The number `(7+5sqrt2)^(1/3)+(7-5sqrt2)^(1/3)`, is equal to

has four statements (A,B,C and D) given in Coumn-I and five statements (P,Q,R,S and T) given in Column-II. Any given statement in Column-I can have correct matching with one or more statement(s) given in Column-II. {:(Column-I,Column-II),((A)"A rectangular box has volume 48,and the sum of",(P)1),("length of the twelve edges of the box is 48. The largest",),("integer that could be the length of an edge of the box,is",),((B)"The number of zeroes at the end in the product of first",(Q)2),("20 prime numbers, is"(p),),((C)"The number of solutions of" 2^(2x)-3^(2y)=55 "in which x and y",(R)3),("are integers,is"(0),(S)4),((D)"The number" (7+5sqrt(2))^(1//3)+(7-5sqrt(2))^(1//3)"is equal to",(T)6):}

Let a=sqrt(57+40sqrt2)-sqrt(57-40sqrt2) and b=sqrt(25^(1/(log_8(5)))+49^(1/(log_6(7)) and c is the value of x^3-3x-14 where x=(7+5sqrt2)^(1/3)-1/(7+5sqrt2)^(1/3). Find the value of (a+b+c)

If x=(7+5sqrt(2))^(1/3) -1/((7+5sqrt(2))^(1/3) , then the value of x^3+3x-14 is equal to 1 (b) 0 (c) 2 (d) 4

If x=(7+5sqrt(2))^(1/3)-1/((7+5sqrt(2))^(1/3)) , then the value of x^3+3x-14 is equal to 1 b. 0 c. 2 d. 4

the value of |((3-i sqrt(2))^(2))/(1+i2)| is equal to (i) (11)/(sqrt(5)) (ii) (18)/(sqrt(7)) (iii) (5)/(sqrt(11)) (iv) (13)/(sqrt(3))

If x=root(3)(7+5sqrt(2))-(1)/(root(3)(7+5sqrt(2))), then the value of x^(3)+3x-14 is equal to 1 b.0 c.2 d.4

If x=root(3)(7+5sqrt(2))-(1)/(root(3)(7+5sqrt(2))), then the value of x^(3)+3x-14 is equal to 1(b)0(c)2 (d) 4

The value of (1)/( sqrt(7) - sqrt(6)) - (1)/( sqrt(6) - sqrt(5) ) +(1)/( sqrt(5) -2) - (1)/( sqrt(8) - sqrt(7) ) +(1)/( 3- sqrt(8)) is