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:

The first and last terms of an arithmetic progression are 25 and ­52. What is the sum of the series if it has 12 terms?

A) -162 B) -110
C) 162 D) 110
 
Answer & Explanation Answer: A) -162

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Q:

In the given figure, from the point P two tangents PA and PB are drawn to a circle with centre Oand radius 5 cm. From the point O, OC and OD are drawn parallel to PA and PB respectively. If the length of the chord ABis 5 cm, then what is the value (in deg) of COD?

A) 90 B) 120
C) 150 D) 135
 
Answer & Explanation Answer: B) 120

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Q:

What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(4, 0) and C(-2, 2)?

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

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Q:

What is the value of (cos45° + 1/3) ?

A) 2+√3 B) (2√2+1)/√2
C) (3+√2)/3√2 D) 5/√3
 
Answer & Explanation Answer: C) (3+√2)/3√2

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Q:

If 7x ­- 5y = 13 and 2x -­ y = 5, then (x -­ y) is

A) 3 B) 4
C) 5 D) 1
 
Answer & Explanation Answer: D) 1

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Q:

In ΔABC measure of angle B is 90 deg. If cosA = 5/13, and AB = 10 cm, then what is the length (in cm) of side BC?

A) 26 B) 24
C) 25 D) 5
 
Answer & Explanation Answer: B) 24

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Q:

The co-ordinates of the centroid of a triangle ABC are (3,-2). What are the co-ordinates of vertex C if co-ordinates of A and B are (-2,5) and (6,-2) respectively?

A) (-5,-9) B) (5,-9)
C) (5,9) D) (-5,9)
 
Answer & Explanation Answer: B) (5,-9)

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Q:

If tan π/3c + cosec π/6c = x, then x is

A) (1-√2)/√2 B) (√3+4)/2√3
C) √3+2 D) (2√2-1)/2
 
Answer & Explanation Answer: C) √3+2

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