……… instruction of 8051 MC is three byte ......... 8051
Answers
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Answer:
1.
Time required No.of customer Class C.F
31−40 12 Less than 40.5 12
41−50 18 less than 50.5 30
51−60 27 less than 60.5 57
61−70 20 less than 70.5 77
71−80 17 less than 80.5 94
81−90 6 less than 90.5 100
2. Let I
n
=∫
0
1
(1−x
m
)
n
dx
Let I
n+1
=∫
0
1
(1−x
m
)
n+1
dx
=∫
0
1
(1−x
m
)(1−x
m
)
n
dx
=∫
0
1
[(1−x
m
)
n
−x
m
(1−x
m
)
n
]dx
=∫
0
1
(1−x
m
)
n
dx−∫
0
1
x
m
(1−x
m
)
n
dx
=I
n
−∫
0
1
x
m
(1−x
m
)
n
dx
=I
n
−∫
0
1
x⋅x
m−1
(1−x
m
)
n
dx
=I
n
−[−
∣
∣
∣
∣
∣
m(n+1)
x(1−x
m
)
n+1
∣
∣
∣
∣
∣
0
1
+∫
0
1
m(n+1)
(1−x
m
)
n+1
dx]
I
n+1
=I
n
−
m(n+1)
1
∫
0
1
(1−x
m
)
n+1
dx
I
n+1
=I
n
−
m(n+1)
1
I
n+1
⇒I
n
=I
n+1
+
m(n+1)
1
I
n+1
⇒I
n
=
m(n+1)
m(n+1)I
n+1
+I
n+1
⇒m(n+1)I
n
=m(n+1)I
n+1
+I
n+1
...(1)
Now
∫
0
1
(1−x
50
)
101
dx
5050∫
0
1
(1−x
50
)
100
dx
=?
Here m=50,n=100
Substitute in (1) we get
50(101)I
100
=50(101)I
101
+I
101
⇒50(101)I
100
=[50(101)+1]I
101
⇒
I
101
I
100
=
50(101)
[50(101)+1]
⇒5050
I
101
I
100
=5050×
50(101)
[50(101)+1]
⇒5050
I
101
I
100
=5050×
5050
5051
⇒
∫
0
1
(1−x
50
)
101
5050∫
0
1
(1−x
50
)
100
dx
=5051