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Let f (n) = |{:(n,,n+1,,n+2),(.^(n)P(n)...

Let `f (n) = |{:(n,,n+1,,n+2),(.^(n)P_(n),,.^(n+1)P_(n+1),,.^(n+2)P_(n+2)),(.^(n)C_(n),,.^(n+1)C_(n+1),,.^(n+2)C_(n+2)):}|` where the sysmbols have their usual neanings .then f(n) is divisible by

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Let f (n) = |{:(n,,n+1,,n+1),(.^(n)P_(n),,.^(n+1)P_(n+1),,.^(n+2)P_(n+2)),(.^(n)C_(n),,.^(n+1)C_(n+1),,.^(n+2)C_(n+2)):}| where the sysmbols have their usual neanings .then f(n) is divisible by

If "^(n)C_(0)-^(n)C_(1)+^(n)C_(2)-^(n)C_(3)+...+(-1)^(r )*^(n)C_(r )=28 , then n is equal to ……

In .^(2n)C_(3) :.^(n)C_(3) = 11 : 1 then n is

Find the sum 1.^(n)C_(0) + 3 .^(n)C_(1) + 5.^(n)C_(2) + "….." + (2n+1).^(n)C_(n) .

If ""^(nP_(r)=""^(n)P_(r+1) and ""^(n)C_(r)=""^(n)C_(r-1) find n and r.

The value of .^(n)C_(0) xx .^(2n)C_(r) - .^(n)C_(1)xx.^(2n-2)C_(r)+.^(n)C_(2)xx.^(2n-4)C_(r)+"…." is equal to

Prove that .^(n)C_(1) + 2 .^(n)C_(2) + 3 .^(n)C_(3) + "…." + n . ^(n)C_(n) = n 2^(n-1) .

The value of sum_(n=1)^(oo)(""^(n)C_(0)+.......+""^(n)C_(n))/(""^(n)P_(n))

If ""^(2n)C_(3) : ""^(n) C_(3)= 11 : 1 then n is

If the value of "^(n)C_(0)+2*^(n)C_(1)+3*^(n)C_(2)+...+(n+1)*^(n)C_(n)=576 , then n is

CENGAGE-DETERMINANTS-All Questions
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  2. If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|...

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  3. Let f (n) = |{:(n,,n+1,,n+2),(.^(n)P(n),,.^(n+1)P(n+1),,.^(n+2)P(n+2)...

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  4. If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e...

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  5. Let x<1, then value of [[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]...

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  13. Prove that the value of determinants is zero: |a-b b-c c-a x-y y-z ...

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  15. Prove that the value of each the following determinants is zero: |...

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  16. If |b+cc+a a+b a+bb+cc+a c+a a+bb+c|=k|a b cc a bb c a| , then value o...

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  17. A triangle has vertices Ai(xi , yi)fori=1,2,3 If the orthocentre of tr...

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  18. If alpha,beta,gamma are the roots of a x^3+b x^2+c x+d=0a n d|alpha ...

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  19. If Delta=|(a1,b1,c1),(a2,b2,c2),(a3,b3,c3)| and Delta1=|(a1+pb1,b1+q...

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