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If (a+bx)/(a-bx) =(b+cx)/(b-cx) =(c + dx...

If `(a+bx)/(a-bx) =(b+cx)/(b-cx) =(c + dx)/(c-dx) (x ne 0)`, then show that a,b,c and d are G.P.

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lim_(x rarr 1)(ax^(2)+bx+c)/(cx^(2)+bx+a), a+b+c ne 0 is :

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OMEGA PUBLICATION-SEQUENCE AND SERIES -IMPORTANT QUESTIONS FROM MISCELLANEOUS EXERCISE
  1. If f(x) is a function satisfying f(x+y)=f(x)f(y) for all xy in n such ...

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  2. The sum of some terms of GP. is 315 whose first term and the common ra...

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  3. The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from t...

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  4. A GP. consists of an even number of terms. If the sum of all the terms...

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  5. If (a+bx)/(a-bx) =(b+cx)/(b-cx) =(c + dx)/(c-dx) (x ne 0), then show t...

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  6. If a(1/b +1/c) , b(1/c +1/a), c(1/a + 1/b) are in A.P. Prove that a,b,...

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  7. If a,b,c,d are in G.P., prove that (a^(n) + b^(n)), (b^(n) + c^(n)), (...

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  8. The ratio of the.A.M. and G.M. of two positive numbers a and b is m : ...

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  9. Find the sum to.n terms of the following series 5+ 55 + 555+………..

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  10. Find the sum to n terms 0.6 + 0.66 + 0.666 + ………..

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  11. The sum of first 9 terms of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)...

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  12. Find the sum of first n terms of the series. 3+7 + 13 + 21 + 31 + ……...

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  13. If S(1), S(2), S(3) are the sum of first n natural numbers, their squa...

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  14. Show that : (1 xx 2^2+2 xx 3^2+. .+n xx(n+1)^2)/(1^2 xx 2+2^2 xx 3+. ...

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  15. Let S be the sum, P the product and R the sum of reciprocals of n term...

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  16. A farmer, buys a used tractor for Rs.. 12000. He pays Rs.6000 cash and...

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  17. Shamshad Ali buys a scooter for Rs 22000 He pays Rs. 4000 cash And ag...

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  18. A manufacturer reckons that the value of a machine, which costs him Rs...

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  19. Dipesh writes letters to four of his friends. He asks each of them to ...

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  20. Find the sum of the sequence 7, 77, 777, 7777,.....up to n terms.

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