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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 56 × 75 × 60 × 84 × 210 = 2p × 3q × 5r × 7s, then what is the value of [(p + q)/s] + r?

A) 6 B) 8
C) 12 D) 10
 
Answer & Explanation Answer: B) 8

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Q:

What is the value of cos [(180 – θ)/2] cos [(180 – 9θ)/2] + sin [(180 – 3θ)/2] sin [(180 – 13θ)/2]?

A) sin 2θ sin 4θ B) cos 2θ cos 6θ
C) sin 2θ sin 6θ D) cos 2θ cos 4θ
 
Answer & Explanation Answer: B) cos 2θ cos 6θ

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Q:

If sec 300° = x, then value of x is

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

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Q:

A hydrogen filled balloon ascending at the rate of 18 kmph was drifted by wind. Its angle of elevation at 10th and 15th minutes were found to be 60° and 45° respectively. The wind speed (in whole numbers) during the last five minutes, approximately, is equal to

A) 7 km/hr B) 11 km/ hr
C) 26 km/hr. D) 33 km/hr
 
Answer & Explanation Answer: D) 33 km/hr

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Q:

If x(2x + 3) = 90 and 7y-1/2+ 2y-1/2= y1/2 (x and y are positive numbers), then what is the value of x2+ y2?

A) 45 B) 109
C) 117 D) 126
 
Answer & Explanation Answer: C) 117

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Q:

A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?

A) 12/π+4 B) 6/π+4
C) 3/π+4 D) 6/π+2√2
 
Answer & Explanation Answer: B) 6/π+4

Explanation:
As it is clear that 2r = a where a is the side of the square and
R is the radius of circle
It is given that 2πr + 4a = 12
a = 12/(π+4)
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Q:

If a : b = c : d = 1 : 6, then what is the value of a2+c2b2+d2?

A) 1/600 B) 1/60
C) 1/36 D) 1/360
 
Answer & Explanation Answer: C) 1/36

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Q:

If Cosec θ = 17/8, then what is the value of Cos θ?

A) 15/8 B) 15/17
C) 8/15 D) 17/15
 
Answer & Explanation Answer: B) 15/17

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