**Dear Students,**

**Q1. A box contains 4 Green, ‘x’ red and 2 blue balls. Find the probability of selecting two balls such that color of both balls will be same if it is given that probability of selecting one red ball from the box is 1/3.**

**Q2. Ratio of A, B and C’s salary is 6 : 8 : 9 while ratio of A, B and C’s saving is 4 : 4 : 3. If A’s expenditure is 20% of his salary then find C’s expenditure is what percent of his salary?**

**Q3. Rahul invested money in scheme ‘A’ and scheme ‘B’ in the ratio 2 : 3. If scheme ‘A’ offer 10% p.a. at SI and scheme ‘B’ offer 10% at CI, then find the interest earned from Scheme ‘B’ is what percent more than interest earned from scheme ‘A’ after 2 years?**

**Q4. Sum of length of two train (A and B)is 540 m and ratio of speed of these two trains A and B is 1 : 2. If train A covers 90 m in 5 sec, then in what time they will cross each other when they travel in opposite direction.**

**Q5. A boat takes 90 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 km/h then speed of the stream is: **

**Directions (6-10): In each of these questions, two equations (I) and (II) are given. Solve both the equations and mark the correct option: **

**Q6. I. 15x² + 11x + 2 = 0 **

**II. 24y² + 11y + 1 = 0**

5x (3x + 1) + 2 (3x + 1) = 0

(5x + 2) (3x + 1) = 0

x = -2/5, -1/3

II. 24y² + 8y + 3y + 1 = 0

8y (3y +1) + 1 (3y + 1) = 0

(8y + 1) (3y + 1) = 0

y = -1/3, -1/8

⇒ x ≤ y

**Q7. I. x² – 30x + 221 = 0 **

**II. y² – 17y + 60 = 0**

x (x – 13) – 17 (x – 13) = 0

(x – 17) (x – 13) = 0

x = 13, 17

II. y² – 12y – 5y + 60 = 0

y (y – 12) – 5 (y – 12) = 0

(y – 5) (y – 12) = 0

y = 5, 12

⇒ x > y

**Q8. I. x² + 6x + 8 = 0 **

**II. 8y² + 22y + 15 = 0**

x² + 2x + 4x + 8 = 0

x (x + 2) + 4 (x + 2) = 0

(x + 4) (x + 2) = 0

x = –2, –4

II. 8y² + 22y + 15 = 0

8y² + 10y + 12y + 15 = 0

2y (4y + 5) +3(4y + 5) = 0

(2y + 3) (4y + 5) = 0

y=(-3)/2,-5/4

⇒ x < y

**Q9. I. x² – 20x + 96 = 0 **

**II. y² – 15y + 56 = 0**

x² – 8x – 12x + 96 = 0

x (x – 8) – 12 (x – 8) = 0

(x – 12) (x – 8) = 0

x = 12, 8

II. y² – 15y + 56 = 0

y² – 7y – 8y + 56 = 0

(y – 7) (y – 8) = 0

y = 7, 8

⇒ x ≥ y

**Q10. I. x² + 2x – 35 = 0 **

**II. y² + 3y – 10 = 0 **

x² + 7x – 5x – 35 = 0

x (x + 7) – 5 (x + 7) = 0

(x – 5) (x + 7) = 0

x = 5, –7

II. y² + 3y – 10 = 0

y² + 5y – 2y– 10 = 0

(y + 5) (y – 2) = 0

y= –5, 2

⇒ no relation can be established between x and y

**Directions (11-15): What comes at the place of question mark in the following number series? **

**Q11. 27, 1358, 1277, 1620, ? , 1622**

27+11³=1358

1358-9²=1277

1277+7³=1620

1620-5²=1595

1595+3³=1622

So, ?=1620 – 5² = 1595

**Q12. 48, 72, 180, 810, ?, 69862.5**

48×1.5=72

72×2.5=180

180×4.5=810

810×7.5=6075

So,?= 810 × 7.5 = 6075

**Q13. 8, 288, 512, 680, 792, ?**

**Q14. 57, 65, 74, 138, ?, 379**

**Q15. 16 ?, 32, 128, 64, 256**