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:

In each of the following questions two equations I and II are given. Solve both the equations and give answer:
I. x2+2x-195=0II. y2+30y+225=0

A) x = y or relation can’t be established between x and y B) x > y
C)  x < y D)  x ≥ y
 
Answer & Explanation Answer: D)  x ≥ y

Explanation:

 I. x2 + 2x - 195 = 0 = (x+15) (x-13) => x = -15, 13

II. y2 + 30y + 225 = 0 = (y+15) (y+15) => y = -15, -15

So x ≥ y

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Q:

In the question, two equations I and II are given. You have to solve both the equations and give answer

x2-11x+28=0y2-18y+81=0

A) x > y B) x < y
C)  x=y, or relation cannot be established between x and y D) x ≥ y
 
Answer & Explanation Answer: B) x < y

Explanation:

x2 – 11x + 28=0

x2 – 7x – 4x + 28=0

x (x-7) – 4 (x-7)=0

(x-4) (x-7)=0 x=4, 7

y2 – 18y + 81=0

y2 –9y – 9y + 81=0

y (y-9) – 9 (y-9)=0

(y-9) (y-9)=0 y=9, 9

So, x<y.

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Q:

If tan θ + cot θ = x, then what is the value of tan4θ + cot4θ?

A) (x3 – 3)2 + 2 B) (x4 – 2x) + 4
C) x2 (x2 – 4) + 2 D) x
 
Answer & Explanation Answer: C) x2 (x2 – 4) + 2

Explanation:
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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

Explanation:
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Q:

If (5/9 of x) ­- (2/5 of 9/4) equals ­ -4/5 then find x.

A) 0.18 B) 0.12
C) 2 D) 0.54
 
Answer & Explanation Answer: A) 0.18

Explanation:
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Q:

For which value of ‘g’ the linear graph of 6x + 12y +9 = 0 and 2x + gy + 3 =0 has infinite number of solutions?

A) 3 B) 4
C) 6 D) 9
 
Answer & Explanation Answer: B) 4

Explanation:
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Q:

Out of the 60 students of a class, 29 took Mathematics, 32 took Biology and 8 took none of the two subjects. How many students took both Mathematics and Biology?

A) 8 B) 9
C) 7 D) 6
 
Answer & Explanation Answer: B) 9

Explanation:

Number of students who took only Mathematics n(m) = 29
Number of students who took only biology n(b) = 32
Total number of students n(t) = 60
Total number of students of both mathematics and biology n(m b) = 60 - 8 = 52
Total number of students who took both = 32 + 29 - 52 = 9

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Q:

If 2 cos θ = 2 – sin θ, then what is the value of cos θ?

A) 1 or 3/5 B) 1 or –1/2
C) –1 or–1/2 D) –1 or 3/5
 
Answer & Explanation Answer: A) 1 or 3/5

Explanation:
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