Simplification MCQ Quiz - Objective Question with Answer for Simplification - Download Free PDF

Calculation:

5m ÷ 5-3 = 55

⇒ 5^{(m - (-3))} = 5⁵

⇒ 5^(m+3) = 55

⇒ m + 3 = 5

⇒ m = 5 - 3 = 2

∴ The correct answer is option (4).

Concept Used:

As per the rule of exponents we have

Rule 1: a^x × a^y × a^z = z^{(x + y + z)}

Rule 2: a⁰ = 1

Calculation:

8³ × 8² × 8^-5 = 8^{(3 + 2 - 5)}

8(3 + 2 - 5) = 8⁰ = 1

∴ The correct answer is option (1).

Given:

1.33 × 1.33 + 0.67 × 0.67 + 1.33 × 0.67 × 2 = ?

Formula used:

Expand and simplify the expression.

Calculation:

1.33 × 1.33 + 0.67 × 0.67 + 1.33 × 0.67 × 2

⇒ 1.7689 + 0.4489 + 1.7822 = 4.000

∴ The correct answer is option (2).

Given:

200 - 96 ÷ 4 = ?

Formula used:

Order of operations (BODMAS/BIDMAS): Brackets, Orders (i.e. powers and square roots, etc.), Division and Multiplication, Addition and Subtraction.

Calculation:

⇒ 200 - 96 ÷ 4

⇒ 200 - 24

⇒ 176

∴ The correct answer is option (3).

Given:

100+49" id="MathJax-Element-38-Frame" role="presentation" style="position: relative;" tabindex="0">100−−−√+49−−√100+49" id="MathJax-Element-19-Frame" role="presentation" style="position: relative;" tabindex="0">100−−−√+49−−√100+49 100+49 $\sqrt{100} + \sqrt{49}$ = ?

Formula used:

a+b" id="MathJax-Element-39-Frame" role="presentation" style="position: relative;" tabindex="0">a−−√+b√a+b" id="MathJax-Element-20-Frame" role="presentation" style="position: relative;" tabindex="0">a−−√+b√a+b a+b $\sqrt{a} + \sqrt{b}$

Calculation:

100+49" id="MathJax-Element-40-Frame" role="presentation" style="position: relative;" tabindex="0">100−−−√+49−−√100+49" id="MathJax-Element-21-Frame" role="presentation" style="position: relative;" tabindex="0">100−−−√+49−−√100+49 100+49 $\sqrt{100} + \sqrt{49}$ = ?

⇒ 100" id="MathJax-Element-41-Frame" role="presentation" style="position: relative;" tabindex="0">100−−−√100" id="MathJax-Element-22-Frame" role="presentation" style="position: relative;" tabindex="0">100−−−√100 100 $\sqrt{100}$ = 10

⇒ 49" id="MathJax-Element-42-Frame" role="presentation" style="position: relative;" tabindex="0">49−−√49" id="MathJax-Element-23-Frame" role="presentation" style="position: relative;" tabindex="0">49−−√49 49 $\sqrt{49}$ = 7

⇒ 10 + 7 = 17

As in the option we don't have 17 as the direct value but we have it in the form of the square root.

∴ The correct answer is option (4).289" id="MathJax-Element-43-Frame" role="presentation" style="position: relative;" tabindex="0">289−−− $\sqrt{289}$

Concebt used

a.b̅ = a.bbbbbb

a.0b̅ = a.0bbbb

Calculation

0.7 = 0.700000 ̇....

\(0.\bar7 = 0.77777 \ldots\)

\(0.0\bar7 = 0.077777 \ldots\)

\(0.\overline {07} = 0.070707 \ldots\)

Solution:

\(12\frac{1}{2} + 12\frac{1}{3} + 12\frac{1}{6}\)

= 25/2 + 37/3 + 73/6

= (75 + 74 + 73)/6

= 222/6

= 37

Shortcut Trick

\(12\frac{1}{2} + 12\frac{1}{3} + 12\frac{1}{6}\)

= 12 + 12 + 12 + (1/2 + 1/3 + 1/6)

= 36 + 1 = 37

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

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

Given expression is:

\(\sqrt {8\; + \;2\sqrt {15} \;} \)

⇒  \(\sqrt {5\; + \;3\; + \;2\times \sqrt 5 \times \sqrt 3 \;} \)

⇒  \(\sqrt {{{(\sqrt 5 )}^2}\; + \;{{\left( {\sqrt 3 } \right)}^2}\; + \;2 \times \sqrt 5 \times \sqrt 3 \;} \)

⇒  \(\sqrt {{{\left( {\;\sqrt 5 \; + \;\sqrt 3 \;} \right)}^2}\;} \)

⇒  \(\sqrt 5 + \sqrt 3 \)

\(\sqrt {{{\left( {0.65} \right)}^2} - {{\left( {0.16} \right)}^2}} \)

Since,

a2 - b2 = (a - b) ( a + b)

\(\begin{array}{l} \Rightarrow \sqrt {\left( {0.65 + 0.16} \right)\left( {0.65 - 0.16} \right)} \\ \Rightarrow \sqrt {\left( {0.81} \right)\left( {0.49} \right)} \\ \Rightarrow \sqrt {\left( {0.9} \right)\left( {0.9} \right) \times \left( {0.7} \right)\left( {0.7} \right)} \end{array}\)

⇒ 0.9 × 0.7 = 0.63

Concept:

We can find √x using the factorisation method.

Calculation:

√[(10 + √25) (12 - √49)]

⇒ √[(10 + 5)(12 – 7)]

⇒ √(15 × 5)

⇒ √(3 × 5 × 5)

⇒ 5√3

Given,

2³ × 3⁴ × 1080 ÷ 15 = 6^x

⇒ 2³ × 3⁴ × 72 = 6^x

⇒ 2³ × 3⁴ × (2 × 6²) = 6^x

⇒ 2⁴ × 3⁴ × 6² = 6^x

⇒ (2 × 3)⁴ × 6² = 6^x           [∵ x^m × y^m = (xy)^m]

⇒ 6⁴ × 6² = 6^x

⇒ 6^{(4 + 2)} = 6^x

⇒ x = 6

Given expression,

(81.84 + 118.16) ÷ 5³ = 1.2 × 2 + ?

⇒ 200 ÷ 5³ = 1.2 × 2 + ?

⇒ 200 ÷ 125 = 1.2 × 2 +?

⇒ 1.6 = 2.4 + ?

⇒ ? = -0.8

Method I: (3 + 2√5)²

= (3² + (2√5)² + 2 × 3 × 2√5)

= 9 + 20 + 12√5 = 29 + 12√5

On comparing, 29 + 12√5 = 29 + K√5

we get,

K = 12

 Alternate Method 

29 + 12√5 = 29 + K√5

⇒ K√5 = 29 - 29 + 12√5

⇒ K√5 = 12√5

∴ K = 12