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if a(1),a(2),…….a(n),……. form a G.P. and...

if `a_(1),a_(2),…….a_(n),…….` form a G.P. and `a_(1) gt 0 ,` for all `I ge 1`
`|{:(log a_(n),,loga_(n)+loga_(n+2),,log a_(n+2)),(log a_(n+3),,log a_(n+3)+log a_(n+5),,log a_(n+5)),(log a_(n+6),,log_(n+6)+loga_(n+8),,log a_(n+8)):}|`

A

0

B

1

C

2

D

none of these

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Let a_(1),a_(2),a_(3), …, a_(10) be in G.P. with a_(i) gt 0 for i=1, 2, …, 10 and S be te set of pairs (r, k), r, k in N (the set of natural numbers) for which |(log_(e)a_(1)^(r)a_(2)^(k),log_(e)a_(2)^(r)a_(3)^(k),log_(e)a_(3)^(r)a_(4)^(k)),(log_(e)a_(4)^(r)a_(5)^(k),log_(e)a_(5)^(r)a_(6)^(k),log_(e)a_(6)^(r)a_(7)^(k)),(log_(e)a_(7)^(r)a_(8)^(k),log_(e)a_(8)^(r)a_(9)^(k),log_(e)a_(9)^(r)a_(10)^(k))| = 0. Then the number of elements in S is

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( 1 + x + x^(2))^(n) = a_(0) + a_(1) x + a_(2) x^(2) + …+ a_(2n) x^(2n) , then a_(0) + a_(1) + a_(2) + a_(3) - a_(4) + … a_(2n) = .

OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. Find the non-zero roots of the equation. (i) Delta=|{:(,a,b,ax+b),(,...

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  2. Let Delta(a)=|{:((a-1),n,6),((a-1)^(2), 2n^(2),4m-2),((a-1)^(3),3n^(3)...

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  3. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

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  4. For x ne y ne z , |{:(1+x^(3),,x^(2),,1),(1+y^(3),,y^(2),,1),(1+z^(3...

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  5. " if " |{:(b+c,,c+a,,a+b),(a+b,,b+c,,c+a),(c+a,,a+b,,b+c):}|=k |{:(a...

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  6. If A is a square matrix of order n such that its elements are polynomi...

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  7. Prove the identities: |{:(b^(2)+c^(2),,ab,,ac),(ab,,c^(2)+a^(2),,bc),...

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  8. a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...

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  9. If alpha,beta,gamma are real numbers, then without expanding at any...

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  10. If A,B,C are the angles of triangle ABC, then the minimum value of |{:...

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  11. If x, y , z are in A.P., then the value of the det (A) is , where A ...

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  12. Find the number of real root of the equation |0x-a x-b x+a0x-c x+b x+c...

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  13. If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-...

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  14. Let the following system of equations {:(kx+y+z=1),(x+ky+z=k),(x+y+k...

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  15. Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2

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  16. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

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  17. If B is a non-sinfular matrix and A is square matrix, then det B^(-1)A...

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  18. If 0 lt theta lt pi and the system of equations (sin theta) x + y + ...

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  19. If the determinant |(b -c,c -a,a -b),(b' -c',c' -a',a' -b'),(b'' -c'',...

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  20. If a !=b, then the system of equation ax + by + bz = 0 bx + ay + bz ...

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