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

- I.x^2 – 32x + 252 = 0

II.y^2 – 26y + 168 = 0

y >= xx > yy > xx >= yNo relationOption D

I.x^2 – 32x + 252 = 0

=>x^2 – 18x -14x + 252 = 0

=>(x-14)(x-18) = 0

=>x = 14,18

II.y^2 – 26y + 168 = 0

=>y^2 -12y -14y +168 = 0

=>(y-12)(y-14) = 0

=>y = 12,14

x >= y - I.x^2 + 42x + 441 = 0

II.y^2 + 34y + 289 = 0

x > yx >= yy >= xy > xNo relationOption D

I.x^2 + 42x + 441 = 0

=>x^2 + 21x + 21x+ 441 = 0

=>(x+21)(x+21) = 0

=>x = -21,-21

II.y^2 + 34y + 289 = 0

=>y^2 + 17y + 17y + 289 = 0

=>(y+17)(y+17) = 0

=>y = -17,-17

y > x - I.x^2 + 26x + 165 = 0

II.y^2 + 30y + 209 = 0

x > yy > xx >= yy >= xNo relationOption E

I.x^2 + 26x + 165 = 0

=>x^2 + 15x +11x + 165 = 0

=>(x+15)(x+11) = 0

=>x = -15,-11

II.y^2 + 30y + 209 = 0

=>y^2 + 19y +11y + 209 = 0

=>(y+19)(y+11) = 0

=>y = -19,-11

No relation - I.3x^2 + 19x -14 = 0

II.3y^2 – 31y + 36 = 0

y >= xy > xx > yx >= yNo relationOption B

I.3x^2 + 19x -14 = 0

=>3x^2 -2x + 21x – 14 = 0

=>(x+7)(3x -2) = 0

=>x = -7,2/3

II.3y^2 – 31y + 36 = 0

=>3y^2 -4Y -27Y +36 = 0

=>(y-9)(3y -4 ) = 0

=>y = 9,4/3

y > x - I.x^2 + 4x – 221 = 0

II.y^2 – 4y – 221= 0

x >= yy > xx > yNo relationy >= xOption D

I.x^2 + 4x – 221 = 0

=>x^2 – 13x + 17x – 221 = 0

=>(x+17)(x-13) = 0

=>x = -17,13

II.y^2 – 4y – 221= 0

=>y^2 – 17 y + 13y – 221 = 0

=>(y-17)(y-13) = 0

=>y = -13,17

No relation - Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
48653Option C

[x(x+6)]/[x+x+6]=4

=>x^2+6x=8x+24

=>x^2−2x−24=0

=>(x−6)(x+4)=0

=>x= 6 - A train, having a length of 110 metre is running at a speed of 60 kmph. In what time, it will pass a man who is running at 66 kmph in the direction opposite to that of the train.
84765Option D

Distance =110 metre

Since train and man move in opposite directions, relative speed

=(60+6)=66 km/hr

=66×5/18 m/s=110/6 m/s

Time =110/(110/6) = 6 seconds - A train 108 metre long is moving at a speed of 50 km/hr. It crosses a train 112 metre long coming from opposite direction in 6 seconds. What is the speed of the second train?
89 km/hr.78 km/hr.66 km/hr.70 km/hr.82 km/hr.Option E

Distance covered =(108+112)=220 metre

Time =6 seconds

Relative speed =220/6=110/3 m/s

=110/3×18/5=132 km/hr.

50 + Speed of second train =132 km/hr.

Speed of second train =(132−50)= 82 km/hr. - On my brother’s 15th birthday, his height was 159 cm, having grown 6% since the year before. How tall was he in the previous year?
140 cm150 cm120 cm130 cm160 cmOption B

Height in the previous year

=(159×100)/106 =150 cm - In how many ways can 7 different balls be distributed in 5 different boxes if box 3 and box 5 can contain only one and two number of balls respectively and rest of the boxes can contain any number of balls?
85208448818080008505Option E

Required number of ways

= 7C1 × 6C2 ×3^4

=7×15×81= 8505

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