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:

What is the value of Tan 45° + 4/√3 Sec 60°?

A) (√3 + 8)/√3 B) (√3 + 8)/3
C) (√3 - 8)/√3 D) (√3 - 8)/3
 
Answer & Explanation Answer: A) (√3 + 8)/√3

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Q:

What is the value of sin 75°+ sin 15°?

A) √3 B) 2√3
C) √(3/2) D) 3/√2
 
Answer & Explanation Answer: C) √(3/2)

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Q:

The sum of a number and 4 times its reciprocal is 5. What is the number?

A) 4 B) 5
C) 6 D) 7
 
Answer & Explanation Answer: A) 4

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Q:

If α + β = 90° and α:β = 2:1, then the ratio of cosα to cosβ is

A) 1:√3 B) 1:3
C) 1:√2 D) 1:2
 
Answer & Explanation Answer: A) 1:√3

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Q:

If 5x ­- 3(4 ­ x) < 4x -­ 4 < 4x + 2x/3; then the value of x is

A) -7 B) 3
C) 4 D) 1
 
Answer & Explanation Answer: D) 1

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Q:

If 1/(1+tan2A) = x, then value of x is

A) cosA B) sinA
C) cosecA D) secA
 
Answer & Explanation Answer: A) cosA

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Q:

What is the value of 143 + 163 + 183 + ... + 303?

A) 134576 B) 120212
C) 115624 D) 111672
 
Answer & Explanation Answer: D) 111672

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Q:

If a - b = 1 and ab = 6, then what is the value of a3- b3?

A) 21 B) 23
C) 19 D) 25
 
Answer & Explanation Answer: C) 19

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