the sum to n terms of the series :1^2+(1^2+2^2)+(1^2+2^2+3^2)+dot...

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  17. Let a (l) = (7)/(4) ((2)/(3)) ^( l -1), j in N.lf b (1) = a (j) ^(2)...

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  18. The sequence 9, 18, 27, 36, 45, 54,….. consists of successive mutiple ...

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  19. As show in the figure , the five circles are tangent to one another co...

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  20. The arithmetic mean of the nine number in the given set {9,99,999, ......

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