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Consider the following statements: 1. If x is directly proportional to z and y is directly proportional to z, then (x2 - y2) is directly proportional to z2. 2. If x is inversely proportional to z and y is inversely proportional to z, then (xy) is inversely proportional to z2. Which of the above statements is/are correct?
A database of research articles in a journal uses the following schema. (VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE) The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following functional dependencies exist in the schema. (VOLUME, NUMBER, STARTPAGE, ENDPAGE) → TITLE (VOLUME, NUMBER) → YEAR (VOLUME, NUMBER, STARTPAGE, ENDPAGE) → PRICE The database is redesigned to use the following schemas. (VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE) (VOLUME, NUMBER, YEAR) Which is the weakest normal form that the new database satisfies, but the old one does not?  
How is the degree of emulsion polymerization related to the monomer concentration, and the rate of radical generation, Ri? , inversely proportional to Ri b) inversely proportional to Ri, directly proportional to . c) directly proportional to Ri, independent of . d) directly proportional to , independent of Ri
A suit, a trouser, and a shirt are to be stitched from a cloth. The cloth required for the suit is the average of cloth required for trousers and shirt. The length of the cloth for suit is 1.5 times the cloth required for the shirt. The length of cloth required for shirt is 5 times the even prime number. Which of the following is/are correct? A. Cloth required for trousers is 20 m B. Average length of cloth required for all the dresses = Cloth required for suit C. Initially, the cloth was 45 m D. Cloth required for shirt is 15 m
An alloy A contains two elements, copper and tin in the ratio of 2 : 3, whereas an alloy B contains the same elements in the ratio of 3 : 4. If 20 kg of alloy A, 28 kg of alloy B and some more pure copper are mixed to form a third alloy C which now contains copper and tin in the ratio of 6 : 7, then what is the quantity of the pure copper mixed in the alloy C?
Two alloys used to manufacture the third alloy. The first alloy contains Copper and Zinc only, and the second alloy contains Aluminium and Copper only. The Copper content in the two alloys is 40% and 60% respectively. The Zinc content in the new alloy should be between 30 to 40%. How much will be the minimum and maximum Copper content in the new alloy?
An alloy of copper and tin weights 400 grams. It contains 75% of copper. How much percentage of copper with respect to the initial mixture should be added to the alloy so that percentage of copper increased to 80%?
Alloys A and B contain copper and zinc. In alloy A percentage of copper is 25% and in alloy B ratio of copper and zinc is 3 ∶ 5. In what ratio of A and B to be mixed to get a new alloy containing copper and zinc in the ratio 1 ∶ 2?
A 75 kg mixture of copper and tin contains copper and tin in the ratio 3 ∶ 2. 25 kg of the mixture is removed and replaced with copper and the operation is repeated twice. At the end of the two removals and replacements, what is the ratio of tin and copper in the resultant mixture?
There are two alloys of copper and aluminium, alloy A has 40% aluminium and alloy B has 10% copper. In what ratio should these alloys be mixed so that the cost of total copper becomes equal to the cost of total aluminium in the mixture? (The cost price of aluminium is Rs. 200 per kg and cost price of copper is Rs. 500 per kg)