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The number of integral values of a for w...

The number of integral values of a for which the system of linear equations ` x sin theta -2 y cos theta -az=0`, `x+2y+z=0,-x+y+z=0` may have non-trivial solutions, then

A

The given system will have infinite solutions for a=2

B

The number of integer values of a is 3 for the system to have nontrivial solutions.

C

For a=1 there exists θ for which the system will have infinite solutions

D

For a=3 there exists θ for which the system will have unique solutions

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The correct Answer is:
B, C, D
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ARIHANT MATHS-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Exercise (More Than One Correct Option Type Questions)
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  2. Let x, y, z be elements from interval [0,2pi] satisfying the inequal...

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  5. If x+y=2pi//3 and sin x//sin y=2, then the

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  6. If 0 lt x lt 2 pi and |cos x| le sin x, then

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  7. If xa n dy are positive acute angles such that (x+y) and (x-y) satisfy...

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  8. If x+y=(4pi)/(3) and sin x = 2 sin y , then

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  10. If [sin x]+[sqrt(2) cos x]=-3 , x in [0,2pi], (where ,[.] denotes the...

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  11. If alpha in [-2pi, 2pi] and cos.(alpha)/(2)+sin.(alpha)/(2)=sqrt(2)(co...

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  12. The number of value of alpha in the interval [-pi,0] satisfying sin...

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  13. Find the number of solution of theta in [0,2pi] satisfying the equatio...

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  14. If alpha and beta are the solution of a cos theta + b sin theta = c...

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  15. The solution of the equation sin 2x + sin 4x = 2 sin 3x is

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  17. The value of x , 0 le x le (pi)/2 which satisfy the equation 81^( si...

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  18. The value of x in (0,pi/2) satisfying (sqrt(3)-1)/(sinx)+(sqrt(3)+1)/(...

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  19. The values of alpha for which the equation alpha^2/(1-tan^2x)=(sin^2...

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  20. For which values of a does the equation 4sin(x+pi/3)cos(x-pi/6)=a^2+sq...

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