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:

What is the simplified value of 

117-16-116-15+115-14-114-13+113-12 ?

A) 4 – 2√3 B) √17 – 3√2
C) √17 + √12 D) 4 + 2√3
 
Answer & Explanation Answer: C) √17 + √12

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Q:

0.33 + 0.23 0.3 - 0.22 = ?

 

A) 5/2 B) 2
C) 7/2 D) 3/2
 
Answer & Explanation Answer: C) 7/2

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Q:

Select the option that can replace the '?' symbol in the following equation.

 

122 + 345 - 1 x 1011 ÷ 337 = ?

 

A) 446 B) 644
C) 460 D) 464
 
Answer & Explanation Answer: D) 464

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Q:

The two equations x - 4y = 0 and 4x + 3y = 19 have a solution (a, b). Find the value of aba + 4b.

 

A) 1/4 B) 1/2
C) 1 D) 23
 
Answer & Explanation Answer: B) 1/2

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Q:

If 3x2 + kx + k = 0 has no solution, then the value of k will satisfy

 

A) k > -12 B) k > 12
C) k < 12 D) 0 < k < 12
 
Answer & Explanation Answer: D) 0 < k < 12

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Q:

Use continuity to evaluate the limit.

limx128+x8+x

 

A) 1 B) 2
C) 4 D) 0
 
Answer & Explanation Answer: A) 1

Explanation:

Since, we have that,

The numerator and denominator is (8+x), which is a polynomial is continuous for all the real numbers i.e. for all x belonging to .

Thus, the limit exists and is given by,

limx128+x8+x = 8+128+12= 1.

 

 

 

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Q:

ΔABC is right angled at B. If cotA = 8/15, then what is the value of cosC ?

 

A) 15/8   B) 8/17  
C) 17/15   D) 15/17
 
Answer & Explanation Answer: D) 15/17

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Q:

Find the dividend if the divisor is (x+2), quotient is (4x-5) and the remainder is 12.

 

A) 4x2+5x+2 B) 4x2+3x+2
C) 4x2-3x+2 D) 4x2+3x-2
 
Answer & Explanation Answer: B) 4x2+3x+2

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