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Directions(1-5): **Compare the value of x and y and choose a correct option.

- I. 12x^2 – 40x + 32 = 0

II.8y^2 – 40y + 48 = 0y>xx>=yx > yy>=xCan’t be determinedOption D

I. 12x^2 – 40x + 32 = 0

12x^2 – 24x – 16x + 32 = 0

12x(x – 2) – 16(x – 2) = 0

(12x – 16) (x – 2) = 0

x = 16/12, 2 = 1.33, 2

II.8y^2 – 40y + 48 = 0

8y^2 – 16y – 24y + 48 = 0

8y(y – 2) – 24(y – 2) = 0

(8y – 24) (y – 2) = 0

y = 3, 2

y>=x - I. 5x^2 + 3x -14 = 0

II. 5y^2 + 8y – 21 = 0x > yx>=yy>=xCan’t be determinedy>xOption D

I. 5x^2 + 3x -14 = 0

5x^2 + 10x – 7x -14 = 0

5x(x + 2) – 7(x+ 2) = 0

(5x – 7) (x + 2) = 0

x = 7/5, -2

II. 5y^2 + 8y – 21 = 0

5y^2 + 15y – 7y – 21 = 0

5y(y + 3) – 7(y + 3) = 0

(5y – 7) (y + 3) = 0

y = 7/5, -3

Can’t be determined - I. 2x^2 + 12x + 16 = 0

II. 3y^2 -7y – 6 = 0Can’t be determinedy>=xx > yx>=yy>xOption E

I. 2x^2 + 12x + 16 = 0

2x^2 + 4x + 8x + 16 = 0

2x(x + 2) + 8(x + 2) = 0

(2x + 8)(x + 2) = 0

x = -4, -2

II. 3y^2 -7y – 6 = 0

3y^2 -9y + 2y – 6 = 0

3y(y – 3) + 2(y – 3) = 0

(3y + 2) (y – 3) = 0

y = – 2/3, 3 = -0.667, 3

y > x - I.4x – 5y = 28

II.3x + 4y = -10y>xCan’t be determinedx>=yx > yy>=xOption D

I.4x – 5y = 28

II.3x + 4y = -10

By solving the equation (1) and (2),

x = 2, y = – 4

x > y - I. 3x^2 +14x +15 = 0

II. 3y^2 -13y +14 = 0y>=xx>=yCan’t be determinedy>xx > yOption D

I. 3x^2 +14x +15 = 0

3x^2 +9x + 5x + 15 = 0

3x(x+3) + 5(x+3) = 0

(3x+5) (x+3) = 0

x= -5/3, -3

II. 3y^2 -13y +14 = 0

3y^2 – 6y – 7y +14 = 0

3y(y-2)-7 (y-2) = 0

(3y-7)(y – 2) = 0

yY= 7/3, 2

y>x - The current of a stream runs at the rate of 2 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 55 min. Find the speed of the motor boat in still water?
3025222724Option C

Let the speed of the boat in still water = x km/hr

Speed of the current = 2 km/hr

speed downstream = (x+2) km/hr

speed upstream = (x−2) km/hr

10/(x−2)+10/(x+2) = 11/12

=>11x^2−240x−44 = 0

=>11x^2−242x+2x−44 = 0

=>11x(x−22)+2(x−22) = 0

=>(x−22)(11x+2)=0

x = 22 or −2/11 - Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
5/96/133/105/86/11Option E

Part of the tank filled by pipe A in 1 minute =130

Part of the tank filled by pipe B in 1 minute =120

Part of the tank filled by pipe C in 1 minute =110

Part of the tank filled by pipe C in 3 minutes =3×1/10=3/10

Part of the tank filled by pipe A,B,C together in 1 minute =130+120+110=1160

Part of the tank filled by pipe A,B,C together in 3 minute =3×1160=1120

Required proportion =(3/10)/(11/20) = 6/11 - Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?
27802550242023502140Option C

Speed of sound =1100=1100 ft/s

Time =11/5 second

Dist. =1100×11/5=220×11= 2420 ft - A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B’s share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
79006900750082007170Option C

A : B : C =20000×24:15000×24:20000×18

=20×4:15×4:20×3

=4×4:3×4:4×3=4:3:3

B’s share = 25000×3/10=7500 - There are 5 yellow, 4 green and 3 black balls in a bag. All the 12 balls are drawn one by one and arranged in a row. Find out the number of different arrangements possible.
2257024540268902772022580Option D

Required number of arrangements =12!/5!* 4! *3!

= 27720