What is the value of $$1 + {1 \over 4} + {1 \over {16}} + {1 \over {64}} + {1 \over {256}} + ......$$?

"By giving him the last __________ of the cake, you will ensure lasting ________ in our house today."

The words that best fill the blanks in the above sentence are

"Even though there is a vast scope for its __________, tourism has remained a/an _________ area."

The words that best fill the blanks in the above sentence are

Two alloys A and B contain gold and copper in the ratios of 2 : 3 and 3 : 7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is