Match the statements given in Column I with the values given in Column II.

Step-by-step solution

(A) | a |= 1+3 =2| b |= 1+3 =2| c |= 12 =2 3 Using cosine law, aligned C & = | a |^2+| b |^2-| c |^2 2| a || b | & = 4+4-12 2 2 2 = -4 8 = -1 2 C & =120^ = 2 3 aligned (B) aligned & _a^b f(x) d x-3 ( x^2 2 )_a^b= (a^2-b^2 ) & _a^b f(x) d x- 3 2 (b^2-a^2 )= (a^2-b^2 ) & _a^b f(x) d x= (a^2-b^2 )+ 3 2 (b^2-a^2 ) & = b^2-a^2 2 & _a^b f(x) d x= b^2-a^2 2 & aligned f(x)=x f ( 6 )= 6 (C) aligned & ^2 _e 3 _ 7 / 6 ^ 5 / 6 ( x) d x & ^2 _e 3 | x+ x| _ 7 / 6 ^ 5 / 6 & 3 | 5 6 + 5 6 | . & . - | 7 6 + 7 6 | & 3 | 3 |- | 1 3 |