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Without expanding, prove the following ...

Without expanding, prove the following
`|(x,x+y,x+2y),(x+2y,x,x+y),(x+y,x+2y,x)|=9y^2(x+y)`

A

`9x^(2)(x+y)`

B

`9y^(2)(x+y)`

C

`3y^(2)(x+y)`

D

`7x^(2)(x+y)`

Text Solution

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The correct Answer is:
B
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ACCURATE PUBLICATION-DETERMINANTS-Type-I (Multiple choice questions)
  1. If A=[{:(3,1),(1,2):}], then A(adjA) equals

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  2. If A = ([4,3],[3,4]), then A (Adj A) equals :

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  3. If A=[(3,2),(1,4)] , then A(adj A) equals

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  4. The inverse of a symmetric matrix is :

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  5. Prove that |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|= 0

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  6. If x,y in R then the determinant Delta=|{:(cosx,-sinx,1),(sinx,cosx,1)...

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  7. If |(2x,5),(8,x)|=|(6,-2),(7,3)| , write the value of x.

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  8. The value of determinant |{:(a-b,b+c,a),(b-a,c+a,b),(c-a,a+b,c):}| is

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  9. The area of a triangle with vertices (-3,0),(3,0) and (0,k) is 9 sq. u...

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  10. The determinant |{:(b^(2)-ab,b-c,bc-ac),(ab-a^(2),a-b,b^(2)-ab),(bc-ca...

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  11. The number of distinct real roots of |{:(sinx,cosx,cosx),(cosx,sinx,co...

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  12. If A,B and C are angles of a triangle, then the determinant: {:|(-1,...

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  13. Let f(t)=|{:(cost,t,1),(2sint,t,2t),(sint,t,t):}|, then LT(t to o)(f(t...

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  14. Find the maximum value of : {:|(1,1,1),(1,1+sintheta,1),(1,1,1+costh...

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  15. Consider the determinant f(x)=|{:(0,x^(2)-a,x^(3)-b),(x^(2)+a,0,x^(2...

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  16. If A=[{:(2,lambda,-3),(0,2,5),(1,1,3):}| , then A^(-1) exists if

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  17. If A and B are invertibel , then which of the following is not correct

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  18. If x,y,z are all different from zero and |{:(1+x,1,1),(1,1+y,1),(1,1,1...

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  19. Without expanding, prove the following |(x,x+y,x+2y),(x+2y,x,x+y),(...

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  20. There are two values of a which makes determinant, Delta=|{:(1,-2,5),(...

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