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 tan A = 1/2 and tan B = 1/3, then what is the value of tan (2A + B)?

A) 1 B) 3
C) 5 D) 9
 
Answer & Explanation Answer: B) 3

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Q:

What is the value of tan 7π/6?

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

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Q:

What is the value of 1/√2 Cot 30° + 1/√3 Cosec 60°?

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

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Q:

The value of 16 - [5 - 2{14 of 2 - (8 ÷ 4 x 2 - 1 + 3}] is

A) -12 B) -9
C) -10 D) -14
 
Answer & Explanation Answer: C) -10

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Q:

If x2+1x2 = 2, then the value of x - 1x is

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

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Q:

What should come in place of question mark (?) in the following question? (You do not have to calculate the exact value.)

(√80.997 - √25.001) × (√120.98 + √16.02) = ?

A) 20 B) 30
C) 40 D) 50
 
Answer & Explanation Answer:

Explanation:

Ans. 
Approximating the values:
(√81 - √25) × (√121 + √16) = ?
(9 - 5) × (11 + 4) = ?
4 × 15 = ?
? = 60

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Q:

If a+b+c = 0, then (a^3 + b^3 + c^3)^2 = ?

A) 27abc B) 9abc
C) 3abc D) 9a^2b^2c^2
 
Answer & Explanation Answer: D) 9a^2b^2c^2

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Q:

θ is a positive acute angle and sinθ ­ cosθ = 0, then the value of secθ + cosecθ is

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

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