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

- I. 4x^2 – 25x + 36 = 0

II. 2x^2 – 19x + 44 = 0I>=IIII>=III>II = II or relation cannot be established.I>IIOption B

I. 4x^2 – 25x + 36 = 0

=> 4x^2 – 16x – 9x + 36 = 0

=> x = 9/4,4

II. 2x^2 – 19x + 44 = 0

=> 2x^2 – 8x – 11x + 44 = 0

=> x = 11/2,4

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

II.8x – 4y = 16I>III = II or relation cannot be established.II>II>=IIII>=IOption B

I = II = 4 - I.x^2 – 27x + 180 = 0

II.y^2 – 20y + 96 = 0I>III = II or relation cannot be established.II>=III>II>=IIOption E

I.x^2 – 27x + 180 = 0

=> x^2 – 15x – 12x + 180 = 0

=> x = 15, 12

II.y^2 – 20y + 96 = 0

=> y^2 – 12y -8y + 96 = 0

=> y = 12, 8

I >= II - I.3x^2 – 17x + 10 = 0

II.y^2 – 11y + 30 = 0I = II or relation cannot be established.II>II>=III>IIII>=IOption E

I.3x^2 – 17x + 10 = 0

=> 3x^2 – 2x – 15x + 10 = 0

=> x = 2/3,5

II.y^2 – 11y + 30 = 0

=> y^2 – 6y – 5y + 30 = 0

=> y = 6,5

II >= I - I.x^2 –x – 6 = 0

II.y^2 + 7y + 12 = 0I>=IIII>=II>IIII>II = II or relation cannot be established.Option C

I.x^2 –x – 6 = 0

=> x^2 – 3x + 2x – 6 = 0

=> x = 3, -2

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

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

=> y = – 3 , – 4

I>II - A hemispherical bowl of internal diameter 54 cm contains a liquid. The liquid is to be filled in cylindrical bottles of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl?
100 bottles162 bottles150 bottles174 bottles181 bottlesOption B

Volume of hemi-sphere = 2/3*pi*(27)^3 cm^3

Volume of cylindrical bottle = pi*(3)^2*9 cm^3

Required No. of bottles = Volume of hemi-sphere/ Volume of cylindrical bottle

= 162 bottles - According to a new plan rolled out by HISP Bank, the rate of simple interest on a sum of money is 8% p.a. for the first two years, 10% p.a. for the next three years and 6% p.a. for the period beyond the first five years. Simple interest accrued on a sum for a period of eight years is Rs. 12,800. Find the sum.
Rs. 30000Rs. 25000Rs. 40000Rs. 50000Rs. 20000Option E

Let the sum be Rs. ‘x’.

[x*8*2]/100 + [x*10*3]/100 + [x*6*3]/100 =12800

=> 64x/100 = 12800

=> x = Rs. 20000 - A and B are partners in a business. They invest in the ratio 5 : 6, at the end of 8 months A withdraws. If they receive profits in the ratio of 5 : 9, find how long B’s investment was used?
181220814Option B

5x : 6x Let B investment was used for y months

8 * 5x : 6x * y = 5 : 9

=> 40x/60xy = 5/9

Y = 12 - Two trains, A and B, start from stations X and Y towards each other, they take 4 hours 48 minutes and 3 hours 20 minutes to reach Y and X respectively after they meet if train A is moving at 45 km/hr., then find the speed of the train B.
60 km/hr.58 km/hr.52 km/hr.54 km/hr.44 km/hr.Option D

S2/S1 = (24/5/10/3)^1/2

=> S2 = 45*6/5 = 54 km/hr. - A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
11001212126012421990Option C

A team of 6 members has to be selected from the 10 players. This can be done in 10C6 or 210 ways.

Now, the captain can be selected from these 6 players in 6 ways.

Therefore, total ways the selection can be made is 210×6 = 1260