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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:

What is the value of (cos 40° – cos 140°)/(sin 80° + sin 20°)?

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

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Q:

If x + y = 10 and x2 + y2 = 68, then find xy

A) 21 B) 24
C) 25 D) 16
 
Answer & Explanation Answer: D) 16

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Q:

If x2+ x = 19, then what is the value of (x + 5)2+ [1/(x + 5)2]?

A) 77 B) 79
C) 81 D) 83
 
Answer & Explanation Answer: B) 79

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Q:

P is a point outside the circle at distance of 6.5 cm from centre O of the circle. PR be a secant such that it intersects the circle at Q and R. If PQ = 4.5 cm and QR = 3.5 cm, then what is the radius (in cm) of the circle?

A) 1.5 B) 2
C) 2.5 D) 3
 
Answer & Explanation Answer: C) 2.5

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Q:

If a = 73, b = 74 and c = 75, then what is the value of a3 + b3 + c3 – 3abc?

A) 365 B) 444
C) 666 D) 999
 
Answer & Explanation Answer: C) 666

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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

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Q:

∆XYZ is right angled at Y. If tanX = 24/7, then what is the value of cotZ ?

A) 25/7 B) 24/25
C) 7/24 D) 24/7
 
Answer & Explanation Answer: D) 24/7

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Q:

The value of cos220°+cos270° is

A) 0 B) 1
C) 1/2 D) 13
 
Answer & Explanation Answer: B) 1

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