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Let |[x^2+3x,x-1,x+3],[x+1,-2x,x-4],[x-3...

Let `|[x^2+3x,x-1,x+3],[x+1,-2x,x-4],[x-3,x+4, 3x]|=a x^4+b x^3+c x^2+e` be an identity in `x ,` where `a , b , c , d , e` are independent of `xdot` Then the value of `e` is (a) 4 (b) 0 (c) 1 (d) none of these

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,...

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

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  3. Let |[x^2+3x,x-1,x+3],[x+1,-2x,x-4],[x-3,x+4, 3x]|=a x^4+b x^3+c x^2+e...

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

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  5. If a ,b ,c are different, then the value of |[0,x^2-a, x^3-b], [x^2+a,...

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  6. If the determinant |(a ,b,2aalpha+3b),(b, c,2balpha+3c),(2aalpha+3b,2b...

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  7. If 1.omega, omega^2 are the roots of unity, then Delta=|(1,omega^n,ome...

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  8. If Ar=|(1,r,2^r),(2,n,n^2),(n,(n(n+1))/2 ,2^(n+1))| , then the value o...

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  9. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

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  10. The value of |[5^2 ,5^3, 5^4], [5^3, 5^4, 5^5], [5^4, 5^5, 5^6]| is (a...

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  11. |[(log)3 512,(log)4 3],[(log)3 8,(log)4 9]|xx|[(log)2 3,(log)8 3],[(lo...

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  12. If a, b, c, are in A.P, then the determinant|[x+2,x+3,x+2a], [x+3,x+4,...

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  13. If A+B+C=pi, then the value of |"sin"(A+B+C)sin(A+C)cosC-sinB0tanCcos...

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  14. The number of distinct real roots of |{:(cosec x, secx, secx), (secx...

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  15. Let A=|[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]|, where ...

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  16. If |[2x,5], [8,x]|=|[6,-2], [7, 3]| , then x= (a) 3 (b) +-3 (c) +-6 (...

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  17. If f(x)=|[0,x-a, x-b], [x+a,0,x-c], [x+b, x+c,0]|,t h e n (a)f(a)=0 ...

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  18. The value of the determinant |[a-b,b+c, a], [b-a, c+a, b], [c-a, a+b...

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  19. If x , y , z are different from zero and |[1+x,1 ,1], [1, 1+y,1], [1, ...

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  20. The determinant |{:(b^2-ab, b-c, bc-ac), (a b-a^2, a-b, b^2-ab) ,(b c-...

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