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The determinant |x p+y x y y p+z y ...

The determinant `|x p+y x y y p+z y z0x p+y y p+z|=0` if `x ,y ,z`

A

x,y,z are in AP

B

x , y , z are in GP

C

x,y,z are in HP

D

xy,yz,zx are in AP

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The correct Answer is:
B
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. Let "f(x)"=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x...

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  2. The parameter on which the value of the determinant |[1,a...

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  3. The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

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  4. Consider the set A of all matrices of order 3 xx 3 with entries 0 or 1...

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  5. If A is a 3xx3 non-singular matrix such that A A' = A' A and B = A^(...

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  6. If P is a 3xx3 matrix such that P^(T) = 2 P + I , where P^(T) is the...

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  7. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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  8. Let M and N be two 3xx3 nonsingular skew-symmetric matrices such that ...

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  9. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

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  10. Given , 2x-y+2z=2, x-2y+z=-4, x+y+lambdaz=4, then the value of lam...

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  11. The number of values of k for which the system of the equations (k+1)x...

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  12. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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  13. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

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  14. Let P=[(1,0,0),(3,1,0),(9,3,1)] and Q = [q(ij)] be two 3xx3 matrices s...

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  15. How many 3xx3 matrices M with entries from {0, 1, 2} are there, for wh...

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  16. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

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  17. Let M and N be two 3xx3 matrices such that MN=NM. Further, if M ne N^(...

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  18. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

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  19. the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha...

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  20. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

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