Simplification Questions

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 equation of the line which passes through the points (3,­2) and (5,3)?

A) 5x ­- 2y = ­-19 B) 5x ­- 2y = 19
C) 5x + 2y = ­31 D)  5x + 2y = -31
 
Answer & Explanation Answer: B) 5x ­- 2y = 19

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Q:

If Sin4A - Cos4A = 1 then (A/2) in degrees is 0° < A  90°

 

A) 60 B) 45
C) 40 D) 30
 
Answer & Explanation Answer: B) 45

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Q:

Coefficient of x2  in (x + 7)(5 - 3x)(3x - 6) is

A) 96 B) -30
C) 42 D) -18
 
Answer & Explanation Answer: B) -30

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Q:

If (cosecA -­ 1)/(cosecA + 1) = x, then the value of x is

A) (sinA/(1 + cosA))2 B) cosA/(1 + sinA)
C) (cosA/(1 + sinA))2 D) sinA/(1 + cosA)
 
Answer & Explanation Answer: C) (cosA/(1 + sinA))2

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Q:

If 4x + 3y = 11 and 3x + 2y = 8, then (x,y) is

A) 2, 0 B) 1, 6
C) 2, 1 D) 5, 6
 
Answer & Explanation Answer: C) 2, 1

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Q:

The point P(3,­-2) divides the segment joining the points (x,0) and (0,y) in the ratio 1:3. Find x and y?

A) x = 4; y = -­8 B) x = ­-3; y = -­8
C) x = 3; y = 8 D) x = ­-3; y = 8
 
Answer & Explanation Answer: A) x = 4; y = -­8

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Q:

If (1/4 of x) - (4/5 of 6/7) equals - 9/7, then value of x is

A) -12 B) -2.4
C) -3.6 D) -14
 
Answer & Explanation Answer: B) -2.4

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Q:

Δ ABC is right angled at B. If m∠A = 60°, then what is the value of 2 Sec C x 1/2 Sin A?

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

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