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 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:

What is the value of (1+cosA)/(1-­cosA)?

A) (cosecA ­- cotA)2 B) (cosecA + cotA)2
C) (secA + cotA)2 D) (secA -­ cotA)2
 
Answer & Explanation Answer: B) (cosecA + cotA)2

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Q:

If secθ = cosecq with 0° < θ , q < 90°, then the value of sin (θ + q) is

A) 1 B) 0
C) 2 D) 4
 
Answer & Explanation Answer: A) 1

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Q:

If sec -5π/4 = x, then the value of x is

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

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Q:

If 14/3 + (1/2)(x - 7/3) = -2x/3, then the value of x is?

A) -3 B) 3
C) -6 D) 6
 
Answer & Explanation Answer: A) -3

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Q:

If cotA/(1 + cot2A) = x, then the value of x is

A) sinA B) cosecA
C) secA D) cosA
 
Answer & Explanation Answer: D) cosA

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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:

If a sum of money deposited in a bank at simple interest is doubled in 6 years, then after 12 years, the amount will be

A) 5/2times the original amount B) 3times the original amount
C) 7/2times the original amount D) 4times the original amount
 
Answer & Explanation Answer: B) 3times the original amount

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