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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:

10+10(9) =

A) 180 B) 110
C) 100 D) 19
 
Answer & Explanation Answer: C) 100

Explanation:

According to BODMAS Rule,

10 + 10(9)

= 10 + 90

= 100

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3 2212
Q:

If Cosec θ = 25/7 , then what is the value of Cot θ?

A) 24/25 B) 7/24
C) 7/25 D) 24/7
 
Answer & Explanation Answer: D) 24/7

Explanation:
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3 2208
Q:

If each median of an equilateral triangle has a length of 12cm. Then what will be the value of in-radius (in cm) of the equilateral triangle?

A) 3 B) 4
C) 5 D) 6
 
Answer & Explanation Answer: B) 4

Explanation:
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3 2203
Q:

What is the value of sin225°+ sin265°?

A) 0 B) 1
C) 2 D) 4
 
Answer & Explanation Answer: B) 1

Explanation:
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0 2202
Q:

If p and q are the roots of the equation x2 –15x + r = 0 and p –q = 1, then what is the value of r ?

A) 55 B) 56
C) 60 D) 64
 
Answer & Explanation Answer: B) 56

Explanation:

In the below equation,

x2–15x + r = 0

sum of roots = p + q = -(-15)/1 = 15 (sum of roots for equation ax2+ bx + c is -b/a)

product of roots = pq = r/1 = r     (product of roots for equation ax2+ bx + c is c/a)

given p –q = 1

also we know that p+q = 15

subtracting the squares of both

(p+q)2 + (p-q)2 = 15^2–1

p2 + q2 + 2pq –p2 –q2 +2pq = 225 -1

4pq = 224

4r = 224

r = 56

 

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0 2200
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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0 2199
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

Explanation:
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0 2199
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

Explanation:
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