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If Deltar=|[2^(r-1),1/(r(r+1)),sin rthet...

If `Delta_r=|[2^(r-1),1/(r(r+1)),sin rtheta],[x, y, z],[2^n-1, n/(n+1),((sin)(n+1)/2 theta (sin) n/2 theta) /(sintheta/2)]|, then sum_(r=1)^n Delta_r ` is equal to

A

0

B

Independent of n

C

independent of `theta`

D

independent of x,y and z

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The correct Answer is:
A, B, C, D
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FIITJEE-DETERMINANT-ASSIGNMENT PROBLEMS (OBJECTIVE) Level -II
  1. In a set A=(3^3,7^3,11^3,15^3,……) if 9 elements are selected from set ...

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  2. If ai,i=1,2,....,9 are perfect odd squares, then |[a1,a2,a3],[a4,a5,a6...

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  3. If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-...

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  4. If a^2+8b^2+2c^2+2d^2-4ab-4bc-4bd=0 ,then the value of |{:(a,b),(c,d):...

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  5. If ai,i=1,2,....,9 are perfect odd squares, then |[a1,a2,a3],[a4,a5,a6...

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  6. If Deltar=|[2^(r-1),1/(r(r+1)),sin rtheta],[x, y, z],[2^n-1, n/(n+1),(...

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  7. If equations a^2x+b^2y+c^2=0,a^4x+b^4y+c^4=0 and x+y+1=0 are consisten...

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  8. the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha...

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  9. If |{:(a, b, aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c," "0):}|=0 t...

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  10. यदि f(x)=|(0,x-a,x-b),(x-a,0,x-c),(x-b,x-c,0)|, तब :

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  11. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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  12. The value of x satisfying |{:(x-a,b,c),(a,x+b,c),(a,b,x+c):}|=0 is

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  13. If f(x), g(x) and h(x) are polynomials of degree 4 and |{:(f(x),g(x)...

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  14. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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  15. If p + q + r = a + b + c = 0, then the determinant |{:(pa,qb,rc),(qc,r...

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  16. If a,b,c are sides of DeltaABC such that |{:(c,bcosB+cbeta,acosA+balph...

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  17. If Delta(x)=|{:(x^2+4x-3,2x+4,13),(2x^2+5x-9,4x+5,26),(8x^2-6x+1,16x-6...

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  18. Let ai^2+bi^2+ci^2=1 (for i=1,2,3) and aiaj+bibj+cicj=0 (i != j;i,j=1...

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  19. Suppose |{:(1+x,x,x^2),(x,1+x,x^2),(x^2,x,1+x):}|=Px^5+Qx^4+Rx^3+Mx^2+...

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