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:

A tetrahedron has 4 vertices. How many edges does it have?

A) 8 B) 12
C) 6 D) 10
 
Answer & Explanation Answer: C) 6

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Q:

What is the value of xy if x - y = 3 and x2+y2=15?

A) 1 B) 3
C) 5 D) 7
 
Answer & Explanation Answer: B) 3

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Q:

Find the value of 6813+6413314

A) 5 B) 6
C) 36 D) 216
 
Answer & Explanation Answer: B) 6

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Q:

What is the value of {sin (90 – x) cos [π – (x – y)]} + {cos (90 – x) sin [π – (y – x)]}?

A) -cos y B) -sin y
C) cos x D) tan y
 
Answer & Explanation Answer: A) -cos y

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Q:

If x + y = 3, then what is the value of x3 + y3 + 9xy?

A) 15 B) 81
C) 27 D) 9
 
Answer & Explanation Answer: C) 27

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Q:

The sum of 2xy(3x + 4y - 5z) and 5yz(2x - 3y) is

A) 6x2y - 8xy2 + 15y2z B) 6x2y + 8xy2 - 15y2z
C) 6x2y + 8xy2 - 15y2z - 20xyz D) 6x2y - 8xy2 + 15y2z + 20xyz
 
Answer & Explanation Answer: B) 6x2y + 8xy2 - 15y2z

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Q:

If [a + (1/a)]2  2[a  (1/a)] = 12, then which of the following is a value of 'a'?

A) – 8 + √3 B) – 8 – √3
C) – 8 + √5 D) None of these
 
Answer & Explanation Answer: D) None of these

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Q:

What should be added to 5(2x-y) to obtain 4(2x - 3y) + 5(x + 4y)?

A) 3x - 13y B) 3x + 13y
C) 13x - 3y D) 13x + 3y
 
Answer & Explanation Answer: B) 3x + 13y

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