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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 ab+c=bc+a=Cb+athen which one of the following statements is correct?

A) Each fraction is equal to 1 or -1 B) Each fraction is equal to 1/2 or 1
C) Each fraction is equal to 1/2 or -1 D) Each fraction is equal to 1.2 only
 
Answer & Explanation Answer: C) Each fraction is equal to 1/2 or -1

Explanation:

a/(b+c) = b/(c+a) = c/(a+b)

Taking reciprocal and adding 1 to each ratio we get;

(b+c)/a + 1 = b/(c+a) + 1 = c/(a+b) + 1

Or (a+b+c)/a = (a+b+c)/b = (a+b+c)/c

So this can only be equal when a=b=c or a+b+c = 0

When a=b=c we get

a/(b+c)= ½When a+b+c = 0 we get

b+c = -a

So a/(b+c) = -1

So the ratios are ½ or -1

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Exam Prep: Bank Exams

0 1980
Q:

ΔABC is right angled at B. If m∠A = 45°, then find the value of (cosecC + 1/√3).

A) (3√2+1)/3 B) (2+√3)/2
C) 5/√3 D) (√6+1)/√3
 
Answer & Explanation Answer: D) (√6+1)/√3

Explanation:
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Exam Prep: Bank Exams
Job Role: Bank Clerk

0 1979
Q:

Determine the value of  'a' which satisfies the equation 9a + 40a = 41a

A) 1 B) 2
C) 3 D) 4
 
Answer & Explanation Answer: D) 4

Explanation:
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Exam Prep: Bank Exams , CAT

1 1978
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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3 1976
Q:

In each question two equations numbered I and II are given,you haveto solve both the equation and choose the correctanswer.

I. 5x2+ 28x = -15II. 3y2+ 11y + 6 = 0

A) X > Y B) X ≥ Y
C) X < Y D) X ≤ Y
 
Answer & Explanation Answer:

Explanation:

5x^2+ 28x = -15x = (-3/5, -5)

II. 3y^2+ 11y + 6 = 0y = (-3, -2/3)

So Relationship cannot be established

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Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

0 1974
Q:

In ∆ABC, ∠B=35°, ∠C=65° and the bisector of ∠BAC meets BC in D. Then ADB is

A) 40° B) 75°
C) 90° D) 105°
 
Answer & Explanation Answer: D) 105°

Explanation:
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0 1972
Q:

If tan 45° + cosec 30° = x, then find the value of x.

A) √3 B) (1-2√2)/√2
C) (√3-4)/2√3 D) 3
 
Answer & Explanation Answer: D) 3

Explanation:
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0 1961
Q:

For what value of k, the expression x6– 18x3 + k will be a perfect square?

A) -9 B) 81
C) 9 D) -81
 
Answer & Explanation Answer: B) 81

Explanation:
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0 1960