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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:

The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be α and β (α>β). The height of the tower is h unit. A possible distance (in the same unit) between the points is

A) h(cotβ-cotα)cos(α+β) B) h(cotα - cotβ)
C) h(tanβ - tanα)tanα tanβ D) h(cotα+cotβ)
 
Answer & Explanation Answer: D) h(cotα+cotβ)

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Q:

What is the value of Cot 45° + Cosec 60°?

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

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Q:

What is the simplified value of (sec4 A – tan2 A) – (tan4 A + sec2 A)?

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

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Q:

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

A) -2 B) 3
C) 5 D) -1
 
Answer & Explanation Answer: D) -1

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Q:

In a circle with centre O, AB is a diameter and CD is a chord which is equal to the radius OC. AC and BD are extended in such a way that they intersect each other at a point P, exterior to the circle. The measure of ∠APB is

A) 30° B) 45°
C) 60° D) 90°
 
Answer & Explanation Answer: C) 60°

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Q:

Determine the value of a+1b-1 when ab = 343.

A) 9 B) 64
C) 125 D) 216
 
Answer & Explanation Answer: B) 64

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Q:

What is the equation of the line if its slope is ­2/5 and y-­intercept is 6?

A) 2x + 5y = 6 B) 2x + 5y = 30
C) 2x - 5y = 6 D) 2x + 5y = ­-30
 
Answer & Explanation Answer: B) 2x + 5y = 30

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Q:

If 5x + 4(1 -­ x) > 3x - ­4 > 5x/3 -­ x/3; then x can take which of the following values?

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

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