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

- I. 6 y^2 + 1/2 = 7/2y

II. 12 x^2 + 2 = 10 xx>=yx=y or relation cannot be established.x>yy>=xy>xOption A

6y^2 + 1/2 = 7/2 y

=> 12y^2 – 7 y + 1 = 0

=>12y62 – 44y – 3y + 1 = 0

=> 4y (3y – 1) – 1 (3y –1) = 0

=> (3y – 1) (4y – 1) = 0

y = 1/3,1/4

12x^2 – 10x + 2 = 0

=> 6x^2 – 5x + 1 = 0

=>3x (2x –1) – 1 (2x –1)

x = 1/3,1/2

x>=y - I. √x + 6 = √121 – √36

II. y^2 + 112 = 473x=y or relation cannot be established.y>=xx>=yy>xx>yOption E

x = 19

y= + 19, -19

x > y - I. 17 x = (13)^2 + √196 + (5)^2 + 4 x

II. 9 y – 345 = 4y – 260x=y or relation cannot be established.x>yy>xy>=xx>=yOption C

17x = 169 + 14 + 25 + 4x

=>17x = 218 + 4x

=>13x = 218

x = 16

9y – 345 = 4y – 260

=>5y = 85

y = 17

y>x - I. (441)^1/2 x^2 – 111 = (15)^2

II. √121 y^2 + (6)^3 = 260x>yy>xx>=yx=y or relation cannot be established.y>=xOption D

441 x^ 2 – 111 = (15)^2

=> 21x^2 – 111 = 225

=>21x^2 = 336

=>X^2 = 16

x = + 4, -4

121 y^2 + (6)^3 = 260

=>11y^2 + 216 = 260

=>11y^2 = 44

=> Y^2 = 4

y = + 2, -2

Cannot established. - I. 17 x + (13)^2 – 114 = (15)^2

II. √121 y^ 2 + (6)^3 = 260y>=xx=y or relation cannot be established.x>yx>=yy>xOption C

17x + (13)^2 – 114 = (15)^2

=> 17x + 169 – 114 = 225

=> 17x = 170

x = 10

121 y ^2 + (6)^3 = 260

=>121 y^2 = 260 – 216

=>11y^2 = 44

y = + 2, -2

x>y - A train travelling at a speed of 75 meter per hour enters a tunnel 3(1/2) miles long. The train is 1/4 miles long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
5 min.8 min.6 min.4 min.3 min.Option E

Total distance covered = 7/2+1/4 miles

=154 miles

Time taken = (15/4*75) hrs. =120 hrs

=(120*60)min. = 3 min. - The simple interest on a sum of money will be Rs.900 after 8 years. If the principal is tripled for the last 4 years, what will be the total interest at the end of the 8th year?
12101350180020001500Option C

Let sum be x

n=8 yrs

SI=900

R=(100×𝑆𝐼)/( 𝑃×𝑛)

=> R=(100×900)/( 𝑥×8) = 11250/𝑥

For 1st 4 yrs SI= (𝑥 × 11250/𝑥 × 4 × 1/100)

= 450

For last 4 yrs.

SI= (3𝑥 × 11250/𝑥 × 4 × 1/100) = 1350

Total interest = 1350 + 450

=1800 - There are three different mixtures (glucose and alcohol) in which the concentration of glucose is 1/2 , 3/5 and 4/5 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. Find the ratio of glucose and alcohol in the new mixture?
3:29:87:52:15:4Option A

Concentration of glucose are in ratio

= 1/2 : 3/5 : 4/5

Quantity of glucose taken from A = 1 litre out of 2 litre.

Quantity of glucose taken from B = 3/5 ×3 = 1.8 lt.

Quantity of glucose taken from C = 0.8 lt.

So, total glucose taken out from A, B & C, = 3.6 lt.

So, quantity of alcohol = (2 + 3 + 1) – 3.6 = 2.4 litre.

Ratio of glucose to alcohol

= 3.6/2.4 = 3:2 - Mr.Pankaj sells kaju katri at Rs. 15 per kg. A kaju katri is madeup of flour and sugar in the ratio of 5 : 3. The ratio of price of sugar and flour is 7 : 3 (per kg). Thus he earns 66(𝟐/𝟑) % profit. What is the cost price of sugar?
1510201418Option D

C.P. = (15×100×3)/500 = Rs. 9

Now, flour : sugar = 5 : 3

In 1 kg = flour = 625 gm.

Sugar = 375 gm.

Let price of sugar = 7x,

Flour = 3x

According to question, 625/1000 ×3x + 375/1000 ×7x = 9

x = 2

So, C.P. of sugar = 7 × 2

= 14 Rs./kg. - A box contains 3 ballons of 1 shape, 4 ballons of 1 shape and 5 ballons of 1 shape. Three ballons of them are drawn at random, what is the probability that all the three are of different shape?
3/117/95/124/133/11Option A

Total = 3+4+5 = 12

N(S) = 12c3 = 220

N(E) = 3c1 * 4c1 * 5c1 = 60

Required Probability = 60/220 = 3/11