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

Given:

50% of 9642 + 40% of 2255 + 12.5% of 384

Concept used:

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

Calculation:

According to the question,

50% of 9642 + 40% of 2255 + 12.5% of 384

⇒ (1/2) × 9642 + (2/5) × 2255 + (1/8) × 384

⇒ 4821 + 902 + 48

⇒ 5771

∴ 5771

Given:

Simplify: 144 ÷ [ (8 ÷ 4) × { 7 + 7 - ( 5 + 8 - (9 + 2) ) } ]

Formula Used:

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

Calculation:

144 ÷ [ (8)/(4) × { 7 + 7 - ( 5 + 8 - (9 + 2) ) } ]

​⇒ 144 ÷ [ 2 × { 14 - ( 5 + 8 - 11 ) } ]

​⇒ 144 ÷ [ 2 × { 14 - ( 13 - 11 ) } ]

​⇒ 144 ÷ [ 2 × { 14 - 2 } ]

​⇒ ​144 ÷ [ 2 × 12 ]

​⇒ 144 ÷ 24 = 6

The correct answer is 6.

Given:

 ×  × 30

Formula Used:

Simplify the given expression step by step using basic arithmetic and powers.

Calculation:

 ×  × 30

 ×  × 30

  × 30 = 5

The correct answer is 5.

Given:

Formula used:

Law of exponents:

a^p × a^q = a^{p + q}

Calculations:

Let's simplify the Left Hand Side (LHS) of the equation:

LHS =

Rewrite as

So, LHS =

Using the property :

LHS =

LHS =

Now, let's simplify the Right Hand Side (RHS) of the equation:

RHS =

RHS =

Now, equate the simplified LHS and RHS:

Since the bases are the same, the exponents must be equal:

12 = -9m - 7

12 + 7 = -9m

19 = -9m

∴ The value of m which satisfies the given equation is .

Given:

194 + [6 × (1 - 6 + 5)] ÷ 12

Calculation:

194 + [6 × (1 - 6 + 5)] ÷ 12

⇒ 194 + [6 × (0)] ÷ 12

⇒ 194 + 0 ÷ 12

⇒ 194 + 0

⇒ 194

∴ The correct answer is option (4).

Concebt used

a.b̅ = a.bbbbbb

a.0b̅ = a.0bbbb

Calculation

0.7 = 0.700000 ̇....

Now, 0.7777…  or  is largest among all.

Solution:

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

= (75 + 74 + 73)/6

= 222/6

= 37

Shortcut Trick

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

= 36 + 1 = 37

Solution:

We have to follow the BODMAS rule

Calculation:

⇒ ? = 3²

∴ ? = 9

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

Given expression is:

⇒  

⇒  

⇒  

⇒  

Since,

a2 - b2 = (a - b) ( a + b)

⇒ 0.9 × 0.7 = 0.63

∴ Answer is 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:

√3n = 729

Formulas used:

(x^a)^b = x^ab

If x^a = x^b then a = b 

Calculation:

√3n = 729

⇒ √3n = (3²)³

⇒ (3n)^1/2 = (32)3

⇒ (3n)1/2 = 3⁶

⇒ n/2 = 6 

∴  n = 12 

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