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:

The difference between two numbers is 1146. When we divide the larger number by smaller we get 4 as quotient and 6 as remainder. Find the larger number

A) 1526 B) 1431
C) 1485 D) 1234
 
Answer & Explanation Answer: A) 1526

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4 1987
Q:

If cot2A -­ cos2A = x, then value of x is

A) tan2Asec2A B) cotAcosA
C) cot2Acos2A D) tanAsecA
 
Answer & Explanation Answer: C) cot2Acos2A

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1 1984
Q:

A bag contains 25 paise, 50 paise and 1 Rs coins. There are 220 coinsinall and the total amount in the bag is Rs. 160. If there arethrice as many 1 Rs. coins as there are 25 paise coins, then what is the number of 50 paise coins?

A) 60 B) 40
C) 120 D) 80
 
Answer & Explanation Answer: A) 60

Explanation:

Let there be x one rupee coin, y 50 paise coin, z 25 paise coinx + y + z = 220......(i)

Total amount = 160

Now, x + (y/2) + z = 160 ......(ii)

⇒4x + 2y + z = 640

Thrice as many 1 re coin as 25 paise

⇒x = 3z ......(iii)

On solving equation (i), (ii) and (iii), we get

z = 40x= 3* 40 = 120y = 220 –(120 + 40 ) = 60

So, 50 paise coin =60

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0 1977
Q:

Tan 45° + Cosec 60° =

A) (1 + 2√2)/2 B) (√3 + 2)/√6
C) 5/√3 D) (3 + 2√3)/3
 
Answer & Explanation Answer: D) (3 + 2√3)/3

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1 1974
Q:

If 4x = √5+ 2, then the value of x - 1/16x is

A) 1 B) -1
C) 4 D) 2√5
 
Answer & Explanation Answer: A) 1

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11 1973
Q:

If  x = a + 1/a, y = a - 1/a, then the value of x4+y4-2x2y2

A) 4 B) 8
C) 16 D) 64
 
Answer & Explanation Answer: C) 16

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0 1965
Q:

If pq(p+q) = 1, then the value of 1p3q3-p3-q3 is equal to

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

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0 1964
Q:

If (1 + secA)/tanA = x, then x is

A) cot(A/2) B) tan(A/2)
C) cosec(A/2) D) sec(A/2)
 
Answer & Explanation Answer: A) cot(A/2)

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6 1962