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 cot(A/2) = x, then the value of x is

A) √[(1 + cosA)/(1 -­ cosA)] B) cosecA -­ cotA
C) √[(1 -­ cosA)/2] D) √[(1 + cosA)/2]
 
Answer & Explanation Answer: A) √[(1 + cosA)/(1 -­ cosA)]

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Q:

What is the value of tan4A + tan2A?

A) sec4A - sec2A B) sec4A + sec2A
C) cosec4A - sec2A D) sec4A + cosec2A
 
Answer & Explanation Answer: A) sec4A - sec2A

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Q:

P(4,2) and R(-2,0) are vertices of a rhombus PQRS. What is the equation of diagonal QS.

A) x - 3y = -2 B) 3x + y = 4
C) 3x + y = -4 D) x - 3y = 2
 
Answer & Explanation Answer: B) 3x + y = 4

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Q:

A spherical lead ball of radius 6 cm is melted and small lead balls of radius 3 mm are made. The total number of possible small lead balls is

A) 4250 B) 4000
C) 8005 D) 8000
 
Answer & Explanation Answer: D) 8000

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Q:

If cot A = n/(n + 1) and cot B = 1/(2n + 1), then what is the value of cot (A + B)?

A) -1 B) 0
C) 1 D) 2
 
Answer & Explanation Answer: A) -1

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Q:

If the expression px3  qx2  7x  6 is completely divisible by x2  x  6, then what is the value of p and q respectively?

A) 0, 1 B) 1, 0
C) 2, 1 D) 1, 2
 
Answer & Explanation Answer: B) 1, 0

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Q:

If 310 × 272 = 92 × 3n then the value of n is

A) 10 B) 12
C) 15 D) 20
 
Answer & Explanation Answer: B) 12

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Q:

On dividing 256a2b2c2 by 64a2, we get

A) 2cxc B) 2bxb
C) 4 bxb.cxc D) 4
 
Answer & Explanation Answer: C) 4 bxb.cxc

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