**Directions(1-5):** Compare the values of x and y then choose a required option.

- 3x – 4(x)^1/2 = 4

5y = 2(5y)^1/2 + 8y>xx=<yx>yx>=yx=y or no relationOption E

3x – 4(x)^1/2 = 4

Squaring on both the side,

9x^2 – 24x + 16 = 16x

=>9x^2 – 40x + 16 = 0

=> 9x^2 – 36x – 4x + 16 = 0

=> x = 4,4/9 5y = 2(5y)^1/2 + 8

Squaring on both the side,

25y^2 – 80y + 64 = 20y

=> 25y^2 -100y + 64 = 0

=> 25y^2 – 20y – 80y + 64 = 0

=> y = 4/5,16/5

No relation - y² – x² = 32

y – x = 4x>=yx>yx=<yy>xx=y or no relationOption D

y² – x² = 32

=>y – x = 4

=>(y + x) (y – x) = 32

=>(y + x) 4 = 32

=>y + x = 8

y – x = 4

y = 16 and x = 12

x < y - 35x^2 – 13x – 12 = 0

56y^2 = 53y – 12x=<yx>=yy>xx>yx=y or no relationOption E

35x^2 – 13x – 12 = 0

=> 35x^2 + 15x – 28x – 12 = 0

=> 5x(7x+3)-4(7x+3) = 0

=> x = (-3/7),4/5

56y^2 = 53y – 12

=> 56y^2 – 53y + 12 = 0

=> 56y^2 – 21y – 32y + 12 = 0

=> 7y(8y-3) -4(8y-3) = 0

=> y = 4/7,3/8

No relation - x² – 31x + 130 = 0

y² – 53y + 702 = 0x>=yx=y or no relationx=<yy>xx>yOption C

x² – 31x + 130 = 0

=>x² – 31x + 130 = 0

x = 26, 5

y² – 53y + 702 = 0

=>y² – 53y + 702 = 0

=>y = 26, 27

x ≤ y - x^2 + 4x = 12

y^2 – 7y + 10 = 0x=y or no relationx>yy>xx=<yx>=yOption D

x^2 + 4x = 12

=> x^2 + 4x – 12 = 0

=> x^2 + 6x – 2x – 12 = 0

=> x(x+6) – 2(x+6) = 0

=> (x+6)(x-2) = 0

=> x = -6,2

y^2 – 7y + 10 = 0

=>y^2 – 5y -2y + 10 = 0

=> y(y-5)-2(y-5) = 0

=> (y-2)(y-5) = 0

=> y = 2,5

x=<y - What is the average production of maize in all the years together?
61.5 quintals52.3 quintals60.8 quintals64.4 quintals55.7 quintalsOption D

Average production of maize in all the years = (50+63+80+54+75)/5

= 322/5 = 64.4 quintals - What is the percentage rise in the production of rice and wheat together in 2014 as compared to 2012?
17%18%20%10%15%Option D

Total production of rice and wheat in 2012 = 75+45 = 120 quintals

Total production of rice and wheat in 2014 = 62+70 = 132 quintals

% rise in production = (132-120)/120*100 = 10% - 60% of the wheat produced in 2014 is exported to Japan and 65% of the wheat produced in 2015 is exported to Japan. Find the difference in the quantity of wheat exported to Japan in 2014 and in 2015?
6 quintals5 quintals8 quintals4 quintals3 quintalsOption E

Quantity of wheat exported to Japan in 2014 = 0.6*70

= 42 quintals

Quantity of wheat exported to Japan in 2015 = 0.65*60 = 39 quintals

Required difference = 42 – 39 = 3 quintals - What is the average production of all the three grains in 2014?
57 quintals55 quintals48 quintals62 quintals60 quintalsOption D

Total production of all the three grains in 2014 = 62+70+54

= 186 quintals

Average production in 2014 = 186/3 = 62 quintals - Production of rice in 2016is increased by 25% as compared to previous year and production of rice is increased by 20% in 2017 as compared to previous year. Find the quantity of rice produced in 2017.
120 quintals90 quintals115 quintals102 quintals98 quintalsOption D

Production of rice in 2016 = 1.25*68 = 85 quintals

Production of rice in 2017 = 1.2*85 = 102 quintals

**Directions(6-10): **Answers the questions based on the information given below.

The column graph below shows the production (in quintals) of wheat, rice and maize in five different years.

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