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If x=(a sin theta+b cos theta )/(a+b), t...

If `x=(a sin theta+b cos theta )/(a+b)`, then

A

the dimensions of `x` and `a` are same

B

the dimensions of `a` and `b` are not same

C

`x` is dimensions

D

None of the above

Text Solution

Verified by Experts

(c) `x=(a sin theta + b cos theta)/(a+b)`
`:.[x]=[(a sin theta)/(a+b)]=[(b cos theta)/(a+b)]` or `[x]=` dimensionless
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Knowledge Check

  • If Z = (A sin theta + B cos theta)/(A + B) , then

    A
    the dimensions of Z and A are the same
    B
    the dimensions of Z and B are the same
    C
    Z is dimensionless quantity
    D
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    A
    `(a^(2)-b^(2))/(a^(2)+b^(2))`
    B
    `(b^(2)-a^(2))/(b^(2)+a^(2))`
    C
    `(a^(2)+b^(2))/(a^(2)-b^(2))`
    D
    none of these

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    A
    `pmsqrt(-a^2 + b^2 + c^2)`
    B
    `pm sqrt(a^2 + b^2 -c^2)`
    C
    `pm sqrt(a^2 - b^2 - c^2)`
    D
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