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If x ,y ,z are real and 4x^2+9y^2+16 z^2...

If `x ,y ,z` are real and `4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx , y,z` are in a. A.P. b. G.P. c. H.P. d. none of these

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If x ,2y ,3z are in A.P., where the distinct numbers x ,y ,z are in G....

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  2. If a,b,c,d are in GP then prove that, (a^2-b^2), (b^2-c^2), (c^2-d^2)...

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  3. If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx ,...

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  4. If a, b, care in GP then prove that a^3, b^3, c^3 are in GP.

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  5. The second term of an H.P. is 3/14 and the fifth term is 1/10 . Find...

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  6. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

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  7. If the sixth term of an H.P. is 10 and the 11th term is 18 Find the 16...

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  8. If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then ...

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  9. Let Tr be the rth term of an A.P., for r=1,2,3,..... If for some pos...

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  10. Let An = (3/4) -(3/4)^2 + (3/4)^3 +.....+(-1)^(n - 1) (3/4)^n , Bn = 1...

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  11. For a positive integer n let a(n)=1+1/2+1/3+1/4+.......+1/((2^n)-1) th...

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  12. If x >1,y >1,a n dz >1 are in G.P., then 1/(1+lnx),1/(1+l ny)a n d1/(1...

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  13. Compute the 100th term of HP if the 10th and 20th term of HP are 20 an...

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  14. Find the 6th and nth term of the GP 2, 6, 18, 54,.....

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  15. If a,b,c are in AP and a^2,b^2,c^2 are in HP, then

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  16. Let a ,b be positive real numbers. If a, A1, A2, b be are in arithmeti...

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  17. The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, ...

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  18. If a^2+b^2,a b+b c and b^2+c^2 are in G.P., then a ,b ,c are in a. A.P...

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  19. If y^2=x za n da^x=b^y=c^z , then prove that (log)6a=(log)c bdot

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  20. The geometric mean between -9 and -16 is a.12 b. -12 c. -13 d. none of...

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