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 Simplification Questions

Popular Latest Rated Important Formulae

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 a--b = 4 and ab = 45, find the value of a3 - b3

A) 604 B) 370
C) 253 D) 199
 
Answer & Explanation Answer: A) 604

Explanation:

(a – b)2 = a2 + b2 -2ab ⇒ 16 = a2 + b2 – 90 ⇒ a2 + b2 = 106 a3 – b3 = (a – b) (a2 + b2 + ab) ⇒ a3 – b3 = 4 X (106 + 45) ⇒ a3 – b3 = 4 X 151 ⇒ a3 – b3 = 604

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Q:

The number whose square is equal to the difference of the squares of 37 and 23 is:-

A) 45.09 B) 28.98
C) 47.09 D) 28
 
Answer & Explanation Answer: B) 28.98

Explanation:

372 – 232 =840 Required number =840 = 28.98

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Q:

0 is the circumference of a triangle ∆ABC. The point A and the chord BC are on the opposite side of O. If ∠BOC=150° then the value of ∠BAC is

A) 65° B) 60°
C) 70° D) 75°
 
Answer & Explanation Answer: D) 75°

Explanation:
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Q:

If one more cobbler is hired the output of a shoe making unit will increase from 50 pairs of shoes to 55 pairs per day, but then the shoe making unit will have to reduce the price of a pair of shoes from Rs 3200 to Rs 3000 per pair to sell the additional output, the marginal revenue product of the last cobbler is

A) Rs 1000 B) Rs 5000
C) Rs 4000 D) Rs 200
 
Answer & Explanation Answer: B) Rs 5000

Explanation:
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Q:

If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 9, then what is the value of x3 + y3 + z3 – 3xyz?

A) 81 B) 361
C) 729 D) 6561
 
Answer & Explanation Answer: C) 729

Explanation:
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Q:

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

A) cosecA + cotA B) cosecA­ - cotA
C) cosec2A + cot2A D) √[cosec2A + cot2A]
 
Answer & Explanation Answer: A) cosecA + cotA

Explanation:
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Q:

What is the value of [tan2 (90 – θ) – sin2 (90 – θ)] cosec2 (90 – θ) cot2 (90 – θ)?

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

Explanation:
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Q:

If 17/3 + [3(2x - 5/3)]/2 = 1/6, then what is the value of x?

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

Explanation:
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