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:

If x = (√2 + 1)/(√2 – 1), then what is the value of (x5 + x4 + x2 + x)/x3 ?

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

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Q:

Determine the value of a2+b2a3+b3 when a = 2+√3 and b = 2-√3.

A) 0.27 B) 0.42
C) 0.58 D) 0.93
 
Answer & Explanation Answer: A) 0.27

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Q:

DEF is right angled at E. If cosD = 5/13, then what is the value of tanF?

A) 5/13 B) 5/12
C) 13/5 D) 13/12
 
Answer & Explanation Answer: B) 5/12

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Q:

If the equation 4x + 3y + 5 = 0 and 6x - ky - 7 = 0 have no solution, then the value of k is

A) -4.5 B) -8
C) 8 D) 4.5
 
Answer & Explanation Answer: A) -4.5

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Q:

If a - b = 2 and ab = 15, then what is the value of a3- b3?

A) 152 B) 112
C) 108 D) 98
 
Answer & Explanation Answer: D) 98

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Q:

If x2 + y2 + 6x + 5 = 4(x - y) then x - y is

A) 1 B) -1
C) 0 D) 4
 
Answer & Explanation Answer: A) 1

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Q:

If a – b = 11 and ab = 24, then value of a2 + b2 is

A) 169 B) 37
C) 73 D) 48
 
Answer & Explanation Answer: A) 169

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Q:

Square of (3x – 5xy) is

A) 9x2 - 30x2y + 25x2y2 B) 9x2 - 15x2y + 25x2y2
C) 25x2 - 15x2y + 9x2y2 D) 25x2 - 30x2y + 9x2y2
 
Answer & Explanation Answer: A) 9x2 - 30x2y + 25x2y2

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