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If the system of linear equations {:(x...

If the system of linear equations
`{:(x+2ay+az=0),(x+3by+bz=0),(x+4cy+cz=0):}`
has a non zero solutions, then `a, b, c` are in

A

are in AP

B

are in GP

C

are in HP

D

satisfy a+2b+3c=0

Text Solution

Verified by Experts

The correct Answer is:
C
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
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  2. Let A=[(1,-1,1),(2,1,-3),(1,1,1)] and 10 B=[(4,2,2),(-5,0,alpha),(1,-2...

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  3. If the system of linear equations {:(x+2ay+az=0),(x+3by+bz=0),(x+4cy...

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  4. If A=[{:(a,b),(b,a):}] and A^(2)=[{:(alpha, beta),(beta, alpha):}] the...

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  5. If omega is a non-real cube root of unity and n is not a multiple o...

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  6. if a,b,c are positive and are the pth qth and rth terms respectively ...

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  7. If one of the cube roots of 1 be omega, then |(1,1+omega^2,omega^2),(...

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  8. If A is a symmetric matrix and B is a skew-symmetric matrix such that ...

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  9. The total number of matrices A = [{:(0, 2y, 1), (2x, y, -1), (2x, -y,...

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  10. Let A={:(cosalpha,-sinalpha),(sinalpha,cosalpha):},(ainR) such that A...

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  11. Let P=[(1, 0, 0),(3, 1, 0),(9, 3, 1)]Q=[q(ij)] and Q=P^5+I3 then (q21+...

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  12. Let A = ((0,2q,r),(p,q,-r),(p,-q,r)). If A A^(T) = I(3), then |p| is

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  13. The value of theta lying between 0 and pi/2 and satisfying the equatio...

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  14. The sum of the real roots of the equation |{:(x, -6, -1), (2, -3x, x...

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  15. If Delta(1) =|{:(x, sin theta, cos theta),(-sin theta, -x, 1),(cos the...

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  16. If [{:(1, 1), (0,1):}]*[{:(1, 2), (0,1):}]*[{:(1, 3), (0,1):}]cdotcdot...

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  17. Let alpha and beta be the roots of the equation x^(2) + x + 1 = 0. ...

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  18. If |(1,1,1),(2,b,c),(4,b^(2),c^(2))| and |A| = in [2, 16]. 2, b, c and...

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  19. If A = [(1,sin theta, 1),(-sintheta, 1, sin theta),(-1, -1sin theta, 1...

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  20. |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|

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