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 (cosec2A - 1) = x, then the value of x is

A) tanA B) sinA
C) cosA D) cotA
 
Answer & Explanation Answer: D) cotA

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Q:

What is the value of cosec 5π/3?

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

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Q:

If 4(2x - ­4) -­ 2 > 3x -­ 1 ≥ 4x - ­7, then x can take which of the following values?

A) 7 B) 6
C) 2 D) 0
 
Answer & Explanation Answer: B) 6

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Q:

Square of (7 ­- 4x) is

A) 16x2 - 28x + 49 B) 49 -­ 28x ­- 16x2
C) 49 - ­ 56x -­ 16x2 D) 16x2 - 56x + 49
 
Answer & Explanation Answer: D) 16x2 - 56x + 49

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Q:

Find k, if the line 4x - y = 1 is perpendicular to the line 5x - ky = 2?

A) 20 B) -20
C) 4 D) -4
 
Answer & Explanation Answer: B) -20

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Q:

If tan2A - tan2B = x, then the value of x is

A) (sin2A - sin2B)/(cos2A cos2B) B) (sin2A sin2B)/(cos2A - cos2B)
C) (sin2A + sin2B)/(cos2A cos2B) D) (sin2A sin2B)/(cos2A + cos2B)
 
Answer & Explanation Answer: A) (sin2A - sin2B)/(cos2A cos2B)

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Q:

What is the x-intercept of line joining (4, 2) and (6, 3)?

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

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Q:

What is the reflection of the point (3,-5) in the origin?

A) (-3, -5) B) (5,-3)
C) (-5,-3) D) (-3, 5)
 
Answer & Explanation Answer: D) (-3, 5)

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