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 x, y, z are the three factors of a3 -7a - 6, then value of x+y+z will be

A) 3a B) 3
C) 6 D) a
 
Answer & Explanation Answer: A) 3a

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Q:

Solve the following : 3/4+{3/4 + 3/4 ÷ (3/4 + 3/4)} = ?

A) 0 B) 3/4
C) 1 D) 2
 
Answer & Explanation Answer: D) 2

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Q:

If 2 cos θ = 2 – sin θ, then what is the value of cos θ?

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

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Q:

Solve the following: (−18)[36÷7−(−2)]÷{}(−4)19−(−3)×(−5)={}?

A) -4.5 B) 4.5
C) -2.5 D) 2.5
 
Answer & Explanation Answer: B) 4.5

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Q:

If x - y = 6 and xy = 40, then find x2 + y2 ?

A) 116 B) 80
C) 89 D) 146
 
Answer & Explanation Answer: A) 116

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Q:

If tanθ = 43, then the value of 3sinθ+2cosθ3sinθ-2cosθ ?

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

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Q:

If the value of 3-1.732, then calculate the value of 243-12108-147

A) 1.732 B) -1.464
C) 3.464 D) -1.732
 
Answer & Explanation Answer: D) -1.732

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Q:

If cosec θ + sinθ = 5/2 then the value of cosecθ - sinθ is

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

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