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 5(4­-x) - ­4 < 3x - ­2 > 4x - 6; then the value of x is

A) 3 B) 1
C) 2 D) 5
 
Answer & Explanation Answer: A) 3

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Q:

Calculate the total numbers of prime factors in the expression (5)11 x (5)7 x (7)5 x (3)2 x (17)2.

 

A) 35 B)  36
C) 37 D) 38
 
Answer & Explanation Answer: D) 38

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Q:

If (5x – y)/(5x + y) = 3/7, then what is the value of (4x2 + y2  4xy)/(9x2 + 16y2 + 24xy) ?

A) 0 B) 3/7
C) 18/49 D) 1/6
 
Answer & Explanation Answer: A) 0

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Q:

If x + y = 10 and xy = 4, then what is the value of x4 + y4?

A) 8464 B) 8432
C) 7478 D) 6218
 
Answer & Explanation Answer: B) 8432

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Q:

If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, then what is the value of y?

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

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Q:

What is the value of [(tan 5θ + tan 3θ)/4 cos 4θ (tan 5θ – tan 3θ)]?

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

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Q:

If a-b=1 and a3-b3 = 61, then the value of ab will be

A) -20 B) 20
C) 30 D) 60
 
Answer & Explanation Answer: B) 20

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Q:

If 31x + 31y = 403, then what is the average of x and y?

A) 3.5 B) 5
C) 6.5 D) 13
 
Answer & Explanation Answer: C) 6.5

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