Question

(b) ( a=sqrt{4+2 sqrt{3}}-sqrt{4 cdot 2 sqrt{3}} )
( =sqrt{(sqrt{3}+1)^{2}}-sqrt{(3-1)^{2}} )
( =left(frac{sqrt{3}+1}{2}right)-(5 x+2) )
( b=sqrt{11+6 sqrt{2}}-sqrt{11-6 sqrt{2}} )
( =sqrt{(3+sqrt{2})^{2}}-5(3-sqrt{2})^{2} )
( =3+sqrt{2}-3+sqrt{2} )
( =2 sqrt{2} )
( log _{2} 2 sqrt{2}=3 / 2(5) )
(0) ( a=sqrt{3+2 sqrt{2}}=sqrt{3}+sqrt{2}+1 )
( b=sqrt{3-25}=sqrt{3}-sqrt{2}-1 times frac{sqrt{2}+1}{sqrt{2}+1}=frac{1}{sqrt{2}+1} )
( therefore log _{a} b=log _{h+1}(sqrt{2+1})^{-1}=-1 )
a) ( a=(2+sqrt{3}) )
( b=(2-sqrt{3}) quad therefore log _{a} b=-1 )

# Column-11 (P) - 1 (0) 1 [MATRIX MATCH TYPE] Column- (4) If a =3[18+277-8-27), b = (42) (30) +36. then the value of log b is equal to (B If a = 14 +23-14-23.b = V11+6V-VI-6v2. then the value of log bis equal to (C) If a=v3+23.6=v3-23. then the value of logb is equal to If a=v7+72-1,b=V7-172-1.then then the value of log bis equal to The number of zeroes at the end of the product of first 20 prime numbers, is (F) The number of solutions of 22-3-= 55, in which x and y are integers, is (T) None

Solution