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:

The simplest form of 3774/2958 is

A) 43/19 B) 37/29
C) 31/13 D) 31/23
 
Answer & Explanation Answer: B) 37/29

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Q:

A T.V was sold at a profit of 5% If it had been sold at a profit of 10% , the profit would have been Rs. 1000 more. What is its cost price ?

A) Rs.20000 B) Rs.5000
C) Rs.10000 D) Rs.15000
 
Answer & Explanation Answer: A) Rs.20000

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Q:

If tan x = 1, 0 < x < 90, then what is the value of 2 sin x cos x?

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

Explanation:

tan x = 1

then x = 45

2sin x. cos x = 2× 1/√2 x 1/√2 = 1

an x = 1
then
x = 45
o
2sin x. cos x =
2
×
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Q:

If x - y = 6 and xy = 40, then find x2 + y2 ?

A) 116 B) 80
C) 89 D) 146
 
Answer & Explanation Answer: A) 116

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Q:

If x+1x 0 and x3+1x3 = 0, then the value of x+1x4 is :

A) 9 B) 12
C) 15 D) 16
 
Answer & Explanation Answer: A) 9

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Q:

If 2 cos θ = 2 – sin θ, then what is the value of cos θ?

A) 1 or 3/5 B) 1 or –1/2
C) –1 or–1/2 D) –1 or 3/5
 
Answer & Explanation Answer: A) 1 or 3/5

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Q:

If x = 1/(√2+1) then the value of x2 + 2x - 1 is

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

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Q:

ABC is right angled at B. If mA = 30°, then find the value of (sinC + 1/3).

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

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