Question
Which of the following Flat is
vacant? Answer the questions based on the information given below. Eleven persons A, B, C, D, P, Q, R, S, X, Y and Z live in four storey building having four floors such that lowermost floor is numbered as 1 and floor immediately above the lowermost floor is numbered as 2 and so on. Each floor has 3 flats numbered as 1, 2 and 3 from west to east such that flat – 1 is in west of flat – 2 and flat – 2 is in west of flat – 3. One of the flats on a floor is vacant. The dimensions of each of the flats are same. Note: If there is one/two floor(s) between two flats then they may or may not have the same flat number of different floors. Z lives in an even numbered flat on floor number 2. B and C live on same floor. B lives in an even numbered flat on lowermost floor. R and A live on same floor. All the flats on the floor on which Q lives are occupied. X lives to the west of R. B lives on the floor on which two other persons live. There is one floor between R and Q. P’s flat is immediately above C’s flat and the numbers of their flats is same. R lives immediately below the vacant flat and the flat number of vacant flat and R is same. D lives somewhere above Y in same flat number, but not on flat 3.A lives in flat – 1.Solution
B lives in an even numbered flat on lowermost floor i.e. B lives on floor ground floor in flat 2. Z lives in an even numbered flat on floor number 2. B and C live on same floor. P lives immediately above C and the numbers of their flats is same. So, Now, C either lives immediate west or east of B which means P either lives in flat 3 or flat 1. So, we have two possibilities. Case I: When C and P live on flat – 3: 
Case-2 When C and P live on Flat-1 
R and A live on same floor. X lives to the immediate west of R. R lives immediately below the vacant flat and the flat number of vacant flat and R is same. A lives in flat –1. There is one floor between R and Q. Now, R lives immediately below vacant flat so, the vacant flat must be in topmost floor. Case I: When C and P live on flat – 3: 
Case II: When C and P live on flat – 1 
D lives somewhere above Y in same flat number, but not on flat 3. Now, we cannot fix D and Y in same flat number in case II, so, case II is invalid. The final arrangement is as follows: 
I. 3x2 - 16x - 12 = 0
II. 2y2 + 11y + 9 = 0
I. 2x2 + 5x + 2 = 0
II. 4y2 = 1
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 29x² - 137x + 108 = 0
Equation 2: 31y² - 146y + ...
If a quadratic polynomial y = ax2 + bx + c intersects x axis at a and β, then
- For what value of a does the quadratic equation x² + ax + 81 = 0 have real and identical roots?
I. 66x² - 49x + 9 = 0
II. 46y² - 37y - 30 = 0
I. 56x² - 99x + 40 = 0
II. 8y² - 30y + 25 = 0
I. 99 x² + 31 x – 110 = 0
II. 6y² - 31y + 35 = 0
Equation 1: x² - 200x + 9600 = 0
Equation 2: y² - 190y + 9025 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 50x + 600 = 0
Equation 2: y² - 51y + 630 = 0
Relevant for Exams:
