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=aCosθCosΦ, y = aCosθSinΦ and z= aSinθ, then the value of x2+ y2 + z2 is

A) 2a2 B) 0
C) 4a2 D) a2
 
Answer & Explanation Answer: D) a2

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Q:

If sinA + sin2A =1 then what is the value of cos2A + cos4A

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

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Q:

What is the simplified value of 22433+393-11253?

A) 593 B) 493
C) 793 D) 1193
 
Answer & Explanation Answer: A) 593

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Q:

If 4(x + 5) -­ 3 > 6 -­ 4x ≥ x -­ 5; then the value of x is

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

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Q:

If x -­ y = ­7 and x + y = 13, then x2 - y2 is

A) 91 B) -30
C) 30 D) -­91
 
Answer & Explanation Answer: D) -­91

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Q:

If a3+1a3 = 2, then the value of a2+1a?

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

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Q:

If the angle of elevation of the sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60m. The height of the pillar is

A) 60(√3+1) m B) 30(√3-1) m
C) 30(√3+1) m D) 60(√3-1) m
 
Answer & Explanation Answer: C) 30(√3+1) m

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Q:

If a+1a2 = 3, then the value of  a3+1a3 is

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

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