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

- 18x^2 – 39x + 20 = 0

9y^2 – 51y + 52 = 0x>=yx>yy>=xy>xx=y or relation cannot be established.Option C

18x^2 – 39x + 20 = 0

=>18x^2 – 15x – 24x + 20 = 0

=> (6x-5)(3x-4) = 0

=> x = 5/6 or 4/3

9y^2 – 51y + 52 = 0

=> 9y^2 – 12y – 39y + 52 = 0

=> (3y-4)(3y-13) = 0

=> y = 4/3 or 13/3

y>=x - 9x + 4y = 79

7x – 5y = 29x=y or relation cannot be established.y>xy>=xx>yx>=yOption D

On equating both the equations.

X = 7

y = 4

x>y - X^2 – 35x + 306 = 0

3y^2 – 23y + 44 = 0x>=yx>yy>=xy>xx=y or relation cannot be established.Option B

X^2 – 18x – 17x + 306 = 0

=> (x – 17)(x – 18) = 0

=> x = 17 or 18

3y^2 – 12y – 11y + 44 = 0

=> (y-4)(3y-11) = 0

=> y = 4 or 11/3

x>y - 3x^2 – 37x + 110 = 0

6y^2 – 40y + 132 = 0x=y or relation cannot be established.y>=xy>xx>=yx>yOption A

3x^2 – 37x + 110 = 0

=> 3x^2 – 15x – 22x + 110 = 0

=> (3x – 22)(x – 5) = 0

=> x = 5 or 22/3

6y^2 – 40y + 132 = 0

=> 3y^2 – 18y – 22y + 132 = 0

=> (3y – 22)(y – 6) = 0

=> y = 22/3 or 6

X=y or no relation can be established. - 12x^2 + 13x – 35 = 0

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

12x^2 + 13x – 35 = 0

=> 12x^2 + 28x – 15x – 35 = 0 => (3x+7)(4x-5) = 0 => x = -7/3 or 5/4

10y^2 = 21y -9

=> 10y^2 – 21y + 9 = 0

=> 10y^2 – 15y – 6y + 9 = 0

=> (2y – 3)(5y – 3) = 0

=> y = 3/2 or 3/5

X=y or relation cannot be established. - 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. Find the area of the plot.
2500 m^22420 m^22020 m^22000 m^22520 m^2Option B

Perimeter of the rectangular plot = 2*(5x+4x)

= 198

=> x = 11m

Length = 55 m

Breadth = 44 m

Area = 55*44 = 2420 m^2 - A vessel contains mixture of petrol and kerosene in the ratio 5:3 resp. If 16 litres of the mixture is taken out and replaced by 3 litres of kerosene the ratio of petrol to kerosene becomes 3:2 resp. Find the initial quantity of mixture in the vessel.
62 litres80 litres75 litres88 litres90 litresOption D

[5x – 10]/[3x – 6+ 3] =3/2

=> x = 11

Initial quantity of the mixture = 55+33

= 88 litres - Raj scored 37% marks in an examination but failed by 24 marks. Kiran scored 45% marks in the same examination and got 40 marks above the passing marks. Find the passing marks in the examination.
280295320333300Option C

Let maximum marks be x.

Passing marks = 37% of x + 24

Also. Passing marks = 45% of x – 40

37% of x + 24 = 45% of x – 40

=> x = 800

Passing marks = 37% of 800 + 24 = 320 - A train moving with a speed of 54 kmhr. Crosses a pole in 16 seconds. Find the time taken by it to cross a platform 120 m long moving at the same speed.
18 sec.24 sec.30 sec.22 sec.20 sec.Option B

Speed of train in m/s = 54*5/18 =15 m/s

Length = 15*16 = 240 m

Time = 240+120/2 = 24 sec. - A box contains 20 bulbs out of which 5 are defective. 3 bulbs are randomly taken out of the box. What is the probability that out of the three at least one bulb is defective?
137/232133/228131/225137/228137/221Option D

Probability that atleast one bulb is defective

= 1 – 15C3/20C3 = 137/228