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If A(i)=[(a^(i),b^(i)),(b^(i),a^(i))] an...

If `A_(i)=[(a^(i),b^(i)),(b^(i),a^(i))]` and `|a| lt 1,|b| lt 1` then the value of `sum_(i=1)^(oo)` det `(A_(i))` is -

A

`(a^(2)-b^(2))/((1-a^(2))(1-b^(2)))`

B

`(a^(2))/((1-a)^(2))-(b^(2))/((1-b)^(2))`

C

`(a^(2))/((1-a)^(2))+(b^(2))/((1-b)^(2))`

D

`(a^(2))/((1+a)^(2))-(b^(2))/((1+b)^(2))`

Text Solution

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A
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CHHAYA PUBLICATION-MCQ ZONE -Question Paper 3
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  2. The inverse of the matrix [(5,-2),(3,1)] is -

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  3. If A(i)=[(a^(i),b^(i)),(b^(i),a^(i))] and |a| lt 1,|b| lt 1 then the ...

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  4. If A is a singular matrix of order n then A*(adj A) is equal to -

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  5. If the determinant of the matrix [(a(1),b(1),c(1)),(a(2),b(2),c(2))...

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  6. If |(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64)|=0, then the va...

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  7. If a, b, c, d , e and f are in G.P. then the value of |("a"^(2),"d"^(...

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  8. If a, b, c are respectively the p-th, q-th, r-th terms of an A.P. th...

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  9. If for a triangle ABC, |(1,a,b),(1,c,a),(1,b,c)|=0 then the value of ...

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  10. If the points with position vectors 10hati+3hatj, 12 hati-5hatj and p...

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  11. If ABCDEF be a regular hexagon then (vec(AD)+vec(EB)+vec(FC)) is equa...

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  12. The value of cos[cos^(-1)(-(1)/(7))+sin^(-1)(-(1)/(7))] is -

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  13. The vector equation of yz-plane is -

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  14. The foot of the perpendicular drawn from the origin to a plane is (2,...

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  15. The direction cosines of the line (x+3)/(2)=(2y-3)/(-3)=(z-1)/(0) are...

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  16. Let f(x)=a^(x)(a gt 0) be written as f(x)=g(x)+h(x) where g(x) is an e...

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  17. The area of the parallelogram formed by the vectors 3hati-2hatj+hatk ...

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  18. If veca=2hati-5hatj+4hatk and vecb=hati-4hatj+6hatk, then a unit v...

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  19. If veca+vecb+vec c=vec0 and |veca|=3,|vecb|=5 and |vec c|=7, then the ...

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  20. If vec alpha, vec beta, vecgamma be three unit vectors such that |ve...

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