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 slope of the line passing through the points (2,-1) and (x,5) is -1. Find x?

A) 4 B) -4
C) 8 D) -8
 
Answer & Explanation Answer: B) -4

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Q:

If (1+12)(1+14)(1+16)(1+18)(1-13)(1-15)(1-17) = 1+ 1x, then what is the value of x?

A) 6 B) 8
C) 5 D) 7
 
Answer & Explanation Answer: B) 8

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Q:

What are the co­ordinates of the mid point of the segment joining points C(5,­-2) and D(­-1,8).

A) (­-2, ­3) B) (2, 3)
C) (­2, -3) D)  (-2, -­3)
 
Answer & Explanation Answer: B) (2, 3)

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Q:

If 7 + 4x > 3 + 3x and 3x -­ 2 < 5 -­ x; then x can take which of the following values?

A) 2 B) 3
C) 1 D) -5
 
Answer & Explanation Answer: C) 1

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Q:

If cosec 45° - sin 30° = x, then x is

A) 5/√3 B) (√6-1)/√2
C) √3+2 D) (2√2-1)/2
 
Answer & Explanation Answer: D) (2√2-1)/2

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Q:

Which of the following is correct?

A) (4x + 5y)(5x - 4y) = 20x2 + 9xy - 20y2 B) (4x + 5y)(5x - 4y) = 20x2 + 41xy - 20y2
C) (4x + 5y)(5x - 4y) = 20x2 - 9xy + 20y2 D) (4x + 5y)(5x - 4y) = 20x2 - 41xy + 20y2
 
Answer & Explanation Answer: A) (4x + 5y)(5x - 4y) = 20x2 + 9xy - 20y2

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Q:

Coefficient of x in (x + 11)(3 -­ 5x) is _____.

A) 33 B) -5
C) 3 D) -52
 
Answer & Explanation Answer: D) -52

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Q:

What is the value of a2 + b2a3 - b3, when a + b = 8 and a - b = 2?

A) 0.313 B) 0.347
C) 0.368 D) 0.381
 
Answer & Explanation Answer: B) 0.347

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