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Given a matrix A=[a b c b c a c a b],w h...

Given a matrix `A=[a b c b c a c a b],w h e r ea ,b ,c` are real positive numbers `a b c=1a n dA^T A=I ,` then find the value of `a^3+b^3+c^3dot`

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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  2. If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an iden...

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  3. Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positiv...

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  4. Let a,b,c be real numbers with a^(2) +b^(2) +c^(2)=1. Then show tha...

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  5. The value of the determinant |(sintheta, costheta, sin2theta) , (sin(t...

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  6. Suppose f(x) is a function satisfying the following conditions: f(0)=...

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

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

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

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

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

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

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

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

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

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

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  18. about to only mathematics

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

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

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