# Railway Exam Aptitude Questions(Simplification)

Railway Exam Aptitude Questions(Simplification) Set-7:
Dear Readers, Here we have given Aptitude from Time& Work Questions for Railway Exam 2016. Candidates those who are all preparing for these exams can use this material.

1). [13 (4 / 7) ร13 (4 / 7) – 8 (3 / 7) ร 8 (3 / 7) ] / [13 (4 / 7) – 8 (3 / 7)]  to get
a)   18
b)   22
c)   20
d)   24
2). If x = 1 + โ2 + โ3, then the value of (2x4 โ 8x3 โ 5x+ 26x โ 28) is
a)   6 โ6
b)   0
c)   3 โ6
d)   2โ6
3). If x [(3) โ 2 / x] = 3 / x, x โ  0, then the value of x2 + (1 / x) is
a)   2 (1 / 3)
b)   2 (2 / 3)
c)   2 (4 / 9)
d)   2 (5 / 9)
4). If x โ (1 / x) = 4, then [x + (1 / x)] is equal to
a)   5โ2
b)   2โ5
c)   4โ2
d)   4โ5
5).[(50)3 + (-30)3 + (-20)3 ] is equal to
a)   170000
b)   -15000
c)   90000
d)   – 90000
6).The value of (0.98)3 + (0.02)3 + 3 x 0.98 x 0.02 โ 1 is
a)   1.98
b)   1.09
c)   1
d)   0
7).If x = 0.5 and y = 0.2, then the value of โ0.6 ร (3y)x is
a)   1.0
b)   0.5
c)   0.6
d)   1.1
8).(137 ร 137 + 137 ร 133 + 133 ร 133) / (137 ร 137 ร 137 –  133 ร 133 ร 133) is equal to
a)   4
b)   270
c)   1 / 4
d)   1 / 270
9).The value of (1 / 2) + [ (1 / 2) ร (1 / 2) ] / { (1 / 2) ร (1 / 2) / (1 / 2) + ( ( 1 / 2) / (1 / 2) ) } ] is
a)   2 / 3
b)   1 / 2
c)   1 / 4
d)   1 / 5
10).(8 / 125)-4/3 simplifies to
a)   625 / 16
b)   625 / 8
c)   625 / 32
d)   16 / 625
1). b) 2). a) 3). c) 4). b) 5). c) 6). d) 7). c) 8). c) 9). a) 10). a)
Solution:

1). A = 13(4 / 7) and b = 8(3 / 7)
Expression = (a ร a โ b ร b) / (a โ b)
=(a2 โ b2) / (a โ b) = 13(4 / 7) + 8(3 / 7) = 22

2). x = 1 + โ2 + โ3
x – 1 = โ2 + โ3
On squaring both sides, we get
x2 โ 2x + 1 = 2 + 3 + 2โ6
x2 โ 2x  = 4 + 2โ6                     โฆ(i)
x2 โ 2x  – 4 = 2โ6
on squaring both sides, we get
x4 + 4x2 + 16 โ 4x3 + 16x โ 8x2 = 24
x4 โ 4x3 – 4x2 + 16x โ 8 = 0
2x4 โ 8x3 – 8x2 + 32x โ 16 = 0
2x4 โ 8x3 – 5x2 + 26x โ 28 = 0
= 3xโ 6x โ 12 = 3(x2 โ 2x) โ 12
= 3(4 + 2โ6) โ 12
= 12 + 6โ6 โ 12 =   6โ6

3). Given, x[3 โ (2 / x)] = (3 / x) (x โ  0)
3x โ (3 / x) = 2
3(x โ (1 / x) )  = 2
x โ (1 / x) = 2 / 3
On squaring both sides, we get
x2 + (1 / x2) โ 2 = 4 / 9
x2 + (1 / x2) = (4 / 9) + 2 = 22 / 9
x2 + (1 / x2) = 2(4 / 9)

4). x โ (1 / x) = 4
We know that,
(x + (1 / x))2 = (x – (1 / x) ) 2 + 4 ร( x (1 / x))
(x + (1 / x))2 = (4)2 + 4
(x + (1 / x))2 = 20
x + (1 / x) = 2โ5

5). [(50)3 + (-30)3 + (-20)3 ]
= 103 [ (5)3 + (-3)3 + (-2)3]
=  103 [ 125 โ 27 โ 8] = 1000 ร 90 = 90000

6). Let a = 0.98, b = 0.02, c = -1
But a + b + c = 0.98 + 0.02 โ 1 = 0
If a + b + c = 0 then
a3 + b+ c3 โ 3abc = 0
(0.98)3 + (0.02) โ 1 +  3 ร 0.98 ร 0.02 = 0

7). Here, x = 0.5 and y = 0.2
โ0.6 ร (3y)x = โ0.6 ร ( 3 ร 0.2)0.5
= โ0.6 รโ0.6  = 0.6

8). (137 ร 137 + 137 ร 133 + 133 ร 133) / (137 ร 137 ร 137 –  133 ร 133 ร 133)
We know that,
a – b3 = (a โ b) (a2 + ab + b2)
= (137 ร 137 + 137 ร 133 + 133 ร 133) / [ (137 –  133 )(137 ร 137 + 137 ร 133 + 133 ร 133)
= 1 / (137 โ 133) = 1 / 4

9). 1 / 2 + [ (1 / 2) ร (1 / 2) ] / { (1 / 2) ร (1 / 2) / (1 / 2) + ( ( 1 / 2) / (1 / 2) ) } ]
= 1 / 2 + [ (1 / 2) ร (1 / 2) ] / { (1 / 2) ร (1 / 2) / (1 / 2) + ( 1 ) } ]
= 1 / 2 + [ (1 / 2) ร (1 / 2) ] / {  (1 / 2) + ( 1 ) }
= 1 / 2 + [ (1 / 2) ร (1 / 2) ] /  (3 / 2)
= 1 / 2 + [ (1 / 2) ร (1 / 2)  ร (2 / 3)  ]
= (1 / 2) + (1 / 6)
= (3 + 1) / 6 = 4 / 6  = 2 / 3