**Directions(1-5): **Find the values of x and y, compare their values and choose a correct option.

- (i) 3x² + 11x + 10 = 0

(ii) 2y² + 11y + 14 = 0

x > yy > xx >= yNo relation between x and y.y >= xOption C

(i) 3x² + 11x + 10 = 0

3x² + 6x + 5x + 10 = 0

3x (x + 2) + 5 (x + 2) = 0

x = – 2, –5/3

(ii) 2y² + 11y + 14 = 0

2y² + 7y + 4y + 14 = 0

y (2y + 7) +2 (2y + 7) = 0

y = –2, – 7/2

x ≥ y - (i) 2x² + 9x + 9 = 0

(ii) 15y² + 16y + 4 = 0

y >= xx >= yNo relation between x and y.y > xx > yOption D

(i) 2x² + 9x + 9 = 0

2x² + (6 + 3) x + 9 = 0

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

x = –3/2 , –3

(ii) 15y² + 16y + 4 = 0

15y² + 10y + 6y + 4 = 0

5y (3y + 2) + 2 (3y + 2) = 0

y = –2/5 , –2/3

x < y - (i). x² – 17x + 72 = 0

(ii). 6y² – 31y + 35 = 0

No relation between x and y.x > yy > xx >= yy >= xOption B

x² – 17x + 72 = 0

x = 8, 9

6y² – 31y + 35 = 0

y = 1.6, 3.5

x>y - (i). x² – 37x + 300 = 0

(ii). y² – 43y + 372 = 0

x > yy >= xNo relation between x and y.y > xx >= yOption C

x² – 37x + 300 = 0

x = 25, 12

y² – 43y + 372 = 0

y = 31, 12

No relation between x and y. - (i) 12x² + 11x + 2 = 0

(ii) 12y²+ 7y + 1 = 0

x >= yy >= xy > xx > yNo relation between x and y.Option E

(i) 12x² + 8x + 3x + 2 = 0

4x (3x + 2) + 1 (3x + 2) = 0

x = –2/3 , –1/4

(ii) 12y² + 7y + 1 = 0

12y² + 4y + 3y + 1 = 0

4y (3y + 1) +1 (3y + 1) = 0

y = –1/3 , –1/4

No relation between x and y. - Average number of students got selected for PhD program is by what percent more/less the average number of students applied for PG programs.
65% less77% less68% less72% less70% lessOption D

Average students selected for PhD program = (2160+4550+2850+4455+3402+3900)/6

= 21317/6 = 3553 (approx)

Average number of student applied for PG program

= (8000+17000 +10000 +14000 +16500 +11000)/6

= 76500/6 = 12750

Required percentage = (12750 −3553)/12750 × 100 = 72% less - Which year shows the highest quantum difference between the number of students applied and got selected for PhD programs.
20082006200920072005Option C

Difference for year 2004 = 4000 − 2160 = 1840

For year, 2005 = 13000 −4550 = 8450

For year, 2006 = 6000 − 2850 = 3150

For year, 2007 = 9000 − 4455 = 4545

For year, 2008 = 13500 −3402 = 10098

For year, 2009 = 15000 −3900 = 11100

2009 - What is the respective ratio of the percentage increase/decrease in the students got selected for PG in 2005 over Year 2004 to the percentage increase/decrease in the number of students applied for PhD in year 2008 over year 2007.
47 ∶ 1447 ∶ 1049 ∶ 1241 ∶ 1047 ∶ 13Option B

Percentage increase in selected students in PG in 2005= (6035−1800)/1800 × 100 = 235%

Percentage increase in number of applied students in PhD in 2008 = (13500 −9000)/9000 × 100 = 50%

Required ratio = 235 ∶ 50 = 47 ∶ 10 - Find the ratio of Number of students selected in 2005, 2007 and 2009 for PhD course to number of students applied in 2004, 2006 and 2008 for same course.
2647 ∶ 44002551 ∶ 43002577 ∶ 47002581 ∶ 47002581 ∶ 4100Option D

Number of students selected in 2005, 2007 and 2009 for PhD course

= 13000 × 35/100 +9000 × 49.5/100 + 15000 × 26/100

= 4550 +4455 +3900 = 12905

Number of students applied in 2004, 2006 and 2008 for PhD course

= 4000 + 6000 +13500 = 23500

Ratio = 12905 ∶ 23500 = 2581 ∶ 4700 - In PG program which year shows highest percentage increase/decrease in number of student selected over previous year?
20062009200720052008Option D

Percentage increase/decrease in the number of selected students

For year 2005 = 6035−1800/1800 × 100 = 235%

For year 2006 = 6035−2350/6035 × 100 = 61%

For year 2007 = 6370−2350/2350 × 100 = 171%

For year 2008 = 9570−6370/6370 × 100 = 50%

For year 2009 = 9570−5280/9570 × 100 = 44.8%

2005

**Directions(6-10):** Read the following graph carefully and answer the questions given below: Delhi University offers two courses PG and PhD. The information regarding number of students applied for these two courses and among how many got selected from year 2004-2009 are shown by the graph given below: