**Directions(1-5):** What will come in place of question mark “?” in the following questions.

- I. 16x^2 + 20x + 6 = 0

II. 10y^2 + 38y + 24 = 0y>xy>=xx>=yx>yx=y or relation cannot be established.Option D

Divide both equations by 2 I. 16x^2 + 20x + 6 = 0

=> 8x^2 + 10x + 3 = 0

=> 8x^2 + 4x + 6x + 3 = 0

x = -1/2, -3/4

II. 10y^2 + 38y + 24 = 0

=> 5y^2 + 19y + 12 = 0

=> 5y^2 + 15y + 4y + 12 = 0

y = -4, -4/5

x > y - I. 2x^2 – (2 + 2√5)x + 2√5 = 0

II. 4y^2 – (6 + 2√2)y + 3√2 = 0x>yx>=yy>xy>=xx=y or relation cannot be established.Option E

I. 2x^2 – (2 + 2√5)x + 2√5 = 0

=> 2x^2 – 2x – 2√5x + 2√5 = 0

=> 2x (x – 1) – 2√5 (x – 1) = 0

So, x = 1, √5 (2.2)

II. 4y^2 – (6 + 2√2)y + 3√2 = 0

=> 4y^2 – 6y – 2√2y + 3√2 = 0

=> 2y (2y – 3) – √2 (2y – 3) = 0

So, y = 3/2, 1/√2 (0.7)

x = y or relation cannot be established. - I. 6x^2 + x – 2 = 0

II. 3y^2 – 22y + 40 = 0y>xx>=yy>=xx=y or relation cannot be established.x>yOption A

I. 6x^2 + x – 2 = 0

=> 6x^2 + x – 2 = 0

=> 6x^2 + 4x – 3x – 2 = 0

x = 1/2, -2/3

II. 3y^2 – 22y + 40 = 0

=> 3y^2 – 22y + 40 = 0

=> 3y^2 – 12y – 10y + 40 = 0

y = 10/3, 4

x < y - I. x^² – (1+√2)x + √2 = 0

II. y^² – 3y + 2 = 0x=y or relation cannot be established.x>yy>=xx>=yy>xOption A

I. x^² – x −√2x + √2 = 0

=>x(x – 1) – √2(x − 1) = 0

=> (x − √2)(x − 1) = 0

=>x = √2 or 1

II. y^² – 3y +2 = 0

=> y^² – 2y – y+ 2 = 0

=>y (y – 2) – 1 (y – 2) = 0

=> (y – 1) (y – 2) = 0

=> y= 1 or 2

Relation cannot be established between x and y. - I. x^ 2 − 19x + 84 = 0

II. y^ 2 − 25y + 156 = 0y>xy>=xx>yx=y or relation cannot be established.x>=yOption B

I. x ^2 − 19x + 84 = 0

=> x ^2 − 7x − 12x + 84 = 0

=> (x − 7)(x − 12) = 0

x = 7, 12

II. y^ 2 − 25y + 156 = 0

y ^2 − 13y − 12y + 156 = 0

=> (y − 13)(y − 12) = 0

=> y = 13, 12

y>=x - Abhishek took a loan at simple interest rate of 6% in the year with an increase of 0.5% in each subsequent year. He paid interest of Rs. 6125 after 5 year. How much loan did he take?
Rs. 19900Rs. 17500Rs. 18200Rs. 15500Rs. 11400Option B

Total interest = Rs. 6125

Rate = 6% and increasing by 0.5% every year

Let total Loan Amount = P

P = [6125 × 100]/[ 6 × 1 + 6.5 × 1 + 7 × 1 + 7.5 × 1 + 8 × 1] = 612500/35 = Rs. 17500 - A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?
190 km.170 km.180 km.150 km.200 km.Option C

Speed in downstream = (14 + 4) km/hr = 18 km/hr

Speed in upstream = (14 – 4) km/hr = 10 km/hr.

Let the distance between A and B be x km.

Then, x/18 + (x/2)/10 = 19

=> x/18 + x/20 = 19

=> x = 180 km. - Every year before the festive season,a shopkeeper increases the price of the product by 35% and then introduce two successive discount of 10% and 15% respectively.what is percentage loss and percentage gain ?
3.27%2.12%5.05%4.15%2.21%Option A

Let CP = 100

35 % Increase in SP = 135

10 % Discount = 135((135*10)/100)=13.5

So, 1st SP =(135-13.5) = 121.5

Again,

15 % Discount in 1st SP = ((121.5*15)/100) = 18.225

2nd SP = (121.5-18.225) = 103.275

So,finally CP = 100

SP = 103.275

Gain = 103.275 – 100 = 3.27% - Neha’s father was 38 years of age when she was born while her Mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
7 years5 years10 years6 years8 yearsOption D

Let Neha’s age = x and her brother’s age = x−4

Neha’s father’s age = x+38

Neha’s mother’s age =(x−4)+36 = x+32

Neha’s father’s age – Neha’s mother’s age = (x+38) − (x+32) = 6 years - Out of the 35 players attending the opening ceremony of an event there are 12 cricketers, 10 wrestlers, 5 badminton players and 8 hockey players. The management wants a cricketer or a wrestler to lead the group in the parade. In how many ways can this be done?
1820151222Option E

Required ways = 22 ways