**Directions(1-5):** Compare both the equations and choose a correct option.

- I.12x^2 – 13x + 3 = 0

II.2y^2 + 7y – 4 = 0y >= xx > yNo relationy > xx >= yOption C

I.12x^2 – 13x + 3 = 0

=>12x^2 – 9x – 4x + 3 = 0

=>(4x-3)(3x – 1) = 0

=>x = 1/3,3/4

II.2y^2 + 7y – 4 = 0

=>2y^2 + 8y – y – 4 = 0

=>(2y-1)(y+4) = 0

=>y = -4,1/2

No relation. - I.4x + 7y = 209

II.12x – 14y = – 38x >= yx > yy > xy >= xNo relationOption E

On solving both the equations, we get

x=y = 19

No relation. - I.9x^2 – 45x + 56 =0

II. 4y^2 – 17y + 18 = 0y >= xNo relationx >= yy > xx > yOption E

I.9x^2 – 45x + 56 =0

=>9x^2 – 24x – 21x + 56 = 0

=>(3x – 8)(3x- 7) = 0

=>x = 8/3,7/3

II. 4y^2 – 17y + 18 = 0

=>4y^2 – 8y – 9y + 18 = 0

=>(y-2)(4y-9) = 0

=>y = 2,9/4

x>y - I.9x^2 -36x + 35 = 0

II.2y^2 – 15y – 17 = 0No relationx >= yx > yy > xy >= xOption A

I.9x^2 -36x + 35 = 0

=>9x^2 – 21x – 15x + 35 = 0

=>(3x- 7)(3x – 5)= 0

=>x = 5/3,7/3

II.2y^2 – 15y – 17 = 0

=>2y^2 – 17y + 2y – 17 =0

=>(y+1)(2y – 17)= 0

=>y = -1,17/2

No relation. - I.x^2 – 11x + 24 = 0

II.6y^2 – 101y + 425 =0y > xy >= xx > yNo relationx >= yOption A

I.x^2 – 11x + 24 = 0

=>x^2 – 3x – 8x + 24 = 0

=>(x-3)(x-8) = 0

=>x = 3,8

II.6y^2 – 101y + 425 =0

=>6y^2 – 50y – 51y + 425 = 0

=>(2y – 17)(3y – 25) = 0

=>y = 17/2,25/3

y > x - A fresh fruit contains 80% of water, when it is placed in sunlight after sometime it contains only 25% of water and now its weight is 44 kg. Find the weight o fresh fruit?
152 kg170 kg165 kg136 kg142 kgOption C

Water : pulp

Fresh

=> 4:1

Fry

=>1:3

Multiply ratio of fresh fruit by 3 and 4 unit of dry fruit is 44 kg.

1 unit -> 11 kg

Fresh fruit = 11*15 = 165 kg - A solution containing 45 ml of acid and 60 ml of water is completely mixed with another solution E, which contains 7/11 of acid. If the proportion of acid and water in the final mixture is equal, find the quantity of solution E.
68 ml70 ml55 ml40 ml62 mlOption C

Let the quantity of solution E be x ml.

Amount of acid in final mixture = (45 + 7x/11) ml

Amount of water in final mixture = (60+4x/11) ml

Now, (45 + 7x/11) = (60+4x/11)

=>x = 55 ml - A boat can cover 36 km in still water and the same distance downstream, in 4 hours and 3 hours resp. Find the time taken by the boat to cover 21 km upstream and 48km downstream.
3 hours 10 minutes4 hours 20 minutes7 hours 30 minutes6 hours 15 minutes5 hours 40 minutesOption C

Speed of boat in still water = 36/4 = 9 km/hr.

Downstream speed = 36/3 = 12 km/hr.

Speed of the stream = 24 – 18 = 3 km/hr.

Upstream speed of the boat = 9-3 = 6 km/hr.

Time taken = 21/6 + 48/12 = 7 hours 30 minutes - A,B and C together started a business with initial investments of Rs.4500, Rs.6000 and Rs. 7500 resp. In this business, A is the main working partner for which he gets 16% of the profit to supervise the business, and rest of the profit is shared among them in the ratio of their investments. Find the profit share of A out of the total profit of Rs.5400.
Rs.1662Rs.1998Rs.1850Rs.1998Rs.1880Option D

Respective ratio = 4500:6000:7500 = 3:4:5

Profit of A for being a working partner = 0.16*5400 = Rs.864

Profit of A for his investment = (5400- 864)*3/12 = Rs.1134

Total profit share of A = 864+ 1134 = Rs.1998 - A baseball team of 9 players is to be selected from a group of 7 male players and 6 female players. In how many ways a team having at most four female players is selected?
477 ways550 ways320 ways400 ways470 waysOption E

Total number of ways = 6C4*7C5 + 6C3*7C6 + 6C2*7C7

= 315+140+15 = 470 ways