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:

If x - y = -6 and x + y = 16, then x2- y2 is?

A) 96 B) -96
C) 22 D) -22
 
Answer & Explanation Answer: B) -96

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Q:

If 2cosec2A = x, then the value of x is

A) 1/(1 - cosecA) - 1/(1 + cosecA) B) 1/(1 + sinA) + 1/(1 - tanA)
C) 1/(1 + cosA) + 1/(1 - cosA) D) 1/(1 - tanA) - 1/(1 + sinA)
 
Answer & Explanation Answer: C) 1/(1 + cosA) + 1/(1 - cosA)

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Q:

For the inequation x^2–7x + 12 > 0, which one of the following is correct ?

A) 3 < x < 4 B) –∞ < x < 3 only
C) 4 < x < ∞ only D) –∞ < x < 3 or 4 < x < ∞
 
Answer & Explanation Answer: D) –∞ < x < 3 or 4 < x < ∞

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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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Q:

Two labourers A and B are paid a total of Rs. 1120 per day. If A is paid 180 percent of what is paid to B, how much (in Rs) is B paid?

A) 400 B) 720
C) 500 D) 620
 
Answer & Explanation Answer: A) 400

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Q:

At what point does the line 3x + 2y = 12 cuts the Y-axis?

A) (0, 6) B) (0, -6)
C) (6, 0) D) (-6, 0)
 
Answer & Explanation Answer: A) (0, 6)

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Q:

What is the value of Cot 45°+ 1/3 Cosec 60°?

A) √3 + 2 B) (9 + 2√3)/9
C) √3 D) (2√2 + 3)/√6
 
Answer & Explanation Answer: B) (9 + 2√3)/9

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Q:

If a - b = 2 and ab = 24, then what is the value of a3- b3?

A) 280 B) 124
C) 140 D) 152
 
Answer & Explanation Answer: D) 152

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