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 + y + z = 22 and xy + yz + zx = 35, then what is the value of (x  y)2 + (y  z)2 + (z  x)2?

A) 793 B) 681
C) 758 D) 715
 
Answer & Explanation Answer: C) 758

Explanation:
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2 1785
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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0 1783
Q:

If a+b=5 and a­b=3, then the value of (a2+b2) is

A) 17 B) 18
C) 19 D) 20
 
Answer & Explanation Answer: A) 17

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0 1776
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:

What will come in the place of question mark (?) in the following question (You do not have to calculate the exact value)?

24.97% of 84.01 ÷ 6.995 = ?

A) 3 B) 6
C) 9 D) 12
 
Answer & Explanation Answer: A) 3

Explanation:

Ans. 
25% of 84 ÷ 7 = ?
[(25 × 84)/100]÷ 7 = ?
21÷ 7 = ?
? = 3

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0 1773
Q:

If a + b = ­ 8 and a2 + b2 = 34, then value of ab is

A) 30 B) 64
C) 98 D) 15
 
Answer & Explanation Answer: D) 15

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0 1771
Q:

If √(1 - sin2A) = x, then the value of x is

A) tanA B) cosA
C) cosecA D) secA
 
Answer & Explanation Answer: B) cosA

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1 1769
Q:

The zeros of the cubic polynomial 2x3-x2-2x+1 are a, b and c respectively. Find a+b+c :

A) -1 B) 2
C) 1 D) none
 
Answer & Explanation Answer: D) none

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0 1769