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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 cos ­-11π/6 = x, then the value of x is

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

Explanation:
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Q:

If a + b + c = 11 and ab + bc + ca = 17, then what is the value of a3 + b3 + c3 – 3abc?

A) 121 B) 168
C) 300 D) 770
 
Answer & Explanation Answer: D) 770

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Q:

If a - b = 1 and ab = 6, then what is the value of a3- b3?

A) 21 B) 23
C) 19 D) 25
 
Answer & Explanation Answer: C) 19

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Q:

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

21.003 × 39.998 –209.91 = 126× ?

A) 5 B) 4
C) 3 D) 2
 
Answer & Explanation Answer: A) 5

Explanation:

Take nearest values21.003 × 39.998 –209.91 = 126× ?630 = 126× ?? = 5 (approx)

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Q:

If cosθ1-sinθ+cosθ1+sinθ = 4, then the value of θ (0°<θ<90°)?

A) 60° B) 45°
C) 30° D) 35°
 
Answer & Explanation Answer: A) 60°

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Q:

If 5+x+5-x5+x-5-x = 3,then what is the value of x ?

A) 5/2 B) 25/3
C) 4 D) 3
 
Answer & Explanation Answer: D) 3

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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:

What should come in place of question mark (?) in the following question? (You do not have to calculate the exact value.)

(√80.997 - √25.001) × (√120.98 + √16.02) = ?

A) 20 B) 30
C) 40 D) 50
 
Answer & Explanation Answer:

Explanation:

Ans. 
Approximating the values:
(√81 - √25) × (√121 + √16) = ?
(9 - 5) × (11 + 4) = ?
4 × 15 = ?
? = 60

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