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 3x= 4y= 12, then z is equal to

A) xy B) x + y
C) xy/x+Y D) 4x +3y
 
Answer & Explanation Answer: C) xy/x+Y

Explanation:
Taking log of all 3 we get
xln3 = yln4 =
zln12 = k
z = k/ln12 = k / ln(
3*4) = k/ln3 + ln4 = k / (k/x +k/y) = xy / (x+y)
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Q:

If cosec ­4π/3 = x, then the value of x is

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

Explanation:
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Q:

PQR is right angled at Q. If sinP = 12/13, then what is the value of tanR?

A) 5/13 B) 13/5
C) 13/12 D) 5/12
 
Answer & Explanation Answer: D) 5/12

Explanation:
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Q:

The quadratic equation 1+a2x2+2abx+b2-c2=0 has only one root. What is the value of c21+a2 ?

A) a2 B) b2
C) c2 D) ab
 
Answer & Explanation Answer: B) b2

Explanation:
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Q:

If 2x-y2+(3y-2z)2=0, then the ratio of x:y:z is

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

Explanation:
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Q:

2 sec2A is equal to

A) (1 - tanA)2 - (1 + tanA)2 B) √[(1 - tanA)2 + (1 + tanA)2 ]
C) √[(1 - tanA)2 - (1 + tanA)2] D) (1 - tanA)2 + (1 + tanA)2
 
Answer & Explanation Answer: D) (1 - tanA)2 + (1 + tanA)2

Explanation:
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Q:

Simplify: (213 x 213 + 187 x 187)

A) 80338 B) 80438
C) 60338 D) 60438
 
Answer & Explanation Answer: A) 80338

Explanation:
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Q:

If angles of measure (5y + 62°) and (22° + y) are supplementary , then value of y is

A) 16° B) 32°
C) 8° D) 1°
 
Answer & Explanation Answer: A) 16°

Explanation:
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