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

- I. x^2 – 6x + 135 = 0

II. y^2 – 30y + 225 = 0x=y or relation cannot be established.x>=yx>yy>=xy>xOption D

I.X^2 – 6x + 135 = 0

=> x^2 – 15x + 9x + 135 = 0

=> x = +15, –9

II.Y^2 – 30y + 225 = 0

=>y^2 – 15y – 15y + 225 = 0

=> y = +15, +15

x≤y - I. 25/√x – 4√x = √x

II. 2y + (𝑦^2+50)/𝑦 = 5x=y or relation cannot be established.y>=xy>xx>yx>=yOption E

I.25/ √𝑥 – 4√𝑥 = √𝑥 =>25 – 4x = x

=> 25 = 5x

=>X = 5

II.2y+ (y^2+50)/𝑦 = 5y

=>2y^2 + y2+50 = 5y^2

=> 2y^2 = 50

=>y = √25

=>y = ±5

x≥y - I. 8/√𝑥 + 6/√𝑥 = √𝑥

II. y^3 – (14)^7/2/√𝑦 = 0x>yy>xx>=yx=y or relation cannot be established.y>=xOption D

I. 8/√𝑥 + 6/√𝑥 = √𝑥

=>X = 14

II. Y^3 – (14)^7/2/√𝑦 = 0

=>𝑦^7/2–(14)^7/2 = 0

=> 𝑦^7/2 = (14)^7/2

=>y = 14

x = y - I. x^2 – 3481 = 0

II.y^2 –118y +3481 = 0x>=yx>yy>xy>=xx=y or relation cannot be established.Option D

I. x^2 – 3481= 0

=>x^2 = 3481

=>x = ±59

II. y^2 – 118y + 3481 = 0

=> y^2 –59y–59y +3481=0

=>y = +59, +59

x≤y - I. x^3 – 9×2 + 20x = 0

II. y^3 –14y2 + 48y = 0x=y or relation cannot be established.y>=xx>yx>=yy>xOption A

I. x^3 – 9×2 + 20x = 0

=>x(x^2 – 9x + 20) = 0

=>x^2 – 9x + 20 = 0

=>x^ 2 – 4x–5x + 20 = 0

x = 4, 5 and 0

II. y^3 –14y2 + 48y = 0

=>y(y^2 –14y + 48) = 0

=>y^2 –14y + 48 = 0

=>y^2 –6y –8y+ 48 = 0

y = 6, 8 and 0

No relation. - 10 years ago the age of Krishna was 𝟏/𝟑 𝐫𝐝 of the age of Banshi. 14 years hence the ratio of ages of Krishna and Banshi will be 5 : 9. Find the ratio of their present ages.
12 : 2913 : 2814 : 2713 : 2911 : 21Option D

Let 10 years ago Krishna’s age = x years.

Let 10 years ago Banshi’s age = 3x years

Therefore, [x+10+14]/[3x+10+14] = 5/9 x= 16 years

So, their present age = 16 + 10 = 26 years & 16 × 3 + 10 = 58 years.

Ratio = 13 : 29 - The concentration of glucose in three different mixtures (glucose and alcohol) 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. What is the ratio of glucose and alcohol in the new mixture?
4:53:27:53:29:7Option B

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 - A dealer buys dry fruits at Rs. 100, Rs 80 and Rs. 60 per kilogram. He mixes them in the ratio 4 : 5 : 6 by weight, and sells at a profit of 50%. At what price per kilogram does he sell the dry fruit?
111128112121116Option E

Let he bought 4x kg, 5x kg and 6x kg of dry fruits.

Total cost price for dealer = (4x×100) + (5x×80) + (6x×60)

= 400x + 400x + 360x

= 1160 x

Total selling price for dealer = 1740x

Required price per kg = 1740x 15x = 116 - If Rs.8010 is divided in to three parts such that their amounts after 2 3 and 4 years respectively are equal, the simple interest being at the rate of 2% per annum. Find the difference between the greatest and smallest parts of the sum.
105101889590Option B

Let the amount divided into three parts x y z

According to the question, 𝑥 + [𝑥 × 2 × 2]/100 = 𝑦 + [𝑦 × 3 × 2]/100 = 𝑧 + [𝑧 × 4 × 2]/100 𝑥 + 4𝑥/100

= 𝑦 + 6𝑦/100 = 𝑧 + 8𝑧/100

= x:y:z = 52:53:54

x+y+z = 8010

Required difference = 2 part

= 8010 × 2/159 = 50.37×2 = 100.74 ==101 - How many different four letter words can be formed (the words need not be meaningful using the letters of the word “MEDITERRANEAN” such that the first letter is E and the last letter is R?
4560485950Option D

Case 1: When the two letters are different.

One has to choose two different letters from the 8 available different choices.

This can be done in 8 * 7 = 56 ways.

Case 2: When the two letters are same.

There are 3 options – the three can be either Ns or Es or As.

Therefore, 3 ways.

Total number of possibilities = 56 + 3 = 59