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

- X^2 – 14x + 40 = 0

y^2 – 25y + 144 = 0y>=xx>yx>=yy>xx=y or relation cannot be established.Option E

X^2 – 4x – 10x + 40 = 0

=>x(x-4)- 10(x-4) = 0

=> x = 4,10

Y^2-25y+144 = 0

=>y^2 – 16y – 9y + 144 = 0 => y(y-16)-9(y-16)= 0

=> y = 16,9

x=y or relation cannot be established. - 12x^2 + 13x – 35 = 0

10y^2= 21y-9x>yx>=yy>=xx=y or relation cannot be established.y>xOption D

12x^2 + 13x – 35 = 0

=>12x^2 + 28x -15x – 35 = 0

=>4x(3x+7)-5(3x+7)=0

=>x = -7/3,5/4

10y^2= 21y-9

=> 10y^2 -15y -6y+ 9 = 0

=> 5y(2y-3)-3(2y-3)=0

=>y =3/2,3/5

x=y or relation cannot be established. - X= (1089)^1/2 – (14^2 – 190)

y = 13^3 – (45^2+146)y>=xx>yx=y or relation cannot be established.y>xx>=yOption B

X= (1089)^1/2 – (14^2 – 190)

=> x = 33 – (196-190)

=> x = 27

y = 13^3 – (45^2+146)

=>y =2917-(2025+146)

=>y = 26

x>y - 3x+y = 20

4x+3y = 30y>xx=y or relation cannot be established.y>=xx>yx>=yOption D

X = 6

y = 2

x>y - X^2 -36x + 323 = 0

y^2-29y+210 = 0x>=yx=y or relation cannot be established.y>xx>yy>=xOption D

X^2 -36x + 323 = 0

=> x^2 – 17x – 19x + 323 = 0

=> x(x-17)-19(x-17) = 0

=> x = 17,19

y^2-29y+210 = 0

=>y^2 – 15y – 14y + 210 = 0

=> y(y-15)-14(y-15) = 0

=> y = 15,14

x>y - The length and the breadth of a rectangular plot are in the ratio 5:4. If the cost incurred for fencing the boundary of the plot at Rs. 15 per metre is Rs. 2970, the find the area of the plot.
2550 m^22250 m^22000 m^22420 m^22500 m^2Option D

Perimeter = 2970/15 = 198 m

Now, 2(5x+4x) = 198

=> x = 11 metres

Length = 55 m

Breadth = 44 m

Required area = 2420 m^2 - A boy cycles from his home to his school with a speed of 12 km/hr. and reaches his school in 45 minutes. If he returns home at a speed of 3 km/hr. more than the speed of going to his school. Find his average speed for the whole journey.
11.11 km12.25 km13.33 km10.11 km9.52 kmOption C

Distance between his home and his school = 45/60*12

= 9 km

Speed of boy while returning = 12+3 = 15km/hr.

Time taken to cover the distance between home and school = 9/15 = 0.6 hour

Required average speed = (9+9)/(0.6+0.75) = 13.33 km - A man sold an article at 15% discount and earned 36% profit. The discount given on the article was Rs. 576. What should be the selling price if the shopkeeper wanted to earn 42% profit.
Rs. 3500Rs. 4150Rs. 3408Rs. 3333Rs. 3000Option C

Let MP be x. 15% of x = 576 x = (576*100)/15

=> x = Rs. 3840

SP = 3840-576 = RS.3264

CP = (3264*100)/136 = Rs.2400

Required SP = 142% of 2400 = Rs. 3408 - Pipe A fills (1/4)th of the tank in 5 minutes and another pipe B fills (1/5)th of the tank in 6 minutes. Find the time taken to fill half of the tank if both the pipes work together.
6 minutes7 minutes9 minutes5 minutes4 minutesOption A

Time taken by pipe A = 5*4 = 20 minutes

Time taken by pipe B = 6*5 = 30 minutes

Let the total capacity of the tank LCM (20 and 30) = 60 units

Number of units of water filled by A alone in one minute = 3 units

Number of units of water filled by B alone in one minute = 2 units

Number of units of water filled by both pipes in one minute = 5 units

Required time taken by both pipes to fill the tank = 60/(2*5) = 6 minutes - A bag contains 5 red balls, 3 black balls and 5 white balls. A man draws 3 balls at random from the bag. Find the probability that out of 3 balls at least 2 balls are white.
40/14345/14333/14345/11141/134Option B

Required Probability = [ (5C2*3C1)+(5C2*5C1)+5C3]/13C3

= 45/143

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