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 a--b = 4 and ab = 45, find the value of a3 - b3

A) 604 B) 370
C) 253 D) 199
 
Answer & Explanation Answer: A) 604

Explanation:

(a  b)2 = a2 + b2 -2ab  16 = a2 + b2  90  a2 + b2 = 106 a3  b3 = (a  b) (a2 + b2 + ab)  a3  b3 = 4 X (106 + 45)  a3  b3 = 4 X 151  a3  b3 = 604

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Q:

What is the simplified value of (1– sin A cos A)(sin A + cos A)?

A) sin2A – cos2A B) sin3A + cos3A
C) 0 D) 1
 
Answer & Explanation Answer: B) sin3A + cos3A

Explanation:
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Q:

If 1 + secA = x, then the value of x is

A) sinAtanA/(1 + cosA) B) √[sinAtanA/(1 - cosA)]
C) sinAtanA/(1 - cosA) D) √[sinAtanA/(1 + cosA)]
 
Answer & Explanation Answer: C) sinAtanA/(1 - cosA)

Explanation:
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Q:

If (4a-3)2=0, then the value of 64a3+12a+13 is

A) 0 B) 11
C) 22 D) 33
 
Answer & Explanation Answer: C) 22

Explanation:
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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 x - 1/x = 1 then what is the value of 1x1x-1-1x+1+1x2+1-1x2-1?

A) ±√5 B) 2/5
C) ±2/√5 D) ±√5/2
 
Answer & Explanation Answer: C) ±2/√5

Explanation:
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Q:

If Sec θ = 5/3, then what is the value of Cosec θ?

A) 0.8 B) 1.25
C) 4/3 D) 3/4
 
Answer & Explanation Answer: B) 1.25

Explanation:
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Q:

What is the value of (cos 40° – cos 140°)/(sin 80° + sin 20°)?

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

Explanation:
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