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The roots of equation x^2+2(a-3)x+9=0 li...

The roots of equation `x^2+2(a-3)x+9=0` lie between -6 and 1 and 2 ,` h_1,h_2,.....h_20` [a] are in HP where [a] denotes the integral part of a and 2,`a_1,a_2,......a_20`,[a] are in AP, then `((a_3h_18)/3)` is equal to

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Which one of the following statements is correct ?

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  2. Match List-I with List-II

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  3. The roots of equation x^2+2(a-3)x+9=0 lie between -6 and 1 and 2 , h1,...

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  4. If a,b,c ,d are distinct integer in AP such that d=a^2+b^2+c^2, then a...

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  5. If log2(a+b)+log2(c+d)ge4 . Then the minimum value of the expression a...

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  6. Let a1,a2,a3,.......a11 be real number satisfying a1=15,27-2a2gt0 anda...

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  7. The interior angles of a polygon are in arithmetic progression. The sm...

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  8. Find the sum of the first n terms of the series 1^3+3.2^2+3^3+3.4^2+5^...

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  9. Find the sum of the first n terms of the series 1^3+3.2^2+3^3+3.4^2+5^...

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  10. Does there exist a GP containing 27,8 and 12 as three of its terms ? I...

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  11. The sum of the squares of three distinct real numbers, which are in GP...

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  12. Prove that the three successive terms of a GP will form the sides of ...

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  13. If (m+1)^th ,(n+1)^th and (r+1)^th terms in AP are in GP m,n,r are in ...

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  14. If p be the first of n arithmetic means between two numbers and q be t...

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  15. Show that 1^4/13+2^4/3.5+3^4/5.7+.....+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5...

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  16. Solve the following equations for x and y log10xx+1/2log10xx+1/4log10x...

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  17. Find the sum of the series 1/1.3+2/(1.3.5)+3/(1.3.5.7)...upto infinit...

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  18. If sum(r=1)^nTr =n/8(n+1)(n+2)(n+3) then find sum(r=1)^n1/Tr

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  19. If 1,log9(3^(1-x)+2) and log3(4.3^x-1) are in AP , then x is equal to

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  20. If the sum of the first 2n terms of the AP 2,5,8.....is equal to the s...

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