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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 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

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Q:

If tan 45° + cosec 30° = x, then find the value of x.

A) √3 B) (1-2√2)/√2
C) (√3-4)/2√3 D) 3
 
Answer & Explanation Answer: D) 3

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Q:

If x + y = 12 and xy = 32, then what is the value of  x2 + y2 ?

A) 24 B) 144
C) 128 D) 80
 
Answer & Explanation Answer: D) 80

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Q:

If 5 sec θ – 3 tan θ = 5, then what is the value of 5 tan θ – 3 sec θ?

A) 1 B) 2
C) 3 D) 4
 
Answer & Explanation Answer: C) 3

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Q:

Δ DEF is right angled at E. If m∠F = 45, then what is the value of Sin F x Tan F?

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

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Q:

If x + y + z = 22 and xy + yz + zx = 35, then what is the value of (x – y)2 + (y – z)2 + (z – x)2?

A) 793 B) 681
C) 758 D) 715
 
Answer & Explanation Answer: C) 758

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Q:

What approximate value should come at the place of question mark (?) in the following questions (You are not expected to calculate the exact value).

(111.93 × 5) ÷ 14.02 = 11.002 + ?

A) 11 B) 10
C) 29 D) 34
 
Answer & Explanation Answer: C) 29

Explanation:

Ans.
112 × 5 ÷ 14 = 11 + ?
112 × 5 ÷ 14 = 11 + ?
560 ÷ 14 = 11 + ?
40 = 11 + ?
? = 40 - 11 = 29

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Q:

If tanA - cotA = x, then value of x is?

A) (1 + 2cos2A)/(sinA cosA) B) (sinA cosA)/(1 - 2cos2A)
C) (sinA cosA)/(1 + 2cos2A) D) (1 - 2cos2A)/(sinA cosA)
 
Answer & Explanation Answer: D) (1 - 2cos2A)/(sinA cosA)

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