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Consider the system of equations : x sin...

Consider the system of equations : `x sintheta-2ycostheta-az=0`, `x+2y+z=0`, `-x+y+z=0`, `theta in R`

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 `theta` for which the system will have infinite solutions

D

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

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
`(b,c,d)` For the system to have nontrivial solution
`|{:(sintheta,-2costheta,-a),(-1,1,1),(1,2,1):}|=0`
i.e. `sintheta+4costheta=3a`
`implies-(sqrt(17))/(3) le a le (sqrt(17))/(3)`
`implies` a has three integer values.
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