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Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^...

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)|` .

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

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

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

If (1+2x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then a=(^(n)C_(2))^(2) b.^(n)C_(r).^(n)C_(r+1) c.^(2n)C_(r) d.^(2n)C_(r+1)

RESONANCE DPP-JEE MAINS-All Questions
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  2. A bag initially contains 1 red and 2 blue balls. An experiment consist...

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  3. Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^y C(r+1)^y C(r+2)^z Cr^z C(r+1...

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  4. If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x...

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  5. The number of 2xx2 matrices X satisfying the matrix equation X^2=I(I...

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  6. The equation x^3-3/4x=-(sqrt(3))/8 is satisfied by x=cos((5pi)/(18))...

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  7. Let trianglePQR be a triangle. Let veca = vecQR, vecb= vecRP and vec c...

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  8. If A is a non-singular matrix of order nxxn such that 3ABA^(-1)+A=2A^(...

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  9. The number of triangles that can be formed using the vertices of a 20 ...

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  10. If (x)=|x^2+4x-3 2x+4 13 2x^2+5x-9 4x+5 26 8x^2-6x+1 16 x-6 104|=a x^3...

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  11. The function f:R->R defined by f(x) =(e^|x|-e^-x)/(e^x+e^-x) is

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  12. If vec aa n d vec b are two vectors and angle between them is thet...

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  13. Range of function f(x)=|6sin^(-1)x-pi|+|6cos^(-1)x-pi| is (a)[0,9pi]...

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  14. veca and vecc are unit vectors and |vecb|=4 with vecaxxvecb=2vecaxxvec...

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  15. Given a tctrahecdrone D-ABC with AB=12,CD=6. If the shortest distance ...

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  16. Let f : R ->R defined by f(x) = min(|x|, 1-|x|), then which of the fol...

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  17. The x-y plane is rotated about its line of intersection with the y-...

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  18. The domain of the function f(x)= cos^(-1)(x-[x]) is

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  19. Let vec v1= hat i+ hat j+ hat k&( hat v)2=a hat i+b hat j+c hat k be ...

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  20. The complete set f values of ' a ' for which (a^2-1)x^2+2(a-1)x+2 i...

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