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:

(1 + sec 20° + cot 70°)(1 - cosec 20° + tan70°) is equal to

A) 0 B) 1
C) 2 D) 3
 
Answer & Explanation Answer: C) 2

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0 1898
Q:

If a+b=3 then the value of a3+b3+9ab-­27 is

A) 24 B) 25
C) 0 D) 27
 
Answer & Explanation Answer: C) 0

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1 1896
Q:

If a : b = c : d = 1 : 6, then what is the value of a2+c2b2+d2?

A) 1/600 B) 1/60
C) 1/36 D) 1/360
 
Answer & Explanation Answer: C) 1/36

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0 1896
Q:

A crate of egg holds one rotten egg out of every 25 egg in it. If 5 out of 8 rotten eggs are unusable and there are total 10 unusable eggs in the crate,then calculate the number of eggs in the crate.

A) 380 B) 400
C) 420 D) 440
 
Answer & Explanation Answer: B) 400

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5 1893
Q:

If p and q are the roots of the equation x2 –15x + r = 0 and p –q = 1, then what is the value of r ?

A) 55 B) 56
C) 60 D) 64
 
Answer & Explanation Answer: B) 56

Explanation:

In the below equation,

x2–15x + r = 0

sum of roots = p + q = -(-15)/1 = 15 (sum of roots for equation ax2+ bx + c is -b/a)

product of roots = pq = r/1 = r     (product of roots for equation ax2+ bx + c is c/a)

given p –q = 1

also we know that p+q = 15

subtracting the squares of both

(p+q)2 + (p-q)2 = 15^2–1

p2 + q2 + 2pq –p2 –q2 +2pq = 225 -1

4pq = 224

4r = 224

r = 56

 

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0 1876
Q:

If x3  y3 = 81 and x – y = 3, then what is the value of x2 + y2?

A) 18 B) 21
C) 27 D) 36
 
Answer & Explanation Answer: B) 21

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2 1874
Q:

If sec 300° = x, then value of x is

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

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0 1874
Q:

The two roots of a quadratic equation are given as x = 1/7 and x = -1/8 . The equation can be written as:

A) (7x − 1)(8x − 1) = 0 B) (7x − 1)(8x + 1) = 0
C) (7x + 1)(8x − 1) = 0 D) (7x + 1)(8x + 1) = 0
 
Answer & Explanation Answer: B) (7x − 1)(8x + 1) = 0

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0 1869