aptitude : : surds and indices
 
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Important Formulas
  Exercise
   Exercise 1
1.
Find the value of (1/(216)(-(2/3)))+(1/(256)(-(3/4)))+(1/(32)(-(1/5)))
 
A.
109

B.

107
C.
105
D.
102
   
  Answer Discuss in Forum Calculator Workspace
Answer: D
Explanation :
=> (1/(216)(-(2/3)))+(1/(256)(-(3/4)))+(1/(32)(-(1/5)))
                    = (6(3))(2/3)+(4(4))(3/4)+(2(5))(1/5)
                    = 6(2)+4(3)+2
                    = 36+64+2
                    = 102






 
2.
If (a/b)(x-1)= (b/a)(x-3), then the value of x is:
 
A.
7/2

B.

2
C.
1
D.
1/2
   
  Answer Discuss in Forum Calculator Workspace
Answer: B
Explanation :
Here, (a/b)(x-1)= (b/a)(x-3)
=>  x-1 = 3-x
=> 2x = 4
=> x = 2






 
3.
Find the value of 300.
 
A.
17.32

B.

10.62
C.
20.45
D.
15.62
   
  Answer Discuss in Forum Calculator Workspace
Answer: A
Explanation :
√300 = √(10*10*3) = 10√3 = 10*1.732 = 17.32






 
4.
The expression 3*√15√5-4*√27 is equivalent to:
 
A.
√24

B.

√27
C.
√25
D.
3√5
   
  Answer Discuss in Forum Calculator Workspace
Answer: B
Explanation :

=> 3*√15√5-4*√27  = 3*√(3*5)*√5-4*√(9*3)

                                = 3*(√5)2*√3-4*√9*√3

                                = 3*5*√3-4*3*√3

                                = 15√3-12√3

                                = 3√3

                                = √27







 
5.
The ((2+ 2)+((1/(2+2))) is equivalent to:
 
A.
(6+2)/2

B.

(3+2)/2
C.
(6-2)/2
D.
(6+2)/4
   
  Answer Discuss in Forum Calculator Workspace
Answer: A
Explanation :
=> 2+2+(1/(2+2))  = 2+2+(1/(2+2))*((2-2)/(2-2))
                                    = 2+2+((2-2)/(4-2))
                                    = 2+2+((2-2)/2)
                                    = (4+22+2-2)/2
                                    = (6+2)/2






 
6.
Which of the following has the highest value?
(A) 6*(5)(1/3)
(B) 8*(2)(1/3)
(C) 2*(130)(1/3)
(D) (900)(1/3)
 
A.
8*(2)(1/3)

B.

6*(5)(1/3)
C.
2*(130)(1/3)
D.
(900)(1/3)
   
  Answer Discuss in Forum Calculator Workspace
Answer: B
Explanation :

=> (5)(1/3)= (6(3))*5(1/3) = (216)(1/3)*5(1/3)= (1080)(1/3)

=> 8*21/3 = (8(3)).2(1/3)= (512)(1/3).2(1/3)

                  = (1024)(1/3)(80)+ 3*245-1

=> 2*(130)(1/3)= (2(3))(130)(1/3)= (8)(1/3).(130)(1/3)

                           = (1040)(1/3)and (900)(1/3)= (900)(1/3)

Hence it is clear that (1080)(1/3)has the greatest value.

Therefore, 6*5(1/3)is the greatest number.







 
7.
The expression ((7+5)/(7-5)) is equivalent to:
 
A.
6-35

B.

2+35
C.
4-35
D.
6+35
   
  Answer Discuss in Forum Calculator Workspace
Answer: D
Explanation :
=> ((7+5)/(7-5)) = [(7+5)/(7-5)]*[(7+5)/(7+5)]
                                    = ([7+5]2)/((7)2-(5)2))
                                    = (7+5+235)/(7-5)
                                     = 6+35






 
8.
The expression ((2+2+(1/(2+2))+(1/(2-2))) equivalent to:
 
A.
5

B.

2
C.
3
D.
8
   
  Answer Discuss in Forum Calculator Workspace
Answer: B
Explanation :

=> ((2+2+(1/(2+2))+(1/(2-2)))

                      = 2+2+((2-2)/((2+2)(2-2)))+((2+2)/((2-2)(2+2)

                      =2+2+[((2-2)/(4-2))+((2+2)/(2-4))]

                      = 2+2+[((2-2)/2)-((2+2)/2))]

                      = 2+2+((-22)/2)

                      = 2+2-2

                      = 2







 
9.
Value of ((5+3)/(5-3)) will be equivalent to:
 
A.
4+√15

B.

3-√15
C.
2+√15
D.
4-√15
   
  Answer Discuss in Forum Calculator Workspace
Answer: A
Explanation :
((5+3)/(5-3)) = ((5+3)2)/((5)2-(3)2
                               = (5+3+215)/(5-3)
                                = 4+15






 
10.
What will be the value of ((80)+3*(245)-√(125))?
 
A.
185

B.

20√5
C.
22√5
D.
28√2

   
  Answer Discuss in Forum Calculator Workspace
Answer: B
Explanation :
=> ((80)+3*(245)-(125)) = ((16*5)+3*(49*5)-(25*5))
                                                  = 45+215-55
                                                  = 205






 

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