Study the following information carefully and answer the given questions.
Eight balls are arranged in a stack from bottom to top numbered from 1-8 each from a different e commerce games; Cricket, Football, Hockey, Golf, Tennis, Rugby, Table Tennis and Badminton not necessarily in the same order.Each ball has different colours viz,Red, Blue, Green, Yellow, White, Black, Pink and Orange not necessarily in the same order. The arrangement is based on the following rules:
• The ball from Tennisgame is kept at an even numbered position
• There are 3 balls between the ball from Tennisgame and the ball with Orangecolour
• The ball from Golfgame is either at the top or at the bottom of the stack
• Ball number 2 has Redcolour and it is not from Tennisgame
• Ball with the Whitecolour is kept between the ball from Table Tennisgame and the ball having Yellowcolour
• The ball from Cricketgame is kept one ball above the ball from Hockeygame
• There are 4 balls between the ball with Bluecolour and the ball from Table Tennisgame
• There are 3 balls between the ball with Whitecolour and the ball with Greencolour
• The ball from Badmintongame is between the ball with Pinkcolour and the ball from Rugbygame
• The ball from Table Tennisgame does not have Pinkcolour .
Study the following information carefully and answer the given questions.
Seven games - High jump, Pole vault, Long jump, Triple jump, Shot put, Discus throw and Javelin throw–held on Bhubaneswar on Sunday. Each game starting at different times 4 AM, 7 AM, 8 AM, 10 AM, 1 PM, 3 PM and 6 PM not necessarily in the same order. And ends at different times.
• Long jump is the earliest to start. Its starting time is not after 7 a.m. and its total time is two hours less than the total time of Discus throw.
• Since High jumpis the least duration game, it starts before 7 p.m. and the games end at 9 p.m.
• Triple jumpstarts at Sunday 10 a.m. and takes 19 hours to finish the game.
• There is a four hour gap between the starting times of Shot put, starting at 8 a.m. and Long jump.
• Shot put takes one hour more than the total time of Long jump to finish the game.
• High jumpstarts five hours after Pole vaultstarts but takes only three hours to finish the game.
• Discus throw and Javelin throw take 10 hours and 8 hours to finish the game.
• Discus throwstarts at 3 p.m. and there is gap of 8 hours between the starting times of Discus throw and Javelin throw.
• One game ends at 6 p.m.
Directions (Q. 1-10): In the following questions numbered I and II are given. You have to solve out the equations and Give answer
a) if x > y
b) if x ≥ y
c) if x < y
d) if x ≤ y
e) if x = y or the relationship cannot be established
1). I. x² – 1 = 0
II. y² + 4y + 3 = 0
2). I. x² – 7x + 12 = 0
II. y² – 12y + 32 = 0
3). I. x³ – 371 = 629
II. y³ – 543 = 788
4). I. 5x + 2y = 31
II. 3x + 7y = 36
5). I. 2x² + 11x + 12 = 0
II. 5y² + 27y + 10 = 0
6). I. 4x² + 27x + 35 = 0
II. 3y² - 23y +42 = 0
7). I. 9x² + 15x - 14 =0
II.7y² – 23y + 16 =0
8). I.x² = 1156
II. y = 3√(35937)
9). I. 2x - 3y = 43
II. 3x + 4y = -12
10). I. 5x² - 44x + 63 = 0
II. 10y² + 23y + 12 = 0
Solution with Answer keys:
1). B)
I. x2 – 1 = 0
x2 = 1
x = ± 1
II. y2 + 4y + 3 = 0
y2 + y + 3y + 3 = 0
y (y + 1) + 3 (y + 1) = 0
(y + 1) (y + 3) = 0
y = -1, -3
hence x ≥ y
2). D) I. x2 -7x + 12 = 0
x2 - 4x – 3x + 12 = 0
x (x - 4) - 3 (x - 4) = 0
(x - 4) (x -3) = 0
x = 4, 3
II. y2 - 12y + 32 = 0
y2 - 8y - 4y + 32 = 0
y (y-8) – 4 (y- 8) = 0
(y - 8) (y - 4) = 0
y = 8, 4
Hence, x ≤ y
3). C) I. x3 - 371= 629
x3 = 629 + 371
x3 = 1000
x =10
II. y3 - 543 = 788
y3 = 788 + 543
y3 = 1 331
y = 11
Hence, x< y
4). A) I. 5x + 2y =31} x3 …(i)
II. 3x + 7y = 36} x 5 …(ii)
[ (i) – (ii)] we get
- 29y = - 87
y = 3
By putting value of y in I
5x + 2 x 3 = 31
5x = 25
x = 5
Hence, x> y
5). E) I. 2x2 + 11x + 12 = 0
2x2 + 8x + 3x + 12 = 0
2x(x+4) + 3(x+4) = 0
(x + 4) (2x + 3) = 0
x = -4, - (3/2)
II.5y2+27y+10=0
5y2 + 25y + 2y + 10 = 0
5y (y + 5) + 2 (y + 5) = 0
(y + 5) (5y + 2) = 0
y = -5, -(2/5)
Hence, relationship of x and y cannot be established.
6). C)
I. 4x2 + 27x + 35 = 0
x = +(20/4), +(7/4)
x = -5, -(7/4)
II. 3y2 - 23y +42 = 0
y = -(14/3), -(9/3)
y = (14/3), 3
hence x < y.
7). C)
I. 9x2 + 15x - 14 =0
x = +(21/9), -(6/9)
x = -(7/3), +(2/3)
II.7y2 – 23y + 16 =0
y = -(16/7), -(7/7)
y = (16/7), 1
hence x < y.
8). E) I.x2 = √1156
x = 1156 = ± 34
II. y = 3√(35937) = 33
Hence no relation can be established.
9). A) 2x - 3y = 43 ..(i)
3x + 4y = -12 …(ii)
Solving equation (i)×3 – (ii) ×2
(6x – 9y = 129) – (6x + 8y = -24) = -17y = 153
Y = -(153/7) = -9
Putting the value of y in equation (i), we get
2x – 3(-9) = 43
Or, 2x + 27 = 43
X = (43-27) / 2 = 16/2 = 8
Hence x > y
10).A) I. 5x2 - 44x + 63 = 0
x = -(35/5), -(9/5)
x = 7, (9/5)
II. 10y2 + 23y + 12 = 0
y = (15/10), (8/10)
y = -(3/2), -(4/5)
hence x > y.
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