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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:

If sin 3θ sec 2θ = 1, then what is the value of [3 tan2(5θ/2) – 1]?

A) 0 B) 1
C) 2 D) 3
 
Answer & Explanation Answer: C) 2

Explanation:
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Q:

If a = √2 + 1, b = √2 - 1 then the value of 1a+1+1b+1 ?

A) 0 B) 1
C) 2 D) 3
 
Answer & Explanation Answer: B) 1

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Q:

A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?

A) 12/π+4 B) 6/π+4
C) 3/π+4 D) 6/π+2√2
 
Answer & Explanation Answer: B) 6/π+4

Explanation:
As it is clear that 2r = a where a is the side of the square and
R is the radius of circle
It is given that 2πr + 4a = 12
a = 12/(π+4)
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Q:

If x3 – y3 = 81 and x – y = 3, then what is the value of x2 + y2?

A) 18 B) 21
C) 27 D) 36
 
Answer & Explanation Answer: B) 21

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Q:

In the question given below, two equations are provided. Solve the equations and establish the relationship between x and y

I. 2x2-13x-189=0 II. 2y2-3y-189=0

A) x>y B)  x≥y
C)  x<y D) x≤y
 
Answer & Explanation Answer:

Explanation:

I. 2x2 - 13x - 189 = 0 2x2 - 27x + 14x - 189 = 0 x(2x - 27) + 7(2x - 27) = 0 x = -7, 27/2

II. 2y2 - 3y - 189 = 0 2y2 - 21y + 18y - 189 = 0 y(2y - 21) + 9(2y - 21) = 0 y = -9, 21/2

When x, as well as y, have both positive and negative values then no relationship can be established between them because if we consider x to be positive then the negative value of y will be lesser than x. If we consider x to be negative then positive value of y will be greater than x.

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Q:

If 3P/5 = 7Q/2 = 7R/5, then what is the ratio of p, Q and R respectively?

A) 3 : 2 : 5 B) 3 : 35 : 14
C) 5 : 7 : 5 D) 35 : 6 : 15
 
Answer & Explanation Answer: D) 35 : 6 : 15

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Q:

If x(2x + 3) = 90 and 7y-1/2+ 2y-1/2= y1/2 (x and y are positive numbers), then what is the value of x2+ y2?

A) 45 B) 109
C) 117 D) 126
 
Answer & Explanation Answer: C) 117

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Q:

What is the value of cos [(180 – θ)/2] cos [(180 – 9θ)/2] + sin [(180 – 3θ)/2] sin [(180 – 13θ)/2]?

A) sin 2θ sin 4θ B) cos 2θ cos 6θ
C) sin 2θ sin 6θ D) cos 2θ cos 4θ
 
Answer & Explanation Answer: B) cos 2θ cos 6θ

Explanation:
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