Bodmas Rule MCQ Quiz - Objective Question with Answer for Bodmas Rule - Download Free PDF

Given:

\(\dfrac{2\{3+3(\dfrac{1}{4} ÷ \dfrac{15}{20}+2)-18 × \dfrac{1}{3}\}}{2(4+20 ÷ 4)}\)

Formula used:

Order of Operations (PEMDAS/BODMAS)

Calculation:

\(\dfrac{2\{3+3(\dfrac{1}{4} ÷ \dfrac{15}{20}+2)-18 × \dfrac{1}{3}\}}{2(4+20 ÷ 4)}\)

First, simplify inside the parentheses:

\(\dfrac{1}{4} ÷ \dfrac{15}{20}\)

⇒ \(\dfrac{1}{4} × \dfrac{20}{15}\)

⇒ \(\dfrac{1×20}{4×15}\)

⇒ \(\dfrac{20}{60}\)

⇒ \(\dfrac{1}{3}\)

Now, continue simplifying inside the braces:

\(\dfrac{2\{3+3(\dfrac{1}{3}+2)-18 × \dfrac{1}{3}\}}{2(4+5)}\)

⇒ \(\dfrac{2\{3+3(\dfrac{7}{3})-6\}}{2(9)}\)

⇒ \(\dfrac{2\{3+7-6\}}{18}\)

⇒ \(\dfrac{2\{4\}}{18}\)

⇒ \(\dfrac{8}{18}\)

⇒ \(\dfrac{4}{9}\)

∴ The correct answer is option (3).

Given:

The fractions are: (4/9), (5/8), (2/3), and (3/4).

Method:

We will compare the fractions by converting them to decimals or finding a common denominator. First, let's convert each fraction to a decimal:

4/9 = 0.4444

5/8 = 0.625

2/3 = 0.6666

3/4 = 0.75

Comparing the decimals:

0.4444, 0.625, 0.6666, and 0.75

Conclusion:

The largest value is 0.75, which corresponds to the fraction 3/4.

Therefore, the largest fraction is 3/4.

Given:

The expression is: (20 × 13) × {4 ÷ 4 × (19 - 13) / 3}

Formula Used:

Follow the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

Calculation:

⇒ (20 × 13) × {4 ÷ 4 × (19 - 13) / 3}

⇒ (20 × 13) × {4 ÷ 4 × 6 / 3}

⇒ (20 × 13) × {1 × 6 / 3}

⇒ (20 × 13) × 2

⇒ 20 × 13 = 260

⇒ 260 × 2 = 520

The value of the expression is 520.

Given:

Expression: [(91 ÷ 7) × {(64 ÷ 4) + (17 ÷ 6) × (8 - 2)}]

Formula Used:

Order of operations (BODMAS): Solve inside brackets first, then division/multiplication, and finally addition/subtraction.

Calculation:

⇒ [(91 ÷ 7) × {(64 ÷ 4) + (17 ÷ 6) × (8 - 2)}]

⇒ (13) × {(16) + (17 ÷ 6) × (6)}

⇒ (13) × {16 + (17 × 6 ÷ 6)}

⇒ (13) × {16 + 17}

⇒ 13 × 33

⇒ 429

∴ The value of [(91 ÷ 7) × {(64 ÷ 4) + (17 ÷ 6) × (8 - 2)}] is 429.

Given:

(828/4) × 3 - (8 × (6/24) × 10) + (105/35) - 15 

Concept used: 

Follow the BODMAS rule according to the table given below:

Calculation:

⇒ (828/4) × 3 - (8 × (6/24) × 10) + (105/35) - 15 

⇒ (207) × 3 - (8 × (1/4) × 10) + (3) - 15 

⇒ 207 × 3 - (2 × 10) + 3 - 15 

⇒ 621 - 20 + 3 - 15 

⇒ 621 - 17 - 15 

⇒ 621 - 32

⇒ 589

∴ (828/4) × 3 - (8 × (6/24) × 10) + (105/35) - 15 = 589

Solution:

We have to follow the BODMAS rule

Calculation:

\(? = \sqrt[5]{{{{\left( {243} \right)}^2}}}\)

\(⇒ ? = (243)^{\frac{2}{5}}\)

\(⇒ ? = (3 × 3 × 3 × 3 × 3)^{2⁄5}\)

\(⇒ ? = (3^5)^{2⁄5}\)

⇒ ? = 3²

Concept used:

ax × ay = ax + y

ax ÷ ay = ax - y

Calculation:

(4 × 4)³ ÷ (512 ÷ 8)⁴ × (32 × 8)⁴ = (2 × 2)^{(? + 4)}

⇒ 4⁶ ÷ (64)⁴ × 256⁴ = (4)^{(? + 4)}

⇒ 4⁶ ÷ (4³)⁴ × (4⁴)⁴ = (4)^{(? + 4)}

⇒ 4^{(6 + 16 - 12)} = (4)^{(? + 4)}

⇒ 4¹⁰ = (4)^{(? + 4)}

So, ? + 4 = 10

⇒ ? = 10 - 4

Shortcut Trick Formula:

(a+b)2 - 4ab = (a-b)2

Calculation:

(957 + 932)2 - 4 × 957 × 932

= (957 - 932)2

= 252 = 625

Alternate Method GIVEN:

\(( 957 + 932 )^2\) - 4 × 957 × 932.

FORMULA USED:

BODMAS 

CALCULATION :

⇒ \((1889)^2\) - 4 × 957 × 932 

⇒ 3568321 - 4 × 957 × 932 

⇒ 3568321 - 3567696  =  625 

∴ The value is 625.

Follow BODMAS (Brackets, Of, Division, Multiplication, Addition, Subtraction) rule to solve this question, as per the order given below,

Step-1- Parts of an equation enclosed in 'Brackets' must be solved inside the bracket first,

Step-2-  Then any mathematical 'Of' or 'Exponent' must be solved,

Step-3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4- Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

1251/3 × 271/3 × 1254/3 = 15 × 5?

⇒ 5 × 3 × 5⁴ = 15× 5^x

⇒ 15 × 5 ⁴ = 15× 5^x

⇒ x = 4

Hence option 4 is correct.

Concept used:

Follow BODMAS rule to solve this question, as per the order given below:

\(\frac{{7.2}}{{\sqrt[3]{{0.729}}}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

\(\Rightarrow \frac{{7.2}}{{\sqrt[3]{{\frac{{729}}{{1000}}}}}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

\(\Rightarrow \frac{{7.2}}{{\sqrt[3]{{{{\left( {\frac{9}{{10}}} \right)}^3}}}}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

\(\Rightarrow {\rm{\;}}\frac{{7.2}}{{\sqrt[3]{{{{\left( {0.9} \right)}^3}}}}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

\(\Rightarrow \frac{{7.2}}{{0.9}} = \frac{{{{\left( ? \right)}^3}}}{{{{\left( 2 \right)}^3}}}\)

⇒ 8 = (?)³/(2)³

⇒ (2)³ = (?)³/(2)³

⇒ 2³ × 2³ = (?)³

⇒ 4³ = (?)³

⇒ ? = 4

Using BODMAS rule:

⇒ 63 - (- 3)(- 2 - 8 - 4) ÷ [3 {5 + (- 2)(- 1)}]

⇒ 63 - (- 3)(- 2 - 8 - 4) ÷ [3 {5 + 2}]

⇒ 63 - (42) ÷ 21

Concept used:

Calculation:

196² × 56 ÷ 14⁵ × 1021 

⇒ (14²)² × (56/14⁵) × 1021 

⇒ [14⁴ × (56/145)] × 1021 

⇒ (56/14) × 1021 

⇒ 4 × 1021 = 4084

∴ The answer will be 4084.

Concept used:

Calculation:

\(56 \div \left[\frac{1}{3}\left\{ {15 + 12 - \left( {9 + 6 - \overline {5 + 7} } \right)} \right\} \right] \)

⇒ 56 ÷ [(1/3){15 + 12 - (9 + 6 - 12)}]

⇒ 56 ÷ [(1/3){15 + 12 - (15 - 12)}]

⇒ 56 ÷ [(1/3){15 + 12 - 3}]

⇒ 56 ÷ [(1/3){27 - 3}]

⇒ 56 ÷ [(1/3)(24)]

⇒ 56 ÷ 8

⇒ 7 

∴ ? = 7

Important Points

If in any simplification problem there is (  ̅  ) bar sign above any operation then we should perform the operation at the beginning, whatever the operation is. Then we will follow the chart given above. 

1132.757 – 2315.996 – 1753.829 + 2 × 2846.639

= 1133 – 2316 – 1754 + 5694

= (1133 + 5694) – (2316 + 1754 )

= 6827 – 4070

= 2757