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Value of |[x+y, z,z ],[x, y+z, x],[y, y,...

Value of `|[x+y, z,z ],[x, y+z, x],[y, y, z+x]|,` where x ,y ,z are nonzero real number, is equal to a.`x y z` b. `2x y z` c. `3x y z` d. `4x y z`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
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  2. Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-...

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  3. Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonz...

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  4. If e^(itheta)=costheta+isintheta, find the value of |[1,e^(ipi//3),e...

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  5. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

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  6. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

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  7. Let f(x)=a(5)x^(5)+a(4)x^(4)+a(3)x^(3)+a(2)x^(2)+a(1)x, "where" a(i),s...

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  8. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

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  9. Roots of the equation |x m n1a x n1a b x1a b c1|)=0 are independent ...

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  10. Prove that the value of each the following determinants is zero: |[a...

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  11. If a ,b ,c are different, then the value of x satisfying |[0,x^2-a, x^...

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  12. Prove that the value of each the following determinants is zero: |...

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  13. If |(b +c,c +a,a +b),(a +b,b +c,c +a),(c +a,a +b,b +c)| = k |(a,b,c),(...

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  14. A triangle has vertices Ai(xi , yi)fori=1,2,3 If the orthocentre of tr...

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  15. If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,b...

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  16. If Delta=|(a1,b1,c1),(a2,b2,c2),(a3,b3,c3)| and Delta1=|(a1+pb1,b1+q...

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  17. Prove that the value of each the following determinants is zero: |[(a^...

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  18. The value of the determinant |(1^2, 2^2, 3^2, 4^2) ,(2^2, 3^2 ,4^2,5^2...

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  19. If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f...

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  20. Prove that the value of each the following determinants is zero: |[l...

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