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 x+1x=5, then the value of x1+x+x2 is

A) 1/5 B) 1/6
C) 5 D) 6
 
Answer & Explanation Answer: B) 1/6

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Q:

In an acute-angled triangle ABC is Sin(B+A+C)=32 and tan(C+A-B)=1, then C is equal to

A) 37.5° B) 67.5°
C) 52.5° D) 72.5°
 
Answer & Explanation Answer: C) 52.5°

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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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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:

Which of the following quadratic equations has real roots?

A) 3x2 -­ 5x + 2 = 0 B) 3x2 -­ 4x + 2 = 0
C) 4x2 -­ 3x + 2 = 0 D) 5x2 -­ 2x + 2 = 0
 
Answer & Explanation Answer: A) 3x2 -­ 5x + 2 = 0

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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 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 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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