Questions on Mathematical operations will first start with either defining a new meaning to existing symbols or define a new symbol and its mathematical meaning.

You are then required to evaluate the value of an expression by assuming the meaning of the symbols as defined in the question. The following questions will make this question type clear to you.

**Illustration 1:**If '+' means '-', '-' means '¥', '¥' means 'Π', and 'Π' means '+' then which of the
following will be the value of the expression?

32 + 8 ¥ 2 - 3 Π 4

**Ans . **

(d) 24

**Explanation :**Putting the changed signs, the expression can be rewritten as

32 - 8 Π 2 ¥ 3 + 4

Using BODMAS rule, we have

=32 - 4 ¥ 3 + 4

=32 - 12 + 4 = 24

Hence, the correct option is (d).

**Illustration 2:** If A implies '+', B implies '-', C implies '¥', D implies 'Π', then calculate the value
of the expression 2A3B4C5D1.

**Ans . **

(c) -15

**Explanation :**Using the proper signs, the above expression can be written as 2 + 3 - 4 ¥ 5 Π 1

=5 - 20 = -15

Hence, option (c) is correct

**Illustration 3:** Which of the following changes would make the given expression correct?

4 + 4 ¥ 4 - 4 #928 4 = 4

**Ans . **

(d) both 'b' and 'c

**Explanation :**By making inter-changes given in 'a' we get the expression as:

4 ¥ 4 + 4 - 4 #928 4 = 4 which is false.

By making interchanges given in 'b', we get expression as

4 + 4 ¥ 4 #928 4 - 4 = 4 which is true.

By making interchanges given in option 'c', we get the expression as

4 ? 4 ¥ 4 - 4 + 4 = 4 which is also true.

Hence, option (d) is correct.

**Illustration 4:** If A"B means add B to A, A'B implies subtract B from A, A@ B implies divide A by B,
A*B means multiply A with B.

If a train travels with a speed of S_{1}
from point A to B and returns with a speed of S_{2}. The average
speed will be represented using the above explained notations?

**Ans . **

(b) (2*S_{1}*S_{2})/(S1"S_{2})

**Explanation :**We know that the formula for average speed is given by 2S

_{1}S_{2}/(S_{1}+ S_{2})

Hence the correct option is (b).

**Illustration 5:** If (l, m, n) is represented as v [(l + 1)(m + 1)/(n + 1)]:
What is the value of (48, 63, 80)?

**Ans . **

(a) 56/9

**Explanation :**Putting the value in the above equation we get /[(48 + 1)(63 + 1)/(80 + 1)] =/(49 ¥ 64/81) = (7 ¥ 8)/9 = 56/9 Hence, the correct option is (a).

**Directions for Questions 1 to 5: **

If a + b implies a - b

a - b implies a ¥ b,

a ¥ b implies a Π b

a Π b implies a + b

**Ans . **

(a) 5

**Explanation :**The expression will become 5 -8 ¥ 25 Π 5 + 40.

Using the BODMAS rule we will get:

5 - 40 + 40 = 5. Hence, option (a) is correct

**Ans . **

(b) 1 - 2 + 6 ¥ 3 Π 8

**Explanation :**Looking at option (b), we will get, 1- 2 + 6 ¥ 3 Π 8 becomes 1 ¥ 2 - 6 Π 3 + 8 = 8. Hence, option (b) is the correct answer.

**Ans . **

(c) 6 + 4 - 2 ¥ 2 Π 1 = 3

**Explanation :**Option (c) gives us 6 - 4 ¥ 2 Π 2 + 1= 3. Hence, this is correct.

**Ans . **

(b) 1/5

**Explanation :**(1 + 2 -3 ¥ 1 Π 4)/(4 + 5 - 4 ¥ 2 Π 1) ? (1- 2 ¥ 3 Π 1 + 4)/(4 - 5 ¥ 4Π 2 + 1) = -1/-5 =1/5. Hence, (b) is the answer

**Ans . **

(a) -7/3

**Explanation :**(4 + 3 - 5 ¥ 1 Π 4) ¥ (5 + 2 - 3 ¥ 1 Π 4) = (4 - 3 ¥ 5 Π 1 + 4) Π (5 - 2 ¥ 3 Π 1 + 4) = -7/3. Hence, option (a) is the answer.

**Ans . **

(c) -19

**Explanation :**6a7b8c8d2 = 6 + 7 - 8 ¥ 8 Π 2 = -19. Hence, (c) is the answer.

**Ans . **

(c) 670

**Explanation :**(8c7)c(7a5)b(6d3)d(3b2) becomes 56 ¥ 12 - 2 Π 1 = 670. Option (c) is the answer.

**Ans . **

(d) undefined

**Explanation :**The expression contains a division by 0, hence is undefined. Option (d) is the answer.

**Ans . **

(d) none of these

**Explanation :**None of these, i.e. option (d) is correct

**Ans . **

(b) 1 + 2 - 3 ¥ 8 Π 4 = 9

**Explanation :**The given expression will become 1 + 3 Π 2 ¥ 8 - 4 = 9. Option (b) is the answer

**Ans . **

(d) none of these

**Explanation :**Checking each of the four options we will get none of these the answer. Hence, option (d) is the answer.

**Ans . **

(d) 3 + 4 - 12 ¥ 1 Π 10 = 10

**Explanation :**Option (d) becomes correct.

**Ans . **

(a) ¥ and -

**Explanation :**If the signs are changed according to the first option the equation is satisfied. Hence, option (a) is correct

**Ans . **

(b) Π and +

**Explanation :**If the signs are changed according to the second option the equation is satisfied. Hence, option (b) is correct.

**Ans . **

(b)¥, Π, ¥

**Explanation :**Insertion of ¥, Π, ¥ in that order will make 12 ¥ 4 Π 2 ¥ 1 = 24. Hence, option (b) is correct

**Ans . **

(c) a, b, d

**Explanation :**40 + 20 - 30 Π 6 = 60 - 5 = 55. Hence, a, b, d. Option (c) is correct.

**Ans . **

(a) Π, ¥, -, +

**Explanation :**12 Π 8 ¥ 4 - 2 + 1 would mean 12 + 8 Π 4 ¥ 2 - 1 = 12 + 4 - 1 = 15. Hence, the order given in option (a) is correct

**Ans . **

(b) a, b, g, d

**Explanation :**Option (b) is correct.

**Directions for Questions 19 to 21: **

27 + 9 = 3

and 15 + 5 = 3.

**Ans . **

(a) 14

**Explanation :**It is clear that the + sign means Π. Hence

182 + 13 would give us a value of 14. Hence, (a) is the answer

**Ans . **

(a) 10

**Explanation :**50/5 = 10. Hence, (a) is the answer.

**Ans . **

(a) 4

**Explanation :**10/2.5 = 4. Hence, correct option is (a).

**Directions for Questions 22 to 25:**

5 ¥ 12 = 13

Then solve the following question.

**Ans . **

(a) 4

**Explanation :**

7 ¥ 24 = = 25. Hence, option (d) is the answer.

**Ans . **

(b) 12.041

**Explanation :**8 ¥ 9 = = 12.041. Hence, option (b) is the answer.

**Ans . **

(c) 40

**Explanation :**The required value will be got by the square root of the difference between 41

2 and 9 ^{2}Æ 1681 - 81 = 1600. Hence, the required answer is 40. Correct answer is option (c).

**Ans . **

(b) 8.366

**Explanation :**The required value would be square root of 61 + 9 = 8.366. Hence, option (b) is the answer

**Directions for Questions 26 to 30:**

N means equal to

O means not less than

P means less than

Q means not equal to

and R means not greater than

**Ans . **

(b) yPa

**Explanation :**yPz means that y is less than z and zNa means z = a. Thus, y is less than a Æ yPa. Option (b) is correct

**Ans . **

(d) none of these

**Explanation :**10a is greater than 6b. and 12b is greater than 20c Æ 6n is greater than 10c. Thus 10a is greater than 10c or a is greater than c. Option (d) is correct

**Ans . **

(c) bP - 2

**Explanation :**a is negative and b + 2 is less than a implies that b must be below -2. Hence, option (c) is correct

**Ans . **

(d) can`t be determined

**Explanation :**Nothing can be said about the relationships between s, u or v or for that matter about u and v. Hence, cannot be determined. The correct answer is option (d).

**Ans . **

(d) (a), (b) and (c) could be true

**Explanation :**Since the modulus value is always positive, all the three, i.e. the first, second and third relationships are possible. Hence, option (d) is correct.

Directions for Questions 31 to 33:

If aAb implies a + baMb implies a - b

aPb implies a ¥ b

aQb implies a Π b

**Ans . **

(b) 5P2A4Q2P2 = 14

**Explanation :**Option (b) is correct since we will get 10 + 4 = 14.

**Ans . **

(c) 9.5

**Explanation :**11 - 1.5 = 9.5. Option (c) is correct.

**Ans . **

(d) none of these

**Explanation :**(-15)(-7) = 105. Hence, option (d) is correct.

**Directions for Questions 34 to 36:**

A'b implies A - B

A@B implies A Π B

A*B implies A ¥ B

**Ans . **

(d) none of these

**Explanation :**It can be seen that none of these is correct. Hence, (d) is the answer

**Ans . **

(b) 2[(x*a)"(a*c)"(x*c)]

**Explanation :**The surface area of a cuboid box is equal to twice the areas of each of the sides. Hence, option (b) is correct.

**Ans . **

(c) (25*2)"(40*5)"(100*20)

**Explanation :**The correct answer is option (c).

**Directions for Questions 37 to 41: **

AYB implies A

AZB implies (A + B)

AMB implies (A - B)

**Ans . **

(b) -5544

**Explanation :**41

^{2}- 85^{2}= 1681 - 7225 = -5544. Hence, option (b) is correct answer

**Ans . **

(a) 1600

**Explanation :**(- 40)

^{2}=1600. Hence, option (a) is correct answer

**Ans . **

(c) A.B = 0

**Explanation :**The given expression tells us that (A - B)

^{2}= (A + B)^{2}. This can only occur when 2AB = - 2AB= 0. Hence, option (c) is correct.

**Ans . **

(a) 49

**Explanation :**7

^{2}= 49. Hence, correct answer is option (a)

**Ans . **

(b) 256

**Explanation :**16

^{2}= 256. Hence, correct answer is option (b).

**Directions for Questions 42 and 43:**

**Ans . **

(b) 5041

**Explanation :**The maximum value will be obtained when we use multiplication between 2 to 7 and addition between 1 and 2. Hence, option (b) is the answer.

**Ans . **

(b) 9

**Explanation :**The minimum value will be got if we use a multiplication between 1 and 2 and addition between 2, 3, and 4. The value will be 1 ¥ 2 + 3 + 4 = 9. Hence, option (b) is the answer

**Directions for Questions 44 to 46: **

B indicates <

C indicates =

D indicates p

E indicates +

F indicates -

G indicates *

H indicates Π

**Ans . **

(b) (5E6)A(6E12)A(13E6)

**Explanation :**It can be seen that options 1 and 3 are correct, but option (b) is wrong. Hence, option (b) is the correct answer

**Ans . **

(b) 32

**Explanation :**32/1 = 32. Hence, option (b) is correct.

**Ans . **

(c) -4

**Explanation :**5 + 3 – 12 = -4. Hence, option (c) is correct.