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Without expanding evaluate the determina...

Without expanding evaluate the determinant `|[(a^x+a^(-x))^2,(a^x-a^(-x))^2, 1],[(a^y+a^(-y))^2,(a^y-a^(-y))^2, 1],[(a^z+a^(-z))^2,(a^z-a^(-z))^2, 1]|,` where `a>0` and `x , y , z in R`

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Without expanding evaluate the determinant |[41,1,5],[79,7,9],[29,5,3]...

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  2. Show that |1a bc1b c+a1c a+b|=0

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  3. Without expanding evaluate the determinant |[(a^x+a^(-x))^2,(a^x-a^(-x...

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  4. If D1=|[1, 1, 1],[x^2,y^2,z^2],[x, y, z]| and D2=|[1, 1, 1],[yz, zx,xy...

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  5. Without expanding show that |[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2...

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  6. Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alp...

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  7. If A+B+C=pi, then the value of |[sin(A+B+C),sin(A+C),cosC],[-sinB,0...

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  8. If Ar=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|, the value of sum(...

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  9. If the determinant |[a,b,2aalpha+3b],[b,c,2balpha+3c],[2aalpha+3b,2bal...

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

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  11. Using the factor theorem it is found that a+b , b+c and c+a are thr...

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  12. Let |x^2+3xx-1x+3x+1-2xx-4x-3x+4 3x|=a x^4+b x^3+c x^2+e be an identi...

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  13. If Dk=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum(k=1)^...

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  14. If Delta1=|(1, 1 ,1),(a, b, c ),(a^2,b^2,c^2)|,Delta2=|(1,b c, a),(1,c...

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  15. The value of the determinant |a^2a1cosn xcos(n+1)xcos(n+2)xsinn xsin(n...

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  16. Evaluate: (i) |(5 ,4),(-2, 3)| (ii) |(sintheta,costheta),(-costheta,si...

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  17. Evaluate: (i) |(x^2+x y+y^2,x+y ),(x^2-x y+y^2,x-y)|

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  18. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]| by expanding it along th...

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  19. Evaluate the determinant D=|[2 ,3,-2],[ 1, 2 ,3],[-2, 1,-3]| by expa...

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  20. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]|

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