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 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:

Reflection of the point (­2,5) in the x­ axis is

A) (2,5) B) (-2,­5)
C) (­2,-5) D) (­-2,­-5)
 
Answer & Explanation Answer: D) (­-2,­-5)

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Q:

Simplify 11.9983 = ?

A) 1727.136 B) 1331.136
C) 1685.136 D) 1700.136
 
Answer & Explanation Answer: A) 1727.136

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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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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:

If 2x -­ 3 ≤ 5 + x and 5 -­ x < 1 + 5x; then x can take which of the following values?

A) -1 B) 1
C) 9 D) -9
 
Answer & Explanation Answer: B) 1

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Q:

You purchased two pieces of cloth measring 1.2 m and 1.3 m each at Rs. 330 and Rs. 270 per meter respectively and gave Rs. 1000 at the payment counter. How much cash will you get back?

A) Rs. 253 B) Rs. 604
C) Rs. 649 D) Rs. 235
 
Answer & Explanation Answer: A) Rs. 253

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Q:

If 1 = 2, 3 = 6, 4 = 8, and + = -, what would be the value of 41 + 34 + 13 = ?

A) -88 B) 88
C) 12 D) -12
 
Answer & Explanation Answer: D) -12

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