The
basic approach for the questions of this chapter is more or less similar to
that of coding and decoding. As in the questions of coding and decoding, a
basic word is coded in a particular way and the candidate is asked to code another
word using the same logic.

Similarly
in "Symbols and Notations", one lias to study the symbols and their
meanings carefully which are given against them. Then, the meanings given are
to be used in place of those symbols in answering the questions. The word
"Notation" basically stands for the meaning which each symbol will be
assigned.

The
questions can be based on Blood Relations or Mathematical Operations (or
Operator based questions). This chapter deals with Mathematical Operations.

## Mathematical Operations :

Symbols
for these types of questions stand for mathematical operations i.e. +, – , x,
÷, >, <, __>__, __<__, = and #. So one must replace the
symbols by mathematical operations and apply the 'BODMAS' rule to find the
value of the given expression. Symbols like , , *,
@, $ etc are used by giving a proper definition of the symbol used. An example
belonging to this category is also explained below.

## Worked out Examples :

## Example 1.

If'
– ' stands for 'x', 'x' stands for '+','+' stands for '÷' and '÷' stands for '
– ', then what is the value of 9 ÷ 18 x 15 + 3 – 6 × 12?

(a) 24

(b) 30

(c) 33

(d) 42

### Solution.

The
given expression is 9 ÷ 18 × 15 + 3 – 6 × 12. By converting the
symbols according to the given definitions, we get 9 – 18 + 15 ÷ 3 × 6 + 12.
Solving this by BODMAS rule, we get the value as 33. .

Choice
(c)

## Example 2.

If a $ b = a^{2}b^{2} – ab, then 3 $ 8 =

(a) 600

(b) 552

(c) 576

(d)625

### Solution.

Given a $ b = a^{2}b^{2} – ab.

3$8
= 3^{2}x8^{2} – 3 x 8 = 9 x 64 – 24

= 576 – 24 = 552.

Choice (b)

## Example 3.

If p q =
p^{2} + q^{2} – p – q and p q =
pq – p – q, then (6 5) 5 =

(a) 200

(b) 175

(c) 195

(d) 179

### Solution.

65 =
6^{2 }+ 5^{2} – 6 – 5 = 36+ 25 – 6 – 5 = 50

(65)
5 = 505 =
50x5 – 50 – 5 = 195.

Choice
(c)

## Example 4.

If 4 O 5 = 189 and 10 O 8= 1512, then 6 O 9 =

(a) 945

(b) 1148

(c) 983

(d) 764

### Solution.

4^{3} + 5^{3} = 64+125=189405

10^{3} + 8^{3} = 1000 + 512 = 1512 10
O 8

Similarly, 6 O 9 = 6^{3} + 9^{3} = 216 +
729 = 945. Choice (a).

## Example 5.

If ''
means 'is less than', '$' means 'is greater than' and '£' means 'is equal to'
and given that a b,
c £ d and c $ b, then which of the following is true?

(a) d a

(b) b $ d

(c) a £ c

(d) a b c

### Solution.

a b a
< b

c $ b c
> b b
< c

c £ d c =
d

a
< b < c = d

(a) d a d
< a false

(b) b $ db
> d false

(c) a £ ca =
cfalse

(d)
a b ca < b< c true

Choice
(d)