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 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:

Slope of the line AB is -4/3. Co-ordinates of points A and B are (x, -5) and (-5, 3) respectively. What is the value of x?

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

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Q:

PQ is a tangent to the circle at T. If TR = TS where R and S are points on the circle and ∠RST = 65°, the ∠PTS =

A) 65° B) 130°
C) 115° D) 55°
 
Answer & Explanation Answer: C) 115°

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Q:

The point R(a,b) is first reflected in origin to R1 and R1 is reflected in X-axis to (-5,1). The co-ordinates of point R are?

A) (5,-1) B) (-1,5)
C) (1,-5) D) (5,1)
 
Answer & Explanation Answer: D) (5,1)

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Q:

XYZ is a right angled triangle and ∠Y = 90°. If XY = 2.5 cm and YZ = 6 cm then the circumradius of XYZ is

A) 6.5 cm B) 3.25 cm
C) 3 cm D) 2.5 cm
 
Answer & Explanation Answer: B) 3.25 cm

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Q:

If a:b = 3:8, find the value of (5a ­ 3b)/(2a + b).

A) 9/14 B) 14/9
C) -9/14 D) -14/9
 
Answer & Explanation Answer: C) -9/14

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Q:

In ΔUVW measure of angle V is 90 deg. If cosecU = 13/12, and UV = 2.5cm, then what is the length (in cm) of side VW?

A) 6.5 B) 6
C) 4 D) 5.6
 
Answer & Explanation Answer: B) 6

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Q:

If a + b + c = 0 , then the value of a3 + b3+ c3 is

A) abc B) 2abc
C) 3abc D) 0
 
Answer & Explanation Answer: C) 3abc

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