Column-11 (p) - 1 Column-1 (A) If a...
Question

# Column-11 (p) - 1 Column-1 (A) If a = 3 (18+27 - 18-27), b = V(42)(30) + 36 then the value of log, b is equal to If a = 14 +213 - 14-213, b = V11+672 - V11-62, then the value of log b is equal to If a = 13 +212, b= 13-212 then the value of log b is equal to If a = 17+ 72 -1, b = 17-172-1, then the value of log b is equal to The number of zeroes at the end of the product of first 20 prime numbers, is The number of solutions of 22x - 32y = 55, in which x and y are integers, is (t) None

JEE/Engineering Exams
Maths
Solution
55
4.0 (1 ratings)
(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 )