Question : If a + b + c = 1, ab + bc + ca = –1, and abc = –1, then what is the value of a3 + b3 + c3?
Option 1: 1
Option 2: 5
Option 3: 3
Option 4: 2
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Correct Answer: 1
Solution : a3 + b3 + c3 = (a + b + c)(a2 + b2 + c2 – ab – bc – ac) + 3abc = (a + b + c)((a + b + c)2 – 3ab – 3bc – 3ac) + 3abc = (1){12 –3(–1)} + 3(–1) = 1 Hence, the correct answer is 1.
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Question : In a showroom. the marked prices of various items are displayed in such a manner that after giving a 10% discount to the customers, the owner of the showroom earns a profit of 20%. What is the ratio of the marked price and cost price of each item?
Option 1: 3 : 4
Option 2: 4 : 3
Option 3: 5 : 2
Option 4: 2 : 5
Question : Which of the following metal salts is responsible for permanent hardness in water?
Option 1: KCl
Option 2: Nacl
Option 3: Ca(HCO3)2
Option 4: CaCl2
Question : Directions: Which one set of letters when sequentially placed at the gaps in the given letter series shall complete it? _ab _ b _ bc _ ca _
Option 1: accbb
Option 2: abcca
Option 3: cacab
Option 4: abacb
Question : Directions: Which one set of letters when sequentially placed at the gaps in the given letter series shall complete it? _ cb _ ca _ bacb _ ca _ bac_ d
Option 1: badddb
Option 2: bbbddd
Option 3: addddb
Option 4: addbbb
Question : Directions: Four number-pairs have been given, out of which three are alike in some manner and one is different. Select a different one. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding/subtracting/multiplying etc, to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) 17 : 82 31 : 158 19 : 92 47 : 232
Option 1: 31 : 158
Option 2: 47 : 232
Option 3: 17 : 82
Option 4: 19 : 92
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