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 sinC + sinD =X, then the value of X is?

A) 2cos[(C+D)/2]sin[(C-D)/2] B) 2sin[(C+D)/2]cos[(C-D)/2]
C) 2cos[(C+D)/2]cos[(C-D)/2] D) 2sin[(C+D)/2]sin[(D-C)/2]
 
Answer & Explanation Answer: B) 2sin[(C+D)/2]cos[(C-D)/2]

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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 a - b = -7 and a2+ b2= 85, then find ab.

A) 18 B) -30
C) -44 D) 60
 
Answer & Explanation Answer: A) 18

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Q:

If x – y – √18 = –1 and x + y – 3√2 = 1, then what is the value of 12xy(x2  y2)?

A) 0 B) 1
C) 512√2 D) 612√2
 
Answer & Explanation Answer: D) 612√2

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Q:

If aq-r+br-p-cp-q, then find the value of (pa + qp + rc) is

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

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Q:

Given: 2x - 4 ≤ 2 - x/3 and 2(2x + 5) > 3x - 5, then x can take which of the following values?

A) -14 B) 3
C) 4 D) 14
 
Answer & Explanation Answer: A) -14

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Q:

If Cot θ = 21/20, then what is the value of Cosec θ?

A) 21/29 B) 29/21
C) 20/29 D) 29/20
 
Answer & Explanation Answer: D) 29/20

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Q:

If 2x+ 4(x - 3) < -2 - x < 2x - 1, then find the value of x.

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

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