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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:

3cosA is equal to

A) 4cos3A + 3cosA B) 4cos3A - 3cosA
C) 3cos3A + 3cosA D) 3cos3A - 3cosA
 
Answer & Explanation Answer: B) 4cos3A - 3cosA

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Q:

Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?

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

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Q:

An army lost 10% of its men in war, 10% of the remaining died due to disease and 10% of the rest were declared disabled. Thus the strength of the army was reduced to 7,29,000 active men. The original strength of the army was

A) 1500000 B) 1000000
C) 1200000 D) 1100000
 
Answer & Explanation Answer: B) 1000000

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Q:

What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]?

A) 0 B) tan2x
C) 1 D) 2 tan x
 
Answer & Explanation Answer: B) tan2x

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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:

If x – 4y = 0 and x + 2y = 24, then what is the value of (2x + 3y)/(2x – 3y)?

A) 9/5 B) 11/5
C) 13/7 D) 9/7
 
Answer & Explanation Answer: B) 11/5

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Q:

If 4x -7 < x - 2 and 5x +2/3 ≥ 3x + 1; then x can take which of the following values?

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

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Q:

If 5x ­- 40 = 3x, then the numerical value of 2x -­ 11 is

A) 29 B) 39
C) 19 D) 9
 
Answer & Explanation Answer: A) 29

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