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:

Find the unit place digit in the expression (159)144 + (114)123 - (110)510 + (213)25

 

A) 3 B) 4
C) 7 D) 8
 
Answer & Explanation Answer: D) 8

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Q:

If 4x = 10247, then what is the value of x?

 

A) 5/7 B) 4/7
C) 3/7 D) 6/7
 
Answer & Explanation Answer: A) 5/7

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Q:

If 3x2 + kx + k = 0 has no solution, then the value of k will satisfy

 

A) k > -12 B) k > 12
C) k < 12 D) 0 < k < 12
 
Answer & Explanation Answer: D) 0 < k < 12

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Q:

Directions: What value should come in place of question mark (?) in the following question?

150% of 460+24% of 650=?

A) 854 B) 846
C) 895 D) 825
 
Answer & Explanation Answer: B) 846

Explanation:

(150 x 460)/100 + (24 x 650)/100

= 690+156

= 846

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Q:

If p & q = p2 + 4pq - q2 then find the value of (3 & 6) + (4 & 5).

 

A) 98 B) 106
C) 116 D) 126
 
Answer & Explanation Answer: C) 116

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Q:

What is the value of (√2/3 - cosec60)?

 

A) (√6-6)/3√3 B) (2-2√3)/√3  
C) (1-√6)/√2   D) (4-√3)/2√3
 
Answer & Explanation Answer: A) (√6-6)/3√3

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Q:

What is the value of 1054 + 196 + 169 + 64 ?

 

A) 33 B) 37
C) 29 D) 31
 
Answer & Explanation Answer: A) 33

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Q:

Simplify : 528 ÷ 2835 ÷ 20112

 

A) 4/5 B) 5/4
C) 4/7 D) 7/4
 
Answer & Explanation Answer: B) 5/4

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