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 Simplification Questions

Popular Latest Rated Important Formulae

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 cosAcotA/(1 -­ sinA) = x, then the value of x is

A) 1 -­ cosecA B) 1 + cosecA
C) 1 + secA D) 1 -­ secA
 
Answer & Explanation Answer: B) 1 + cosecA

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Q:

In the given questions, two equations numbered I and II are given. Solve both the equation and mark the appropriate answer.

I. x2–5x –24 = 0II. 2y2+ 19y + 35 = 0

A) x > y B) x>y
C) x < y D) x<y
 
Answer & Explanation Answer:

Explanation:

x^2–5x –24 = 0

(x-8) (x+3)

x = 8, -3

II. 2y^2+ 19y + 35 = 0

(2y+7) (y+7)y= -7, -5/2

So can’t be determined

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Q:

The point Q(a,b) is first reflected in y­-axis to Q1 and Q1 is reflected in x­axis to (­-5,3). The co­ordinates of point Q are

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

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Q:

If sec θ (cos θ + sin θ) = √2, then what is the value of (2 sin θ)/(cos θ – sin θ)?

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

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Q:

The average revenues of 13 consecutive years of a company is Rs 70 lakhs. If the average of first 7 years is Rs 65 lakhs and that of last 7 years is Rs 77 lakhs, find the revenue for the 7th year.

A) Rs 86 lakhs B) Rs 84 lakhs
C) Rs 82 lakhs D) Rs 80 lakhs
 
Answer & Explanation Answer: B) Rs 84 lakhs

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Q:

What is the value of sin(11π/6)?

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

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Q:

In the first 10 overs of a cricket game, the run rate was only 3.2. The run rate in the remaining 40 overs to reach the target of 282 runs is

A) 6.4 B) 6.3
C) 6.25 D) 6.5
 
Answer & Explanation Answer: C) 6.25

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Q:

If x = 2 +√3, y = 2 – √3 and z = 1, then what is the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)]?

A) 25 B) 22
C) 17 D) 43
 
Answer & Explanation Answer: A) 25

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