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:

If the value of √30  is approximately 5.477, then what is the approximate value of 56 ?

A) 0.853 B) 0.891
C) 0.913 D) 0.937
 
Answer & Explanation Answer: C) 0.913

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Q:

If θ>0, be an acute angle, then the value of it in degrees satisfying cos2θ-3cosθ+2sin2θ=1 is

A) 90° B) 30°
C) 45° D) 60°
 
Answer & Explanation Answer: D) 60°

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Q:

If 3√2 + √18 + √50 = 15.55, then what is the value of √32 + √72?

A) 13.22 B) 10.83
C) 14.13 D) 16.54
 
Answer & Explanation Answer: C) 14.13

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Q:

What is the value of Tan 45° - 1/√3 Sec 60°?

A) (1 - 2√3)/2 B) (√2 - √3)/√6
C) (3 - 2√3)/3 D) (1 - 2√2)/2
 
Answer & Explanation Answer: C) (3 - 2√3)/3

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Q:

Δ LMN is right angled at M. If m∠N = 60 deg., then Tan L =______.

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

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Q:

Which of the following quadratic equations has real roots?

A) 4x2 -­ 9x + 6 = 0 B) 3x2 -­ 2x + 6 = 0
C) 2x2 -­ 7x + 6 = 0 D) x2 -­ 2x + 2 = 0
 
Answer & Explanation Answer: C) 2x2 -­ 7x + 6 = 0

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Q:

What is the value of (4/3) cot2 (p/6) + 3 cos2 (150)  4 cosec2 45 + 8 sin (p/2)?

A) 25/4 B) 1
C) – 7/2 D) 13/2
 
Answer & Explanation Answer: A) 25/4

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Q:

√[(1 ­ sinA)/(1 + sinA)] is equal to?

A) secA -­ tanA B) cosecA -­ cotA
C) secA + tanA D) cosecA + cotA
 
Answer & Explanation Answer: A) secA -­ tanA

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