Simplification Questions

FACTS  AND  FORMULAE  FOR  SIMPLIFICATION  QUESTIONS

 

 

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 a given expression. Here, 'B' stands for bracket , 'O' for of , 'D' for division and 'M' for multiplication, 'A' for addition and 'S' for 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:

(1) of    (2)division   (3) multiplication   (4)addition   (5)subtraction.

 Modulus of a real number : Modulus of a real number a is defined as |a| = aif a>0-aif a<0

 

2. Virnaculum (or bar) : When an expression contains Virnaculum, before applying the ‘BODMAS’ rule, we simplify the expression under the Virnaculum.

Q:

4 + (16) [-10 x 25 - 13 - 3 ÷ -5] = ?

 

A) 8 B) 9
C) 6 D) 7
 
Answer & Explanation Answer: D) 7

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Q:

If sec θ + tan θ = 2, then sec θ - tan θ = ?

 

A) 0.5 B) 1.5
C) 1 D) 0.75
 
Answer & Explanation Answer: A) 0.5

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Q:

If x32 - 1x16 = 5, then find the value of x96 - 1x48.

 

 

A) 40 B) 70
C) 140 D) 180
 
Answer & Explanation Answer: C) 140

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Q:

What is the value of (sin45 - √3) ?

 

A) (1-√6)/√2   B) (4-√3)/2√3  
C) -1/2√3   D) (2-√3)/2√3
 
Answer & Explanation Answer: A) (1-√6)/√2  

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Q:

Simplify : (27)-23

 

A) 1/18 B) 9
C) 1/9 D) 18
 
Answer & Explanation Answer: C) 1/9

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Q:

Simplify : 528 ÷ 2835 ÷ 20112

 

A) 4/5 B) 5/4
C) 4/7 D) 7/4
 
Answer & Explanation Answer: B) 5/4

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Q:

What is the square root of (√5 + 2)/(√5 – 2)?

 

A) √5 – √4   B) √5 + 2  
C) 5 + √2   D) 7
 
Answer & Explanation Answer: B) √5 + 2  

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Q:

If p + 1p = 10, then the value of p4 + 1p4.

 

A) 52 B) 60
C) 62 D) 65
 
Answer & Explanation Answer: C) 62

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