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:

What is the value of (1/√2) Cot 45° + (1/√3) Cosec 60°?

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

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Q:

If 10x/3 + 5/2(2 - x/3) = 7/2, then the value of x is?

A) 3/5 B) -5/3
C) 5/3 D)  -3/5
 
Answer & Explanation Answer: D)  -3/5

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Q:

If x2+ x = 19, then what is the value of (x + 5)2+ [1/(x + 5)2]?

A) 77 B) 79
C) 81 D) 83
 
Answer & Explanation Answer: B) 79

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Q:

What is the unit digit of 15+25+35+...+205 ?

A) 0 B) 5
C) 2 D) 4
 
Answer & Explanation Answer: A) 0

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Q:

If a = 299, b = 298, c = 297 then the value of 2a3 + 2b3 + 2c3 - 6abc is

A) 5154 B) 5267
C) 5364 D) 5456
 
Answer & Explanation Answer: C) 5364

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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

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Q:

Find the unit place in 194102+294103

A) 0 B) 6
C) 8 D) 2
 
Answer & Explanation Answer: A) 0

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Q:

If θ is positive acute angle and 4sin2θ = 3, then the value of tan θ - cot θ/2 is

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

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