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 (32 cos6x  48 cos4x + 18 cos2x  1)/[4 sin x cos x sin (60  x) cos (60  x) sin (60 + x) cos (60 + x)]?

A) 4 tan 6x B) 4 cot 6x
C) 8 cot 6x D) 8 tan 6x
 
Answer & Explanation Answer: C) 8 cot 6x

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Q:

What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?

A) 1 B) 2 tan x
C) tan 2 x D) tan (3 x/2)
 
Answer & Explanation Answer: B) 2 tan x

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Q:

The value of (sec245 - cot245) - (sin230 + sin260) is

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

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Q:

If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3  3abc?

A) 189 B) 243
C) 361 D) 486
 
Answer & Explanation Answer: B) 243

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Q:

Shaan got a total of Rs. 912 in the denomination of equal numbers of Rs. 1, Rs. 5 and Rs. 10 coins. How many coins do Shaan posses?

A) 16 B) 57
C) 171 D) 323
 
Answer & Explanation Answer: C) 171

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Q:

If 13x2 = 172 - 92, find the value of x?

A) 16 B) 12
C) 8 D) 4
 
Answer & Explanation Answer: D) 4

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Q:

Calculate the value of 55-5, if the value of √5 = 2.236.

A) 0.809 B) 0.89
C) 0.089 D) 0.807
 
Answer & Explanation Answer: A) 0.809

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Q:

If x = 313- 3-13, then 3x3 + 9x value is

A) 8 B) 9
C) 27 D) 16
 
Answer & Explanation Answer: A) 8

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