sinx+cosx=y^2-y+a has no value of x for ...

`sinx+cosx=y^2-y+a` has no value of `x` for any value of `y` if a belongs to (a) `(0,""sqrt(3))` (b) `(-""sqrt(3),0)` (c) `(-oo,-""sqrt(3))` (d) `(""sqrt(3),oo)`

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If (sinx)/(siny)=1/2,(cosx)/(cosy)=3/2 , where x , y , in (0,pi/2), then the value of "tan"(x+y) is equal to (a) sqrt(13) (b) sqrt(14) (c) sqrt(17) (d) sqrt(15)

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If .^(n-1)C_r=(k^2-3)^nC_(r+1), then k belongs to (a) (-oo,-2] (b) [2,oo) (c) [-sqrt3, sqrt3] (d) [sqrt3,2]

If cosx=(2cosy-1)/(2-cosy), where x , y in (0,pi) then tan(x/2)xxcot(y/2) is equal to (a) sqrt(2) (b) sqrt(3) (c) 1/(sqrt(2)) (d) 1/(sqrt(3))

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The equation of the lines passing through the point (1,0) and at a distance (sqrt(3))/2 from the origin is (a) sqrt(3)x+y-sqrt(3) =0 (b) x+sqrt(3)y-sqrt(3)=0 (c) sqrt(3)x-y-sqrt(3)=0 (d) x-sqrt(3)y-sqrt(3)=0

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