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 + 3 ≤ 4x + 4 and 5(4 -­ x) ­- 4 ≥ 5x - ­2; then

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

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Q:

If the value of √42 is approximately 6.480, then what is the approximate value of √(6/7)?

A) 0.925 B) 0.935
C) 0.945 D) 0.955
 
Answer & Explanation Answer: A) 0.925

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Q:

Which of the following is not a quadratic equation?

A) 2x(x + 4) -11 = x(x - 3) + 6 B) 4x(x + 4) -11 = 5x(x - 3) + 5
C) x(x + 2) -15 = x(x - 5) + 11 D) 2x2 + 8x - 11 = 0
 
Answer & Explanation Answer: C) x(x + 2) -15 = x(x - 5) + 11

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Q:

The sum of 2xy(3x + 4y - 5z) and 5yz(2x - 3y) is

A) 6x2y - 8xy2 + 15y2z B) 6x2y + 8xy2 - 15y2z
C) 6x2y + 8xy2 - 15y2z - 20xyz D) 6x2y - 8xy2 + 15y2z + 20xyz
 
Answer & Explanation Answer: B) 6x2y + 8xy2 - 15y2z

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Q:

Reflection of the point (4,-5) in the y-axis is

A) (4,5) B) (-4,-5)
C) (4,-5) D) (-4,5)
 
Answer & Explanation Answer: B) (-4,-5)

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Q:

Find the value of  x3 - y3, if x - y = 4 and xy = 12.

A) 198 B) 208
C) 218 D) 228
 
Answer & Explanation Answer: B) 208

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Q:

Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?

A) 415 B) 465
C) 440 D) Cannot be determined
 
Answer & Explanation Answer: B) 465

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Q:

If cot ­-4π/3 = x, then the value of x is

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

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