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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:

P(3,1) and R(-7,5) are vertices of a rhombus PQRS. What is the equation of diagonal QS?

A) 5x - 2y = 16 B) 5x - 2y = -16
C) 5x + 2y = -16 D) 5x + 2y = 16
 
Answer & Explanation Answer: B) 5x - 2y = -16

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Q:

What is the value of [cos (90 + A)÷sec (270 – A)] + [sin (270 + A)÷cosec (630 – A)]?

A) 3 sec A B) tan A sec A
C) 0 D) 1
 
Answer & Explanation Answer: D) 1

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Q:

In ∆ABC, ∠B=35°, ∠C=65° and the bisector of ∠BAC meets BC in D. Then ADB is

A) 40° B) 75°
C) 90° D) 105°
 
Answer & Explanation Answer: D) 105°

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Q:

If A = 0.216 + 0.0080.36+0.04-0.12 & B = 0.729-0.0270.81+0.09+0.27, then what is the value of A2+B22 ?

A) 0.8 B) 1
C) 1.4 D) 2.2
 
Answer & Explanation Answer: B) 1

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Q:

If ab+c=bc+a=Cb+athen which one of the following statements is correct?

A) Each fraction is equal to 1 or -1 B) Each fraction is equal to 1/2 or 1
C) Each fraction is equal to 1/2 or -1 D) Each fraction is equal to 1.2 only
 
Answer & Explanation Answer: C) Each fraction is equal to 1/2 or -1

Explanation:

a/(b+c) = b/(c+a) = c/(a+b)

Taking reciprocal and adding 1 to each ratio we get;

(b+c)/a + 1 = b/(c+a) + 1 = c/(a+b) + 1

Or (a+b+c)/a = (a+b+c)/b = (a+b+c)/c

So this can only be equal when a=b=c or a+b+c = 0

When a=b=c we get

a/(b+c)= ½When a+b+c = 0 we get

b+c = -a

So a/(b+c) = -1

So the ratios are ½ or -1

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Q:

Determine the value of  'a' which satisfies the equation 9a + 40a = 41a

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

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Q:

∆XYZ is right angled at Y. If m ∠Z = 60. What is the length (in cm) of YZ, if ZX = 9√3 cm?

A) 3√3 B) 3√3/2
C) 9√3/2 D) √3
 
Answer & Explanation Answer: C) 9√3/2

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Q:

If 4x - 5(2x - 1) > 2x + 3 > 2 - 3x; then x can take which of the following values?

A) 1 B) 0
C) 2 D) 3
 
Answer & Explanation Answer: B) 0

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