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 Cot 60°- Sec 45°?

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

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Q:

The sum of two positive integers is 80 & difference between them is 20. Then what is difference of squares of those numbers ?

A) 1400 B) 1600
C) 1800 D) 2000
 
Answer & Explanation Answer: B) 1600

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Q:

If a+bab=21 ,  then the value of (a-b) is

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

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Q:

What is the simplified value of (cos4 A  sin4 A)?

A) 0 B) 2 cos2 A
C) cos2A D) 1
 
Answer & Explanation Answer: C) cos2A

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Q:

If cos 45° - ­ sec 30° = x, then value of x is

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

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Q:

If a1-2a+b1-2b+c1-2c = 12, then 11-2a+11-2b+11-2c value is

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

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Q:

If 2x+29x = 4, then the value of 27x3+127x3

A) 180 B) 198
C) 234 D) 252
 
Answer & Explanation Answer: B) 198

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Q:

Find x, if 5x-6+5x+6 = 6

A) -4 B) 0
C) 2 D) 4
 
Answer & Explanation Answer: C) 2

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