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 Simplification Questions

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 ab-1b=cb-1c=ac-1a, then (ac+ba+cb)

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

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Q:

If x + y = 5, x3 + y3 = 35, then what is the positive difference between x and y?

A) 0 B) 1
C) 5 D) 6
 
Answer & Explanation Answer: B) 1

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Q:

If a - b = 2 and ab = 24, then what is the value of a3- b3?

A) 280 B) 124
C) 140 D) 152
 
Answer & Explanation Answer: D) 152

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Q:

The sum of two numbers is 7 and the sum their squares is 23, their product is equal to:

A) 10 B) 11
C) 12 D) 13
 
Answer & Explanation Answer: D) 13

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0 1340
Q:

If p/q = r/s = t/u = √5, then what is the value of [(3p2 + 4r2 + 5t2)/(3q2 + 4s2 + 5u2)]?

A) 1/5 B) 5
C) 25 D) 60
 
Answer & Explanation Answer: B) 5

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Q:

What is the value of 1x(p-q)+1+1x(q-p)+1?

A) 0 B) 1
C) x D) cant determine
 
Answer & Explanation Answer: B) 1

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Q:

The length of a median of an equilateral triangle is 12√3 cms. Then the area of the triangle is

A) 144 sq. cms B) 288√3 sq. cms
C) 144√3 sq. cms D) 288sq.cms
 
Answer & Explanation Answer: C) 144√3 sq. cms

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Q:

If 3x - 10 = -(2x + 5), then the numerical value of (x - 4)3 is

A) 27 B) 125
C) -125 D) -27
 
Answer & Explanation Answer: D) -27

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