If `0 lt x lty lt pi` ,then which one of the following is correct?

For 0 lt m lt 1 , which one of the following is correct ?

If sin alpha + sin beta = 0 = cos alpha + cos beta . Where 0 lt beta lt alpha lt 2 pi , then which one of the following is correct?

If sinalpha+sinbeta=0=cosalpha+cosbeta,"where"0 lt betaltalphalt2pi , then which one of the following is correct ?

If 0 lt x lt 45^(@) and 45^(@) lt y lt 90^(@) , then which one of the following is correct ?

For the real numbers p, q, r, x, y, let p lt x lt q and p lt y lt r . Which one of the following is correct ?

If 0 lt theta lt phi lt 90^(@) , then which one of the following correct ?

If A and B are independent events such that 0 lt P (A) lt 1 and 0 lt P(B) lt 1 , then which of the following is not correct ?

If 0 lt x lt 5 and 1 lt y lt 2 , then which of the following is true ?

"If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le 0),(,x-1,0 lt x le 1),(,"In "x,x gt 1):} then which one of the following is not correct?

"If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le 0),(,x-1,0 lt x le 1),(,"In "x,x gt 1):} then which one of the following is not correct?