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:

cot2A + cos2A is equal to

A) (cosecA -­ sinA)2(cosecA + sinA) B) (cosecA + sinA)(cosecA -­ sinA)
C) (secA + sinA)(secA -­ sinA) D) (secA -­ sinA)2(secA + sinA)
 
Answer & Explanation Answer: B) (cosecA + sinA)(cosecA -­ sinA)

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Q:

What is the value of Tan 60 + Cosec 60?

A) 5/3 B) 2/√3
C) 5/√3 D) 2/3
 
Answer & Explanation Answer: C) 5/√3

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Q:

Calculate the value of 0.77777 + 0.7777 + 0.777 + 0.77 + 0.7 + 0.07.

A) 3.86274 B) 3.80247
C) 3.85274 D) 3.87247
 
Answer & Explanation Answer: D) 3.87247

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Q:

If 23x + 23y = 184, then what is the average of x and y?

A) 2 B) 4
C) 3 D) 2.5
 
Answer & Explanation Answer: B) 4

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Q:

What is the value of tan4A + tan2A?

A) sec4A - sec2A B) sec4A + sec2A
C) cosec4A - sec2A D) sec4A + cosec2A
 
Answer & Explanation Answer: A) sec4A - sec2A

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Q:

What approximate value should come at the place of question mark (?) in the following questions (You are not expected to calculate the exact value).

(111.93 × 5) ÷ 14.02 = 11.002 + ?

A) 11 B) 10
C) 29 D) 34
 
Answer & Explanation Answer: C) 29

Explanation:

Ans.
112 × 5 ÷ 14 = 11 + ?
112 × 5 ÷ 14 = 11 + ?
560 ÷ 14 = 11 + ?
40 = 11 + ?
? = 40 - 11 = 29

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Q:

If xy = -30 and x2 + y2 = 61, then find the value of (x + y).

A) 2 B) 3
C) 1 D) 4
 
Answer & Explanation Answer: C) 1

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Q:

If 4x - 5(2x - 1) > 2x + 3 > 2 - 3x; then x can take which of the following values?

A) 1 B) 0
C) 2 D) 3
 
Answer & Explanation Answer: B) 0

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