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 - b = 1 and ab = 6, then what is the value of a3- b3?

A) 21 B) 23
C) 19 D) 25
 
Answer & Explanation Answer: C) 19

Explanation:
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Q:

If secA + tanA = x, then the value of x is

A) cosA/(1 + sinA) B) √[cosA/(1 - sinA)]
C) √[cosA/(1 + sinA)] D) cosA/(1 - sinA)
 
Answer & Explanation Answer: D) cosA/(1 - sinA)

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Q:

The value of 2.33+0.0272.33-0.69+0.09

A) 2 B) 2.27
C) 2.33 D) 2.6
 
Answer & Explanation Answer: D) 2.6

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Q:

If x2+ y2+ z2= xy + yz + zx, then what is the value of (7x + 3y – 5z)/5x?

A) 0 B) 1
C) 5 D) 33/5
 
Answer & Explanation Answer: B) 1

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Q:

If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P2) + (1/Q2)?

A) 148 B) 189
C) 194 D) 204
 
Answer & Explanation Answer: C) 194

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Q:

If the simple interest on Rs. 1 for 1 month is 1 paisa, then the rate percent per annum will be

A) 10% B) 8%
C) 12% D) 6%
 
Answer & Explanation Answer: C) 12%

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Q:

If x+19x=4, then 9x2+19x2 is

A) 140 B) 142
C) 144 D) 146
 
Answer & Explanation Answer: B) 142

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Q:

What approximate value should come in place of the question mark (?) in the following questions? (You are not expected to calculate the exact value.)

21.003 × 39.998 –209.91 = 126× ?

A) 5 B) 4
C) 3 D) 2
 
Answer & Explanation Answer: A) 5

Explanation:

Take nearest values21.003 × 39.998 –209.91 = 126× ?630 = 126× ?? = 5 (approx)

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