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Let alpha be a repeated root of a qua...

Let `alpha` be a repeated root of a quadratic equation `f(x)=0a n dA(x),B(x),C(x)` be polynomials of degrees 3, 4, and 5, respectively, then show that `|A(x)B(x)C(x)A(alpha)B(alpha)C(alpha)A '(alpha)B '(alpha)C '(alpha)|` is divisible by `f(x)` , where prime `(')` denotes the derivatives.

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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. Suppose f(x) is a function satisfying the following conditions: f(0)=...

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  2. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

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  3. Let a >0,d >-0. Find the value of the determinant |1/a1/(a(a+d))1/((a+...

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  4. For all values of A ,B ,Ca n dP ,Q ,R show that |"cos"(A-P)"cos"(A-Q)"...

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  5. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

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  6. If a!=p ,b!=q ,c!=r and |[p, b, c ],[a, q, c ],[a ,b, r]|=0, then find...

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  7. Suppose that digit numbers A28,3B9 and 62 C, where A,B and C are integ...

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  8. Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|. Sho...

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  9. Show that |[""^xCr, ""^x C(r+1),""^x C(r+2)],[""^y Cr,""^y C(r+1),""^y...

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  10. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

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  11. " If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x...

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  12. Let a , b and c be positive and not all equal. Show that the va...

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  13. about to only mathematics

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  14. Let lambda and alpha be real. Then the numbers of intergral values ...

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  15. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

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  16. Consider the system of linear equations in x, y, and z: (sin 3 theta...

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  17. about to only mathematics

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  18. For what value of m does the system of equations 3x+m y=m ,2x-5y=20 ha...

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  19. For what value of k, does the following system of equations possess a ...

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  20. If the system of linear equations x=cy+bz, y=az+cx,z=bx+ay has a non t...

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