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 slope of the line, perpendicular to the line 3x - 6y = 4?

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

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Q:

Out of the 60 students of a class, 29 took Mathematics, 32 took Biology and 8 took none of the two subjects. How many students took both Mathematics and Biology?

A) 8 B) 9
C) 7 D) 6
 
Answer & Explanation Answer: B) 9

Explanation:

Number of students who took only Mathematics n(m) = 29
Number of students who took only biology n(b) = 32
Total number of students n(t) = 60
Total number of students of both mathematics and biology n(m b) = 60 - 8 = 52
Total number of students who took both = 32 + 29 - 52 = 9

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Q:

What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)?(55.01+16.0003)×22.01÷10.998 =?

A) 190 B) 130
C) 110 D) 142
 
Answer & Explanation Answer: D) 142

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Q:

If cot(A/2) = x, then the value of x is

A) cosecA -­ cotA B) cosecA + cotA
C) secA + cotA D) secA -­ cotA
 
Answer & Explanation Answer: B) cosecA + cotA

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Q:

2*[­0.3(1.3 + 3.7)] of 0.8 = ?

A) ­1.92 B) -0.72
C) 2.16 D) -­2.4
 
Answer & Explanation Answer: D) -­2.4

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Q:

On dividing 8a2b2c2 by 4a2, we get

A) 2b2 B) 2c2
C) 2b2c2 D) 2
 
Answer & Explanation Answer: C) 2b2c2

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Q:

If x2-2x+1=0, then the value of x4+1x4 is

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

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Q:

What is the value of tan 1° tan 2° tan 3°....... tan 89°?

A) 0 B) 1
C) 2 D) infinity
 
Answer & Explanation Answer: B) 1

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