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The number of all possible values of the...

The number of all possible values of `theta`, where `0 lt theta lt pi`, for which the system of equations
`(y+z) cos 3 theta = (xyz) sin 3 theta`
`x sin 3 theta=(2 cos 3 theta)/y+(2 sin 3 theta)/z`
`(xyz) sin 3 theta = (y+2z) cos 3 theta +y sin 3 theta`
has a solution `(x_(0), y_(0), z_(0))` with `y_(0)z_(0) ne 0` is _______.

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RESONANCE ENGLISH-MATRICES & DETERMINANT-EXERCISE-3
  1. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  2. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  3. The number of all possible values of theta, where 0 lt theta lt pi, fo...

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  4. Let K be a positive real number and A=[(2k-1,2sqrt(k),2sqrt(k)),(2sqrt...

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

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  6. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

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  7. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

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  8. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

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

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  10. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

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  11. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2^(...

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

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  13. If the adjoint of a 3xx3 matrix P is [[1,4,4],[2,1,7],[1,1,3]], then t...

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

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

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

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  17. Let X \ a n d \ Y be two arbitrary, 3xx3 , non-zero, skew-symmetric ma...

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  18. Which of the following values of alpha satisfying the equation |(1+alp...

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  19. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

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  20. The total number of distinct x in R for which |{:(x,,x^(2),,...

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