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 Simplification Questions

Popular Latest Rated Important Formulae

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 the equation 4x + 3y + 5 = 0 and 6x - ky - 7 = 0 have no solution, then the value of k is

A) -4.5 B) -8
C) 8 D) 4.5
 
Answer & Explanation Answer: A) -4.5

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Q:

The average revenues of 13 consecutive years of a company is Rs 70 lakhs. If the average of first 7 years is Rs 65 lakhs and that of last 7 years is Rs 77 lakhs, find the revenue for the 7th year.

A) Rs 86 lakhs B) Rs 84 lakhs
C) Rs 82 lakhs D) Rs 80 lakhs
 
Answer & Explanation Answer: B) Rs 84 lakhs

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Q:

A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c)?

A) 35/3 B) 37/3
C) – 105/11 D) – 105/13
 
Answer & Explanation Answer: C) – 105/11

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Q:

Expand and simplify (3x + 2)2*(4x -­ 3) -­ (2x3 - 9x2 + 12x -­ 24)

A) 34x3 + 30x2 -­ 32x -­ 12 B) 34x3 + 30x2 -­ 32x + 12
C) 34x3 -­ 30x2 -­ 32x + 12 D) 34x3 -­ 30x2 + 32x -­ 12
 
Answer & Explanation Answer: B) 34x3 + 30x2 -­ 32x + 12

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Q:

Δ DEF is right angled at E. If m∠D = 45%., then Cosec F =

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

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Q:

Product of 6ab, 3b and 4a is

A) 72a2b2 B) 144ab
C) 72ab D) 144a2b2
 
Answer & Explanation Answer: A) 72a2b2

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Q:

The point Q(a,b) is first reflected in y­-axis to Q1 and Q1 is reflected in x­axis to (­-5,3). The co­ordinates of point Q are

A) (­-5,­3) B) (5,-3)
C) (­-5,-3) D) (5,­3)
 
Answer & Explanation Answer: B) (5,-3)

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Q:

In the given questions, two equations numbered I and II are given. Solve both the equation and mark the appropriate answer.

I. x2–5x –24 = 0II. 2y2+ 19y + 35 = 0

A) x > y B) x>y
C) x < y D) x<y
 
Answer & Explanation Answer:

Explanation:

x^2–5x –24 = 0

(x-8) (x+3)

x = 8, -3

II. 2y^2+ 19y + 35 = 0

(2y+7) (y+7)y= -7, -5/2

So can’t be determined

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