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If |{:(a,b,aalpha-b),(b,c,balpha-c),(2,1...

If `|{:(a,b,aalpha-b),(b,c,balpha-c),(2,1,0):}|=0`, then

A

A.P.

B

G.P.

C

H.P.

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Applying `C_(3)toC_(3)-alphaC_(1)+C_(1)+C_(2)` to the given determinant, we get
`|{:(a,b," "0),(b,c," "0),(2,1,-2alpha+1):}|=0`
`rArr" "(1-2alpha)(ac-b^(2))=0`
`rArr" "ac=b^(2)" "[becausealpha!=1//2]`
`rArr" "` a,b,c are in G.P.
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Section I - Solved Mcqs
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  2. If x, y, z are in A.P. and tan^(-1) x, tan^(-1) y and tan^(-1)z are al...

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  3. If |{:(a,b,aalpha-b),(b,c,balpha-c),(2,1,0):}|=0, then

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  4. Let a(1),a(2),a(3),a(4)anda(5) be such that a(1),a(2)anda(3) are in A....

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  5. If the expression exp {1+|cosx|+cos^(2)x+|cos^(3)x|+ . . . . oo)log(e...

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  6. If the sides of a triangle are in GP and its largest angle is twice th...

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  7. The first , second and the last terms of an A.P. are a ,b , c respecti...

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  8. If the sides of a right angled triangle are in A.P then the sines of t...

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  9. If the lengths of the sides of a triangle are in A.P. and the greatest...

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  10. If b-c, 2b-x and b-a are in H.P., then a-(x/2), b-(x/2) and c-(x/2) ar...

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  11. The sixth term of an AP is 2, and its common difference is greater tha...

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  12. If a x^3+b x^2+c x+d is divisible by a x^2+c ,t h e na ,b ,c ,d are in...

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  13. The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is:...

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  14. The sum of the series 1+2(1 +1/n)+ 3(1+1/n)^2+.... oo is given by

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  15. The sum to 50 terms of the series 3/1^2+5/(1^2+2^2)+7/(1^+2^2+3^2)+...

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  16. The sum of n terms of the series 1/(sqrt1+sqrt3)+1/(sqrt3+sqrt5)+... i...

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  17. If cos(x-y),cos x and cos(x+y) are in HP, then cos x sec ((y)/(2))=

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  18. Let a1,a2 ,…. , a10 be in A.P. and h1,h2 …. h10 be in H.P. If a1=h1...

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  19. Let S(1),S(2),"…." be squares such that for each n ge 1, the length o...

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  20. Let a, b, c be in an AP and a^2, b^2, c^2 be in GP. If a < b < c and a...

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