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For a fixed positive integer n if D= |(n...

For a fixed positive integer n if `D= |(n!, (n+1)!, (n+2)!),((n+1)!, (n+2)!, (n+3)!),((n+2)!, (n+3)!, (n+4)!)|= the show that D/((n!)^3)-4` is divisible by n.

A

`-4`

B

`-2`

C

`2`

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
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MCGROW HILL PUBLICATION-DETERMINANTS-EXERCISE (LEVEL 1 SINGLE CORRECT ANSWER TYPE QUESTIONS)
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  2. If a!=p,b!=q,c!=r and the system of equations px+by+cz=0 ax+qy+cz=...

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

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  4. If a, b, c are in A.P., and Delta=|[x+2,x+7,a],[x+5,x+11,b],[x+8,x+15,...

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  5. If Delta=|(1+y,1-y,1-y),(1-y,1+y,1-y),(1-y,1-y,1+y)|=0, then value of ...

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  6. The determinant Delta=|(al+a'l',am+a'm',an+a'n'),(bl+b'l',bm+b'm',bn...

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  7. If a =i, b = omega and C= omega^2, then the value of determinant |(a...

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  8. If Delta=|(1,1,1),(""^(m)C(1),""^(m+3)C(1),""^(m+6)C(1)),(""^(m)C(2),"...

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  9. Suppose a,b,c,x,y epsilon R. Let Delta=|(1,2+ax,3+ay),(1,2+bx,3+by),...

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  10. If A,B and C are angles of a triangle then the determinant |(-1,cosC...

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  11. Let f(x)=|(cosx,x,1),(2sinx,x^(2),2x),(tan x,x,1)| then lim(xto0)(f(x)...

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  12. If omega is a complex cube root of unity, then value of Delta=|(a(1)+...

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  13. If p q r!=0 and the system of equation (p+a)x+b y-c z=0 a x+(q+b)y+c ...

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  14. The system of equations ax+by+(a alpha+ b)z=0 bx+cy+(b alpha+c)z=0...

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  15. If the system of equations ax+ay-z=0 bx-y+bz=0 -x+cy+cz=0 (whe...

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  16. The values of lamda for which the system of equations (lamda+5)x+(la...

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  17. If a+b+c!=0, the system of equations (b+c)(y+z)-ax=b-c, (c+a)(z+x)-by=...

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  18. If a,b, c in R and a + b + c =0 and th esystem of equations ax + by + ...

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  19. If f(x)=|{:(x^(3),x^(4),3x^(2)),(1,-6,4),(p,p^(2),p^(3)):}|, where p i...

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  20. suppose D= |{:(a(1),,b(1),,c(1)),(a(2),,b(2),,c(2)),(a(3),,b(3),,c(3...

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