21 May 2016

SBI Clerk Prelims 2016- Practice Aptitude Questions (Simplification)

SBI Clerk Prelims 2016- Practice Aptitude Questions (Simplification) Set-49:
Dear Readers, Important Practice Aptitude Questions with solution for Upcoming SBI Clerk Exam, candidates those who are preparing for those exams can use this practice questions.

1). The index form of 9√(4/5)3 is
a)   (4/5)1/3
b)   (4/5)3
c)   (4/5)1/2
d)   (4/5)1/27
e)   (4/5)

2). The radical form of (13/25)3/4 is
a)   3√(13/25)4
b)   4√(13/25)3
c)   4√(25/13)3
d)   3√(25/13)4
e)   None of these

3). The value of 5/(121)-1/2 is
a)   -55
b)   1/55
c)   –(1/55)
d)   55
e)   60

4). The value of (512)-3/9 is
a)   1/4
b)   8
c)   1/8
d)   -(1/8)
e)   –(3/7)

5). The value of 3 × 9-(3/2)  ×  91/2 is
a)   1/3
b)   3
c)   27
d)   -(1/3)
e)   None of these

6). The value of(2162/3)1/2 is
a)   3
b)   9
c)   12
d)   6
e)   None of these

7). The value of 27-1/3  × [(27)2/3 / (27)1/3] is
a)   4
b)   3
c)   2
d)   1
e)   None of these

8).The value of (6.25)-1/2 is
a)   0.25
b)   25
c)   1/2.5
d)   2.5
e)   1.5

9).The value of (√63 × √7) / (3√27) is
a)   7
b)   9
c)   21
d)   18
e)   None of these

10). If √3 = 1.732, then the value of (√3 + 1) / (√3 – 1) is
a)   3.732
b)   1/3.732
c)   0.732
d)   2.732
e)   None of these

1). a) 2). b) 3). d) 4). c) 5). a) 6). d) 7). d) 8). c) 9). a) 10). a)

Solution:

1). 9√(4/5)3 = (4/5)3/9 = (4/5)1/3

2). The radical form of (13/25)3/4 = 4√(13/25)3

3). 5 / (121)-1/2 = 5 × (121)1/2 = 5 × (112)1/2
= 5 × 11 = 55

4). (512)-(3/9) = (29)-(3 / 9) = 29 × (- 3 / 9)
= 2-3 = (1 / 2)3 = (1/2) × (1/2) × (1/2) = (1/8)

5). 3 × 9-(3 / 2) × 91/2 = 3 × [32 × (- 3 / 2)] × ( 32 ×(1 / 2))
= 3 × (3)-3 × 3 = 3 × (1/3)3 × 3
= 3 × (1 / 27) × 3 = 1/3

6). (2162 / 3 )1/2 = (63 × (2 / 3))1 / 2 = 62 × (1 / 2 )  = 61 = 6

7). 271 / 3 × (272/3 / 271/3) = 33 × - (1/3) × [(33)2/3 / (33)1/3 ]
= 3-1 × (32 / 3)
= (1/3) × ( 9 / 3 ) = (1 / 3) × 3 = 1

8). (625)-(1/2) = (625 / 100)-1/2 = (25 / 4)-1/2
= (4 / 25)1/2 = (22 / 52)1/2 = (2 / 5)2 × ½
= (2 / 5) or (1 / 2.5)

9). (√63 × √7) / 3√27 = √(63 × 7) / 3√33 = √(441) / 33 ×1/3
= (21 / 3) = 7

10). (√3 + 1) / (√3 - 1)
Rationalising, we have
= [(√3 + 1) / (√3 - 1)] ×  [(√3 + 1) / (√3  + 1)] = (√3 + 1)2 / [(√3)2 – (1)2 ]
[(x + y)2 = x2 + y2 + 2 xy and (x - y) (x + y) = (x)2 – (y)2 ]
= (3 + 1 + 2√3) / (3 - 1) = ( 4 + 2√3) / 2 = [2 (2 + √3)] / 2 = 2 + √3
= 2 + 1.732 = 3.732