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 1 + secA = x, then the value of x is

A) sinAtanA/(1 + cosA) B) √[sinAtanA/(1 - cosA)]
C) sinAtanA/(1 - cosA) D) √[sinAtanA/(1 + cosA)]
 
Answer & Explanation Answer: C) sinAtanA/(1 - cosA)

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Q:

If θ is positive acute angle and 7cos2Ɵ + 3sin2Ɵ = 4, then the value of θ is

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

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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)

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Q:

What is the value of cosec 3π/4?

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

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Q:

What is the simplified value of cosec 2A + cot 2A?

A) sec A B) sec (A/2)
C) cot A D) cot2 A
 
Answer & Explanation Answer: C) cot A

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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

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Q:

If secA + tanA = x, then the value of x is

A) cosA/(1 + sinA) B) √[cosA/(1 - sinA)]
C) √[cosA/(1 + sinA)] D) cosA/(1 - sinA)
 
Answer & Explanation Answer: D) cosA/(1 - sinA)

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Q:

If a + b = 4 and ab = 3, then what is the value of a3 + b3?

A) 21 B) 17
C) 28 D) 31
 
Answer & Explanation Answer: C) 28

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