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 question two equations numbered I and II are given,you haveto solve both the equation and choose the correctanswer.

I. x2+ 30x + 81 = 0

II.y2-9y -162 = 0

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

Explanation:

x^2+ 30x + 81 = 0
x^2+ 27x + 3x + 81 = 0
x = -3, -27
y^2-9y -162 = 0
y^2-18y + 9y -162 = 0
y = -9, 18
Hence, no relationship can be established between x and y

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Q:

If [7(5x/3 - 3/2)]/2 + 3/2 = 1/4, then what is the value of x?

A) 35/24 B) 24/35
C) -24/35 D) -35/24
 
Answer & Explanation Answer: B) 24/35

Explanation:
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Q:

If sec (3x – 20°) = cosec (3y + 20°), then what is the value of tan (x + y)?

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

Explanation:
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Q:

At what point does the line 3x + 2y = 12 cuts the Y-axis?

A) (0, 6) B) (0, -6)
C) (6, 0) D) (-6, 0)
 
Answer & Explanation Answer: A) (0, 6)

Explanation:
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Q:

What is the simplified value of [2/(cot A – tan A)]?

A) sin A cos A B) tan 2A
C) sin2 A D) cos2 A
 
Answer & Explanation Answer: B) tan 2A

Explanation:
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Q:

If 17/3 + [3(2x - 5/3)]/2 = 1/6, then what is the value of x?

A) 1 B) 3
C) -3 D) -1
 
Answer & Explanation Answer: D) -1

Explanation:
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Q:

If x2 + (1/x2) = 1, then what is the value of x48 + x42 + x36 + x30 + x24 + x18 + x12 + x6 + 1?

A) -9 B) 0
C) 1 D) 9
 
Answer & Explanation Answer: C) 1

Explanation:
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Q:

If 2x + 2(4 + 3x) < 2 + 3x > 2x + x/2; then x can take which of the following values?

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

Explanation:
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