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Important Formulae

1.'BODMAS' Rule:
This rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of given expression.
Here B - Bracket,
O - of,
D - Division,
M - Multiplication,
A - Addition and
S - Subtraction
Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order (), {} and [ ].
After removing the brackets, we must use the following operations strictly in the order:
(i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction.

2. Modulus of a Real Number:
Modulus of a real number a is defined as
|a| = a, if a > 0
-a, if a < 0
Thus, |5| = 5 and |-5| = -(-5) = 5.

3. Virnaculum (or Bar):
When an expression contains Virnaculum, before applying the 'BODMAS' rule, we simplify the expression under the Virnaculum.

Practice Questions

1.

Simplify: 5005 - 5000 ÷ 10
A.4505B.4605
C.4705D.4805

Report! Answer!

Answer is: A

Let, 5005 – 5000/10 = 5005 – 500 = 4505

2.

Simplify: 343 ÷ 49 ÷ 7 ÷ 7
A.1/12B.1/13
C.1/7D.1/9

Report! Answer!

Answer is: C

Let , 343 x 1/49 x 1/7 x 1/7 = 1/7

3.

The value of 1001 ÷ 11 of 13 is :
A.8B.5
C.6D.7

Report! Answer!

Answer is: D

⇒ 1001 ÷ 11 x 13
⇒ 1001/(11 x 13) = 7.

4.

The value of 25 – 5 [2 + 3 {2 – 2 (5 – 3) + 5} – 10] ÷ 4 is:
A.22.25B.23.75
C.23.25D.22.75

Report! Answer!

Answer is: B

⇒ 25 – 5 [2 + 3 {2 – 2 (5 – 3) + 5} – 10] ÷ 4
⇒ 25 – 5 [2 + 3 {2 – 2 x 2 + 5} – 10] ÷ 4
⇒ 25 – 5 [2 + 3 {2 – 4 + 5} – 10] ÷ 4
⇒ 25 – 5 [2 + 3 {3} – 10] ÷ 4 = 25 – 5 [2 + 9 – 10] ÷ 4
⇒ 25 – 5 ÷ 4
⇒ 25 – 1.25 = 23.75

5.

What mathematical operation should come at the place of ‘?’ in the equation: 2 ? 6 – 12 ÷ 4 + 2 = 11
A.+B.-
C./D.x

Report! Answer!

Answer is: D

⇒ 2 ? 6 – 12 ÷ 4 + 2 = 11
⇒ 2 X 6 – 12 ÷ 4 + 2 = 11
⇒ 2 X 6 – 3 + 2 = 11 = 2 X 6 = 11 +3 -2
⇒ 2 X 6 = 12
So, in place of X, we apply x(multiply)

6.

The value of [(6 + 6 + 6 + 6) ÷ 6]/(4 + 4 + 4 + 4 ÷ 4) is equal to ?
A.13/4B.4/13
C.9/4D.4/9

Report! Answer!

Answer is: B

⇒ (24 ÷ 6)/(4 + 4 + 4 + 1) = 4/13

7.

Evaluate: [8 - {5 - ( - 3 + 2)} ÷ 2]/[(5 - 3) - (6 - 3) ÷3]
A.3B.4
C.5D.6

Report! Answer!

Answer is: C

⇒ [8 - {5 - ( - 3 + 2)} ÷ 2]/[(5 - 3) - (6 - 3) ÷3] = [8 - {5 - (-1)} ÷2]/[2 - 3 ÷3]
⇒ (8 - 6 ÷ 2)/( 2 - 1) = 8 – 3 = 5

8.

If 1/3 + 1/2 + 1/X = 4, then X = ?
A.6 / 19B.19 / 6
C.5 / 19D.19 / 5

Report! Answer!

Answer is: A

1/3 + 1/2 + 1/X = 4
⇒ 1/X = 4 - 1/3 - 1/2
⇒ 1/X = (24 - 2 - 3)/6 = 19/6
⇒ X = 6/19

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