**Directions(1-5):** Compare I and II by solvind them individually and choose a correct options.

- I.x^2 – 27x + 180 = 0

II.y^2 – 20y + 96 = 0x > yx =< yx= y or relation cannot be established.x >= yx < yOption D

I.x^2 – 27x + 180 = 0

=> x^2 – 15x – 12x + 180 = 0

=> (x-15)(x-12) = 0

=>x = 15,12

II.y^2 – 20y + 96 = 0

=> y^2 – 12y – 8y + 96 = 0

=> (y-12)(y-8) = 0

=>y = 12,8

x >= y - I.3x+5y = 32

II.8x – 4y = 16x >= yx =< yx= y or relation cannot be established.x < yx > yOption C

On solving I and II, we get

x = y = 4 - I.x^2 –x – 6 = 0 II. y^2 + 7y + 12 = 0
x < yx >= yx > yx =< yx= y or relation cannot be established.Option C

I.x^2 –x – 6 = 0

=> x^2 – 3x + 2x – 6 = 0

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

=> x = 3,-2

II. y^2 + 7y + 12 = 0

=> y^2 + 3y + 4y + 12 = 0

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

=> y = -3,-4

x > y - I.4x^2 + 7x – 2 = 0

II. 3y^2 – 4y + 1 = 0x= y or relation cannot be established.x > yx < yx >= yx =< yOption C

I.4x^2 + 7x – 2 = 0

=> 4x^2 – x + 8x – 2 = 0

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

=> x = ¼,-2

II. 3y^2 – 4y + 1 = 0

=> 3y^2 – 3y –y + 1 = 0

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

=> y = 1/3,1

x < y - I.3x^2 -17x + 10 = 0

II. y^2 – 11y + 30 = 0x > yx >= yx < yx= y or relation cannot be established.x =< yOption E

I. 3x^2 -17x + 10 = 0

=> 3x^2 – 2x – 15x + 10 = 0

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

=> x = 2/3,5

II. y^2 – 11y + 30 = 0

=> y^2 – 6y – 5y + 30 = 0

=> (y-6)(y-5) = 0

=> y = 6,5

x =< y - A and B individually can complete the work in 30 days and 50 days resp. Both of them started the work together and worked for x days and then A left the work. If the remaining work is completed by B alone and the entire work is completed in 30 days. Find the value of x.
89111012Option E

Total work LCM(30 and 50) = 150 units

Number of units work done by A and B alone = 150/30 = 5 units and 150/50 = 3 units resp. (5+3)*x + 3*(30-x) = 150

=> x = 12 - A,B and C together started a business with initial investments in the ratio of 5:4:9 resp. After one year, A,B and C made additional investments in the ratio of 8:11:19 resp. Find the profit share of C out of the total profit of Rs. 3846 after two years.
Rs.2000Rs.1850Rs.1888Rs.1923Rs.1900Option D

Let initial investments made by A,B and C be 5x, 4x and 9x respectively Additional investments be 8y,11y and 19y.

Ratio of investments of A:B:C = (5x+5x+8y):(4x+4x+11y):(9x+9x+19y)

= (10x+8y): (8x+11y): (18x+19y)

Profit share by C = (18x+19y)/(36x+38y)*3846 = Rs.1923 - A mixture of milk and water contains 40% of water. If 11 litres of water is added to the mixture the quantity of milk and water becomes same. Find the initial quantity of the mixture.
6062555250Option C

Let the initial quantity of the mixture be x litres.

Quantity of water in the initial mixture = 0.4x litres

Quantity of the milk in the initial mixture = 0.6x litres

Now, 0.6x = 0.4x + 11

=> x = 55 - A bag contains balls of three different colours i.e. red, blue and green. The ratio of the number of red balls to blue balls is 9:8 and the ratio of the number of blue balls to green balls is 4:3. If the difference between the number of red balls and green balls in the bag is 6, then find the total number of balls in the bag.
4046383544Option B

Let the number of red, blue and green balls in the bag be 9x:8x:6x resp. Total number of balls in the bag = 9x+8x+6x = 23x

Now, 9x – 6x = 6

=> x = 2

Total number of balls in the bag = 23*2 = 46 - A man picks two cards from a pack of 52 well shuffled cards without replacement. Find the probability that both the cards are even numbered of spades.
3/6605/6637/6661/6635/671Option B

Required Probability = 5/52*4/51 = 5/663

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