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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:

What is the value of tanπ4+A×tan3π4+A ?

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

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Q:

2cos[(C+D)/2]sin[(C-D)/2] is equal to

A) sinC + sinD B) sinC - sinD
C) cosC - cosD D) cosC + cosD
 
Answer & Explanation Answer: B) sinC - sinD

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Q:

What is the equation of line whose slope is -1/2 and passes through the intersection of the lines x - y = -1 and 3x - 2y = 0?

A) x + 2y = 8 B) 3x + y = 7
C) x + 2y = -8 D) 3x + y = -7
 
Answer & Explanation Answer: A) x + 2y = 8

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Q:

∆ABC is right angled at B. If m∠A = 30°, then find the value of (sinC + 1/3).

A) 4/3 B) (√3+1)/2
C) (√3+2)/√3 D) (3√3+2)/6
 
Answer & Explanation Answer: D) (3√3+2)/6

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Q:

If 31x + 31y = 403, then what is the average of x and y?

A) 3.5 B) 5
C) 6.5 D) 13
 
Answer & Explanation Answer: C) 6.5

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Q:

The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60°. The height of the tower in meters is

A) √3 B) 5√3
C) 10√3 D) 20√3
 
Answer & Explanation Answer: C) 10√3

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Q:

Two points P and Q are at the distance of x and y (where y > x) respectively from the base of a building and on a straight line. If the angles of elevation of the top of the building from points P and Q are complementary, then what is the height of the building?

A) xy B) √( y/ x)
C) √( x/ y) D) √( xy)
 
Answer & Explanation Answer: D) √( xy)

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Q:

If 2x - 3(2x - 2) > x - 1 < 2 + 2x; then x can take which of the following values?

A) 2 B) -2
C) 4 D) -4
 
Answer & Explanation Answer: B) -2

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