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 a(x + y) = b(x - y) = 2ab, then the value of 2(x2 + y2)

A) 2(a2 - b2) B) 2(a2 + b2)
C) 4(a2 - b2) D) 4(a2 + b2)
 
Answer & Explanation Answer: D) 4(a2 + b2)

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Q:

If a + b + c = 9, ab + bc + ca = 26, a3 + b3 = 91, b3 + c3 = 72 and c3 + a3 = 35, then what is the value of abc?

A) 48 B) 24
C) 36 D) 42
 
Answer & Explanation Answer: B) 24

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Q:

If x3-2x=3x, then the value of x2+1x2 will be

A) 3 1/9 B) 3 2/9
C) 2 1/9 D) 2 4/9
 
Answer & Explanation Answer: D) 2 4/9

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Q:

Find the roots of the quadratic equation 27x2 + 57x  -­ 14 = 0

A) ­2/9, 7/3 B) 2/9, ­-7/3
C) 9/2, ­-3/7 D) -9/2, 3/7
 
Answer & Explanation Answer: B) 2/9, ­-7/3

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Q:

If a2+1a2 = 38, then find the value of a-1a?

A) 2 B) 4
C) 6 D) 8
 
Answer & Explanation Answer: C) 6

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Q:

Point Q(-2,b) is the midpoint of segment EF. Co-ordinates of E are (-7,-6) and F are (a,0). What is the value of a and b?

A) a = 3; b = -3 B) a = -3; b = -3
C) a = 3; b = 3 D) a = -3; b = 3
 
Answer & Explanation Answer: A) a = 3; b = -3

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Q:

If 3x -­ 7 = 5x ­- 1, then the numerical value of (x ­- 4)2 is 

A) 1 B) 49
C) -1 D) -49
 
Answer & Explanation Answer: B) 49

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Q:

If tanA -­ tanB = X, then the value of X is

A) (tanA + tanB)/(1 -­ tanAtanB) B) (tanA + tanB)/(1 + tanAtanB)
C) (tanA -­ tanB)/(1-­ tanAtanB) D) (tanA -­ tanB)/(1 + tanAtanB)
 
Answer & Explanation Answer: D) (tanA -­ tanB)/(1 + tanAtanB)

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