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 = 2 , b = ­3 then the value of 27a3 - 54a2b + 36ab2 - 8b3 is

A) 1562 B) 1616
C) 1676 D) 1728
 
Answer & Explanation Answer: D) 1728

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Q:

A spherical lead ball of radius 6 cm is melted and small lead balls of radius 3 mm are made. The total number of possible small lead balls is

A) 4250 B) 4000
C) 8005 D) 8000
 
Answer & Explanation Answer: D) 8000

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0 1601
Q:

If Cot θ = 21/20, then what is the value of Sec θ?

A) 29/21 B) 21/29
C) 29/20 D) 20/29
 
Answer & Explanation Answer: A) 29/21

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1 1600
Q:

If (x – 2) and (x + 3) are the factors of the equation x2 + k1x + k2 = 0, then what are the values of k1 and k2?

A) k1 = 6, k2 = – 1 B) k 1 = 1, k 2 = – 6
C) k 1 = 1, k2 = 6 D) k1 = – 6, k2 = 1
 
Answer & Explanation Answer: B) k 1 = 1, k 2 = – 6

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0 1599
Q:

If x2 + (1/x2) = 31/9 and x > 0, then what is the value of x3 + (1/x3)?

A) 70/9 B) 154/27
C) 349/27 D) 349/7
 
Answer & Explanation Answer: B) 154/27

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2 1596
Q:

P(3,1) and R(-7,5) are vertices of a rhombus PQRS. What is the equation of diagonal QS?

A) 5x - 2y = 16 B) 5x - 2y = -16
C) 5x + 2y = -16 D) 5x + 2y = 16
 
Answer & Explanation Answer: B) 5x - 2y = -16

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0 1594
Q:

Value of (4a2+ 12ab + 9b2)/(2a + 3b) is

A) 2a - 3b B) 2a + 3b
C) 2a D) 3b
 
Answer & Explanation Answer: B) 2a + 3b

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0 1593
Q:

If x3 = 62 - 32, then the value of x is

A) 9 B) 6
C) 3 D) 1
 
Answer & Explanation Answer: C) 3

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0 1586