**Directions: In an imaginary language, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are substituted by a, b, c, d, e, f, g, h, I and j. And 10 is written as ba.**

**Q1.baf÷bf × d is equal to**

(a) df

**(b) cb**

(c) be

(d) d

**Ans.(b)**

**Sol. Given expression = 105 ÷ 15 × 3 = 7 × 3 = 21 = cb.**

**Q2.If L denotes ÷, M denotes ×, P denotes + and Q denotes –, then which of the following statements is true?**

(a) 32 P 8 L 16 Q 4 =3/2

(b) 6 M 18 Q 26 L 13 P 7 =173/13

(c) 11 M 34 L 17 Q 8 L 3 =38/3

**(d) 9 P 9 L 9 Q 9 M 9 =-71**

**Ans.(d)**

**Sol. Using the proper notations in (d), we get the statement as:**

**9 + 9 ÷ 9 – 9 × 9 = 9 + 1 – 9 × 9 = 9 + 1 – 81 = 10 – 81 = – 71.**

**Directions:(3-5):In each of these following questions, different alphabets stand for various symbols as indicated below:**

**Addition : O Subtraction : M Multiplication : A**

**Division : Q Equal to : X Greater that : Y**

**Less than : Z**

**Out of the four alternatives given in these questions, only one is correct according to the above letter symbols. Identify the correct answer.**

**Q3.**

(a)1 O 1 Q 1 M 1 Y 3 Q 1

**(b) 2 Q 1 O 10 A 1 Z 6 A 4**

(c) 3 O 2 O 10 Q 2 X 10 A 2

(d) 5 Q 5 A 5 O 5 Y 5 A 2

**Ans.(b)**

**Sol. Using the proper notations in (b), we get the statements as:**

**2 ÷ 1 + 10 × 1 < 6 × 4 or 12 < 24, which is true.**

**Q4.**

(a) 32 X 8 Q 2 A 3 Q 1 A 2

**(b) 14 X 2 A 4 A 2 M 2 Q 1**

(c) 2 Y 1 A 1 Q 1 O 1 A 1

(d) 16 Y 8 A 3 O 1 A 2 M 2

**Ans.(b)**

**Sol. Using the proper notations in (b), we get the statement as:**

**14 = 2 × 4 × 2 – 2 ÷ 1 or 14 = 14, which is true.**

**Q5.**

**(a) 8 Q 4 A 1 M 2 X 16 M 16**

(b) 8 O 2 A 12 Q 10 X 18 Q 9

(c) 6 Q 2 O 1 O 1 X 16 A 1

(d) 2 O 3 M 4 Q 2 Z 1 A 2

**Ans.(a)**

**Sol. Using the proper notations in (a), we get the statement as:**

**8 ÷ 4 × 1 – 2 = 16 – 16 or 0 = 0, which is true.**

**Directions:(6-7):In each of the following questions, if the given interchanges are made in signs and numbers, which one of the four equations would be correct?**

**Q6.Given interchanges : Signs + and × and numbers 4 and 5.**

(a) 5 × 4 + 20 = 40

(b) 5 × 4 + 20 = 85

**(c) 5 × 4 + 20 = 104**

(d) 5 × 4 + 20 = 95

**Ans.(c)**

**Sol. On interchanging + and × and 4 and 5 in (c), we get the equation as:**

**4 + 5 × 20 = 104 or 104 = 104, which is true.**

**Q7. Given interchanges : Sings – and × and numbers 3 and 6**

(a) 6 – 3 × 2 = 9

**(b) 3 – 6 × 8 = 10**

(c) 6 × 3 – 4 = 15

(d) 3 × 6 – 4 = 33

**Ans.(b)**

**Sol. On interchanging – and × and 3 and 6 in (b), we get the equation as:**

**6×3 – 8 = 10 or 18 – 8 = 10 or 10 – 10 which is true.**

**Directions(8-10):In each of the following questions, the given equation becomes correct due to the interchange of two signs. One of the four alternatives under it specifies in the interchange of signs in the equation which when made will make the equation correct. Find the correct alternative.**

**Q8. 5 + 3 × 8 – 12 ÷ 4 = 3**

(a) + and –

**(b) – and ÷**

(c) + and ×

(d) + and ÷

**Ans.(b)**

**Sol. On interchanging – and ÷, we get the equation as:**

**5 + 3 × 8 ÷ 12 – 4 = 3 or 5 + 3 ×2/3 – 4 = 3 or 3 = 3, which is true**

**Q9.16 – 8 ÷ 4 + 5 × 2 = 8**

(a) ÷ and ×

(b) – and ÷

(c) ÷ and +

(d) – and ×

**Ans.(b)**

**Sol. On interchanging – and ÷, we get:**

**Given expression = 16 ÷ 8 – 4 + 5 ×2 = 2 – 4 + 5 × 2 = 2 – 4 + 10 = 8.**

**Q10.10 + 10 ÷ 10 – 10 × 10 = 10**

(a) + and –

(b) ×

**and ÷****(c) + and ×**

(d) ÷ and +

**Ans.(c)**

**Sol. On interchanging + and ×, we get the equation as:**

**10 × 10 ÷ 10 – 10 + 10 = 10 or 10 × 1 – 10 + 10 = 10 or 10 = 10, which is true.**