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If a,b,c gt 0 and x,y,z , in R then the...

If a,b,c ` gt` 0 and `x,y,z , in R` then the determinant :
`|((a^x+a^(-x))^2,(a^(x)-a^(-x))^2,1),((b^y+a^(-y))^2,(b^(y)-b^(-y))^2,1),((c^z+c^(-z))^2,(c^(z)-c^(-z))^2,1)|` is equal to :

A

`a^zb^yc^z`

B

`a^(-x)b^(-y)c^(-z)`

C

0

D

`a^(2x)b^(2y)c^(2z)`

Text Solution

Verified by Experts

The correct Answer is:
C
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MODERN PUBLICATION-DETERMINANTS -Multiple Choice Questions - LEVEL - II
  1. |(b^(2)c^(2),bc,b+c),(c^(2)a^(2),ca,c+a),(a^(2)+b^(2),ab,a+b)|=

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  2. If one of the roots of the equation |(7,6,x),(2,x,2),(x,3,7)|=0 is : ...

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  3. If a,b,c gt 0 and x,y,z , in R then the determinant : |((a^x+a^(-x)...

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  4. If a^2+b^2+c^2=0 and |(b^2+c^2,ab,ac),(ab,c^2+a^2,bc),(ac,bc,a^2+b^2)|...

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  5. If plamda^(4)+qlamda^3+rlamda^2+slamda+t =|(lamda^3+3lamda,lamda-1,lam...

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  6. The value of the determinant : |(1,cos(beta-alpha),cos(gamma-alpha)),(...

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  7. The sum of two non - integral roots of |(x,2,5),(3,x,3),(5,4,x)|=0 is ...

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  8. If Delta1=|(1,1,1),(a,b,c),(a^2,b^2,c^2)|, Delta2=|(1,bc,a),(1,ca,b),(...

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  9. If alpha, beta are non - real numbers satisfying x^3-1=0, then the val...

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  10. The value of |(1,1,1),((2^x+2^(-x))^2,(3^x+3^(-x))^2,(5^x+5^(-x))^2),(...

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  11. The value of |(i^m,i^(m+1),i^(m+2)),(i^(m+5),i^(m+4),i^(m+3)),(i^(m+6)...

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  12. If Delta1=|(7,x,2),(-5,x+1,3),(4,x,7)|, Delta2=|(x,2,7),(x+1,3,-5),(x,...

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  13. Let |(1+x,x,x^2),(x,1+x,x^2),(x^2,x,1+x)|=ax^5+bx^4+cx^3+dx^2+ lamdax+...

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  14. If Delta(x)=|(1,cosx,1-cosx),(1+sinx,cosx,1+sinx-cosx),(sinx, sinx ,1)...

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  15. If the equation a (y+z) = x, b (z+x) =y and c (x+y) = z, where a ne -...

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  16. If p,q, in r and p^2+q^2-pq-q+1 le 0 + alpha + beta + gamma = 0 , the...

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  17. The value of theta lying in (0,pi/2) and satisfying : |(1 + sin^(2)th...

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  18. If a , b , c are unequal , what is the condition that value of the f...

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  19. If a^2+b^2+c^2=-2 and f(x)=|(1+a^2x,(1+b^2)x,(1+c^2)x),((1+a^2)x,1+b^2...

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  20. The system of equations : ax-y-z=alpha-1 x-ay-z=alpha-1 x-y-alph...

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