**Directions(1-5):** Find the relation between x and y and choose a correct option.

- I. x^2 − 6x + 9 = 0

II. y^2 − 11y + 24 = 0y>xx>yy>=xx=y or relation cannot be established.x>=yOption C

I. x^2 − 6x + 9 = 0

=> x = 3, 3

II. y^2 − 11y + 24 = 0

=> y = 8, 3

y ≥ x - I. 18x² + 18x + 4 = 0

II. 12y² + 29y + 14 = 0x>yx>=yy>xy>=xx=y or relation cannot be established.Option B

I.18x² + 18x + 4 = 0

=> 18x² + 12x + 6x + 4 = 0

=>6x (3x + 2) +2 (3x + 2) = 0

=> (3x + 2) (6x + 2) = 0

x = −2/3, −1/3

II. 12y² + 29y + 14 = 0

=>12y² + 21y + 8y + 14 = 0

=>3y(4y + 7) +2 (4y + 7) = 0

=> (4y+ 7) (3y +2) = 0

y = −7/4, −2/3

x ≥ y - I. y² + 2y – 3 = 0

II. 2x² – 7x + 6 = 0y>=xy>xx>yx=y or relation cannot be established.x>=yOption C

I. y² + 2y – 3 = 0

=>y² +3y – y – 3 = 0

=> (y + 3) (y- 1) = 0

y = -3, 1

II. 2x² -7x + 6 = 0

=> 2x² – 4x -3x + 6= 0

=>2x(x – 2) – 3 (x- 2) = 0

=> (x – 2) (2x – 3) = 0

x = 2, 3/2

x > y - I. x^2−5x−14 = 0

II.y^2+7y+10 = 0x>yy>=xx=y or relation cannot be established.x>=yy>xOption D

I. x^2 − 7x + 2x − 14 = 0

=> x(x − 7) + 2(x − 7) = 0

x = 7, −2

II.y^2 + 5y + 2y + 10 = 0

y = −2, −5

x ≥ y - I. 7x^2 – 21x – 33x + 99 = 0

II. 4y^2 – 10y – 6y + 15 = 0x=y or relation cannot be established.x>=yy>xy>=xx>yOption E

I. 7x^2 – 21x – 33x + 99 = 0

=> 7x(x − 3) − 33(x − 3) = 0

=> x = 3, 33/7

II. 4y^2 – 10y – 6y + 15 = 0

=> 2y(2y − 5) − 3(2y − 5) = 0

=> y = 3/2 , 5/2

x>y - What is the ratio of marks obtained by students B and C in Maths together to marks obtained by D and E together in History ?
13:2814:2914:2711:2915:22Option B

Required ratio = (72+68)*3/4 : (85+60)*3/2 = 14:29 - What is the total marks obtained by B in all subjects together ?
590578620581500Option D

Total Marks

= 44*3/4 + 72*3/4 + 58 + 80*3/2 + 95*200% + 72*7/4

= 33 + 54 + 58 + 120 + 190 + 126

= 581 - The marks obtained by student C in Chemistry is what per cent of the total marks obtained by C in Maths ?
140%160%150%100%120%Option A

Required% = 72/51*100 == 140% - What is the average marks obtained by E in all subjects together ?
66%84%77%95%88%Option D

Required average marks = (108* 75% + 82* 100% + 60* 150% + 88 * 200% + 80 *175%) = 95% - The marks obtained by student D in Science is approximately what percent of the mark obtained by the students B in Maths ?
250%222%308%200%278%Option E

Required% = (200%*75)/(72*75%)*100 = 150/54*100 == 278%

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Directions(6-10):** Study the following table shows the percentage of marks scored by 6 students in different subjects :