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|(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2...

`|(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2))|=`

A

`(a-b)(b-c)(c-a)`

B

`-(a-b)(b-c)(c-a)(a+b+c)`

C

`abc(a-b)(b-c)(c-a)`

D

`2(a-b)(b -c)(c-a)`

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-APPENDICES (REVISION EXERCISE)-DETERMINANTS
  1. |(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2))|=

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  2. |(sqrt(13)+sqrt(3),2sqrt(5),sqrt(5)),(sqrt(15)+sqrt(26),5,sqrt(10)),(3...

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  3. If x+y+z=0 and |(xa, yb, zc),(yc,za, xb),(zb,xc, ya)|=k|(a,b,c),(b,c,a...

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  4. If D(r)=|(r,x,n(n+1)//2),(2r-1,y,n^(2)),(3r-1,z,n(3n+1)//2)| then sum(...

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  5. For all values of A, B, C and P, Q, R |(cos(A-P), cos(A-Q),cos(A-R))...

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  6. If f(x)=|(cosx, x,1),(2sinx,x^(2),2x),(tanx,x,1)| then Lt(xto0)(f'(x))...

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  7. If Delta( r)= |(2r-1, ""^(m)C(r ), 1),(m^(2)-1, 2^(m), m+1), ("sin"^(2...

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  8. If |(1+x,1-x,1-x),(1-x,1+x,1-x),(1-x,1-x,1+x)|=0 then x=

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  9. |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=

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  10. If |(x(1),y(1),1),(x(2),y(2),1),(x(3),y(3),1)|=|(a(1),b(1),1),(a(2),b(...

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  11. If |(a+x, a-x, a-x),(a-x,a+x,a-x),(a-x,a-x,a+x)|=0 then

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  12. Let D(r )=|(a, 2^(r ), 2^(16)-1),(b, 3(4^(r )), 2(4^(16)-1)), (x, 7(8^...

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  13. If f(x)=|(1+sin^(2)x,cos^(2)x,4sin2x),(sin^(2)x,1+cos^(2)x,4sin2x),(si...

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  14. If A(K)=[(K,K-1),(K-1,K)] then |A(1)|+|A(2)|+...+|A(2011)|=

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  15. If f(x)=|(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x)| then f(root(3)(2))=

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  16. If f(x)=|(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)...

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  17. |(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b)|=

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  18. |(sin theta, cos theta, sin2theta),(sin(theta+(2pi)/(3)),cos(theta+(2p...

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  19. |(3, a+b+c, a^(2)+b^(2)+c^(2)),(a+b+c, a^(2)+b^(2)+c^(2), a^(3)+b^(3)+...

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  20. |(1,a,a^(2)+bc),(1,b,b^(2)+ac),(1,c,c^(2)+ab)|=k(a-b),(b-c), (c-a) the...

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