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If D=|(1,1,1),(1,1+x,1),(1,1,1+y)| for x...

If `D=|(1,1,1),(1,1+x,1),(1,1,1+y)|` for `x!=0,y!=0` then D is

A

Divisible by y but not x

B

Divisible by neither x nor y

C

Divisible by both x and y

D

Divisible by x but not y

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-MATRICES -DETERMINANTS-PRACTICE EXERCISE
  1. |(cos (alpha+beta),-sin (alpha+beta),cos 2 beta),(sin alpha, cos alpha...

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  2. If |{:(a,b,c),(b,c,a),(c,a,b):}|^(x)=|{:(2bc-a^(2),c^(2),b^(2)),(c^(2)...

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  3. If a="cos"(4pi)/3+I"sin"(4pi)/3,then |(1,1,1),(1,a,a^(2)),(1,a^(2),a)|...

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  4. If A+B+C=pi then the value of |(sin(A+B+C), sinB, cosC),(-sinB,0,tanA)...

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  5. If a,b,c are different and |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 the...

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  6. Let the three digit number A28, 3B9,62C, where A,B,C are integers betw...

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  7. If f(x)=|(2cosx,1,0),(x-pi//2,2cosx,1),(0,1,2cosx)| then (df)/(dx) at ...

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  8. If a,b,c are different and |(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(...

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  9. Statement - I : If |{:(x+1,-3,4),(-5,x+2,2),(4,1,x-6):}|=0 then x=0 ...

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  10. If |{:(5,-3),(a,3):}|=18,|{:(1,0,0),(2,3,4),(5,-6,b):}|=45,|{:(2,1,0),...

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  11. Match the following from List - I to List - II |{:("List - I","-Li...

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  12. Assertion (A) : |{:(1,2,2),(2,3,4),(3,5,6):}|=0 Reason (R) : If the ...

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  13. If |{:(6i , -3i , 1) , (4 , 3i , -1) , (20 , 3 , i):}| = x +iy show t...

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  14. If 1, omega, omega^(2) are the cube roots of unity then Delta=|(1,omeg...

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  15. If a^(2)+b^(2)+c^(2)=-2 and f(x)=|(1+a^(2)x,(1+b^(2))x,(1+c^(2))x),((1...

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  16. If a(1),a(2),…………..,a(n), ……… are in G.P and a(i)gt0 for each i then t...

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  17. If D=|(1,1,1),(1,1+x,1),(1,1,1+y)| for x!=0,y!=0 then D is

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  18. Let a,b, c be such that b(a+c)!=0. If |(a,a+1,a-1),(-b,b+1,b-1),(c,c-1...

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  19. Let P and Q be 3xx3 matrices with P!=Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2...

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  20. |{:(x^(2)+x,x+1,x-2),(2x^(2)+3x-1,3x,3x-3),(x^(2)+2x+3,2x-1,2x-1):}|=a...

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