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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:

There are 10 dozen apples, 15 dozen mangoes and 20 dozen oranges for selling. If 1/2, 1/3 and 1/4 of them are sold respectively. How many of the total fruits are remaining?

A) 420 B) 380
C) 180 D) 360
 
Answer & Explanation Answer: D) 360

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Q:

For triangle PQR, find equation of altitude PS if co-­ordinates of P, Q and R are (1,2), (2,­-1) and (0,5) respectively?

A) x ­- 3y = ­-7 B) x -­ 3y = -­5
C) x + 3y = ­4 D) x + 3y = ­7
 
Answer & Explanation Answer: C) x + 3y = ­4

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Q:

If cosθ = x2-y2x2+y2, then the value of cotθ is

A) 2xyx2-y2 B) 2xyx2+y2
C) x2+y22xy D) x2-y22xy
 
Answer & Explanation Answer: D) x2-y22xy

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Q:

If Cot θ = 24/7, then what is the value of Sec θ?

A) 7/25 B) 25/24
C) 8/25 D) 9/25
 
Answer & Explanation Answer: B) 25/24

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Q:

What is the simplest form of (1 + cosA)(cosecA ­ cotA)?

A) cosA B) tanA
C) cotA D) sinA
 
Answer & Explanation Answer: D) sinA

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Q:

What is the total number of points in the plane of triangle ABC which is equidistant from the vertices of the triangle?

A) 0 B) 1
C) 2 D) 3
 
Answer & Explanation Answer: B) 1

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Q:

The angle of elevation of the top of a tower from two horizontal points (in opposite sides) at distances of 25 meter and 64 meter from the base of tower are x and 90° - x respectively . The height of the tower will be

A) 39 m B) 89 m
C) 1.6 m D) 40 m
 
Answer & Explanation Answer: D) 40 m

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Q:

If sec θ (cos θ + sin θ) = √2, then what is the value of (2 sin θ)/(cos θ – sin θ)?

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

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