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Show that |[""^xCr, ""^x C(r+1),""^x C(r...

Show that `|[""^xC_r, ""^x C_(r+1),""^x C_(r+2)],[""^y C_r,""^y C_(r+1),""^y C_(r+2)],[""^z C_r,""^z C_(r+1),""^z C_(r+2)]|=|[""^(x)C_r, ""^(x+1) C_(r+1),""^(x+2) C_(r+2)],[""^y C_r,""^(y+1) C_(r+1),""^(y+2) C_(r+2)],[""^z C_r,""^(z+1) C_(r+1),""^(z+2) C_(r+2)]|`

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""^(n) C_(r+1)+2""^(n)C_(r) +""^(n)C_(r-1)=

For ""^(n) C_(r) + 2 ""^(n) C_(r-1) + ""^(n) C_(r-2) =

Show that |^x C_r^x C_(r+1)^x C_(r+2)^y C_r^y C_(r+1)^y C_(r+2)^z C_r^z C_(r+1)^z C_(r+1)|=|^x C_r^(x+1)C_(r+1)^(x+2)C_(r+2)^y C_r^(y+1)C_(r+1)^(y+2)C_(r+2)^z C_r^(z+1)C_(r+1)^(z+2)C_(r+1)| .

|{:(.^(x)C_(r),,.^(x)C_(r+1),,.^(x)C_(r+2)),(.^(y)C_(r),,.^(y)C_(r+1),,.^(y)C_(r+2)),(.^(z)C_(r),,.^(z)C_(r+1),,.^(z)C_(r+2)):}| is equal to

""^(n-2)C_(r)+2""^(n-2)C_(r-1)+""^(n-2)C_(r-2) equals :

""^(n)C_(n-r)+3.""^(n)C_(n-r+1)+3.""^(n)C_(n-r+2)+""^(n)C_(n-r+3)=""^(x)C_(r)

""^(n)C_(r+1)+^(n)C_(r-1)+2.""^(n)C_(r)=

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=

f(n)=sum_(r=1)^(n) [r^(2)(""^(n)C_(r)-""^(n)C_(r-1))+(2r+1)(""^(n)C_(r ))] , then

""^(n)C_(r)+2""^(n)C_(r-1)+^(n)C_(r-2) is equal to

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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