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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 πsinθ= 1, πcosθ= 1, then (3tan 23θ+1) is

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

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Q:

In ∆ABC if the median AD=1/2 BC, then ∠BAC is

A) 90° B) 45°
C) 60° D) 75°
 
Answer & Explanation Answer: A) 90°

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Q:

A tower stands on the top of a building which is 40 metres high. The angle of depression of a point situated on the ground from the top and bottom of the tower are found to be 60 and 45 deg respectively. What is the height (in metres) of tower?

A) 20√3 B) 30(√3 + 1)
C) 40(√3 – 1) D) 50(√3 – 1)
 
Answer & Explanation Answer: C) 40(√3 – 1)

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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

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Q:

In each of the following questions two equations I and II are given. Solve both the equations and give answer:
I. x2+2x-195=0II. y2+30y+225=0

A) x = y or relation can’t be established between x and y B) x > y
C)  x < y D)  x ≥ y
 
Answer & Explanation Answer: D)  x ≥ y

Explanation:

 I. x2 + 2x - 195 = 0 = (x+15) (x-13) => x = -15, 13

II. y2 + 30y + 225 = 0 = (y+15) (y+15) => y = -15, -15

So x ≥ y

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Q:

A, B and C are three points on a circle with centre O. The tangent at C meets BA produced at T. If ∠ATC = 30° and ∠ACT = 48°,then what is the value of ∠AOB ?

A) 78° B) 96°
C) 102° D) 108°
 
Answer & Explanation Answer: D) 108°

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Q:

If (5x – y)/(5x + y) = 3/7, then what is the value of (4x2 + y2 – 4xy)/(9x2 + 16y2 + 24xy) ?

A) 0 B) 3/7
C) 18/49 D) 1/6
 
Answer & Explanation Answer: A) 0

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Q:

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

I. x2+ 30x + 81 = 0

II.y2-9y -162 = 0

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

Explanation:

x^2+ 30x + 81 = 0
x^2+ 27x + 3x + 81 = 0
x = -3, -27
y^2-9y -162 = 0
y^2-18y + 9y -162 = 0
y = -9, 18
Hence, no relationship can be established between x and y

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