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 angles of measure (5y + 62°) and (22° + y) are supplementary , then value of y is

A) 16° B) 32°
C) 8° D) 1°
 
Answer & Explanation Answer: A) 16°

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Q:

The quadratic equation 1+a2x2+2abx+b2-c2=0 has only one root. What is the value of c21+a2 ?

A) a2 B) b2
C) c2 D) ab
 
Answer & Explanation Answer: B) b2

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Q:

If sinC - sinD = x, then value of x is

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

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Q:

If x and y are natural numbers such that x + y = 2017, then what is the value of ( 1)x+ ( 1)y?

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

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Q:

In a school there are 1500 students, 44% of them are girls. Monthly fee of each boy is 540 and fee of each girl is 25% less than that of a boy. The sum of fees of boys & girl is

A) Rs. 720600 B) Rs. 720800
C) Rs. 720900 D) Rs. 721000
 
Answer & Explanation Answer: C) Rs. 720900

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Q:

If x=8+215, then what is the value of x+1x?

A) 2√15 B) 3√5
C) (3√5+√3)/2 D) 3√2+3
 
Answer & Explanation Answer: C) (3√5+√3)/2

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Q:

If 2/3(6x/5 - 1/4) + 1/3 = 9x/5, then what is the value of x?

A) 1/6 B) -1/6
C)  1/5 D) -1/5
 
Answer & Explanation Answer: A) 1/6

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Q:

ΔABC is right angled at B. If m∠A = 45°, then find the value of (cosecC + 1/√3).

A) (3√2+1)/3 B) (2+√3)/2
C) 5/√3 D) (√6+1)/√3
 
Answer & Explanation Answer: D) (√6+1)/√3

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