Aje Taiwo Tutor
GEG101 (Engineering Pure Mathematics)
Thursday 8th March, 2012.
Answer all Questions
1.
Given that U n  M
for n  1,2,3..... where M is a
(e) none
constant (independent of n), we say that the sequence
U n  is …?
8.
Which of the underlisted is not a finite set
(a) set of state in Nigeria
(b) set of 1 digit whole number
(c) set of integers between -100 to 100
(d) set of points on a straight line
(e) none
9.
Find
(a) not bounded below
(b) not bounded above
(c) bounded above
(d) not bounded below and above
(e) none of the above
2.
If lim Sn  S exists where Sn is infinite series, then:
(a) the series is lower bound and convergent
(b) the series is divergent
(c) the series is bounded and convergent
(d) the series is lower bound and convergent
(e) none of the above
3.
4.
10.
(d)  sin 2 t


(e)  sin 2 t 5
Find the equation of the tangent to the curve at point
2,4
(b) y  4x  4
(c) y  1 4x  9 2 (d) y  4 x  9 2
Find the lim sin(n)
(b) does not exist
(d) 0
(e) none of the above
(e) none of the above
Find the possible nth term for the sequence whose first
five terms are U n : 1 5 , 3 8 , 5 11, 7 14, 9 17 .........
(a) 1n 2n  1 3n  2
(b)  1n 3n  1 3n  2
(c)  1n 2n  1 3n  2
(d) 1n 2n  1 3n  2
(a) 4 y  x  18
(b) 4 y  x  18
(c) y  4x  4
(d) y  4 x  9 2
dy
at the point x, y   1,1 if x2  3xy  y 2  5
dx
(a) 0
(b) 1
(c) -1 (d) -½ (e) -2
12.
Find
13.
If x4  y3  z 2  8 find
The curve y  x3  2x2  4 at the point (2, 4) can be
(a)⅓
14.
Given that m1 and m2 are the slopes of the tangents to
curve 1 and curve 2 respectively, then the acute angle
of intersection can be found by the relation
(a) tan  m1  m2  1  m1m2 
(b) tan   m1  m2  1  m1m2 
(c) tan  m1  m2  1  m1m2 
(d) tan   m1  m2  1  m1m2 
Mock checks readiness for the real exam
Find the equation of the normal at the point 2,4
(e) y  x 4  9 2
said to have
(a) minimum turning point (b) no turning point
(c) maximum turning point
(d) turning point cannot be determined
(e) none of the above
7.
(c)  cos2 t
(a) y  4x  4
(e) none of the above
6.
(b) sect 5
answer questions 10 and 11
11.
5.
(a) cost
Using the curve y  x3  2x2  4 at the point x, y   2,4
Justify the limit of the series that is formed by the
sequence of partial sums of 1,1,1,1,1,1,1...
(a) diverges
(b) converges monotonically
(c) converges
(d) diverges monotonically
(e) none of the above
(a) 1
(c) infinity
dm
cost
sect
if m 
and s 
ds
5
5
15.
1
(b) -3
dy
at point x, y, x   2,2,2
dx
(c) 2
(d) -½ (e) 3
The sequence 1000000, 1000000.2, 1000000.22,
1000000.222………… is
(a) Monotonic increasing
(b) Bounded and monotonic increasing
(c) Bounded and monotonic increasing. T is also strictly
increasing
(d) Bounded
(e) none
 

Find the limit 2 p  p  2  p  1  p3 p2  1
Join us for the Revision Classes.
Aje Taiwo Tutor
GEG101 (Engineering Pure Mathematics)
(a) -1
16.
(b) -½


(c) 3   1  n
(a) 3  3 1n n3
n
3

 n  1
(d) 3  3 1  n
(b) 3   1n
 
Find the limit 1  4 10n
(a) 1 5
18.
(e) ∞
(d) 1
The nth term of the sequence 6 13 , 0, 6 33 , 0, 6 53....... is
given by
17.
(c) 2
3
(e) none
23.
 5  3 10 
n
(b) 3 2 (c) 4 3 (d) does not exist (e) none
Which of these Is not an infinite sequence?
(a) 3,6,9,12,......, 30
(b) 2,7,12 ,17 ,.......
20.
24.
5
5
2

(d)  ln 2   (e)  ln 2  
18 
18 
3


x3  x 1
dx
x4  x2
1
(a) ln x  tan 1 x   C
x
1
(c) ln x  tan 1 x   C
x
Evaluate
Simplify
Justify the statement below:
A sequence u1 , u 2 , u 3 ,... has a limit L if the successive
terms gets “farther and farther” from where L is the
limit of an infinite sequence
(a) false
(b) false but not always
(c) true but not always
(d) true
(e) none of the above
(c)
3
1
1  x  2  C
3
(d) 
If lim An  A , lim Bn  B , then
25.
Solve

2
0

(d) lim  An Bn   lim An  lim Bn  A  B
 105 


 0.08 
(e) none of the above
(a)
2e 3 x
13
3
1
1  x  2  C
3
(d) None
 105 
(b) 

 0 .8 
 8 
(d) 

 105 
(c)
 0.8 
(e)  10 .5 
cos 2 xdx

3


cos 2 x  sin 2 x  C
2


(b)
2e 3 x 
3

sin 2 x  cos 2 x  C
13 
2

(c)
2e 3 x 
3

cos 2 x  cos 2 x  C
13 
2

(d)
2e 3 x
13
26.
Evaluate
x
5
cos xdx
0
3


sin 2 x  sin 2 x  C
2


27.
(a) 5 4  60 2  240
(b) 5 4  60 2  240
(c)  5 4  60 2  240
(e) None
(d)  5 4  60 2  240
Solve
sin xdy
 cos x
1  ydx
x2
 xC
2
(c) y  A cos3x  2  C
(e) None
(a) ln y 
2
Evaluate
(b) 
sin 5 x cos 2 xdx
 10 .5 
(a) 

 8 
3 x
(d) ln x  tan 1 x  x  C
3
1
1  x  2  C
3
(b) lim  An  Bn   lim Bn  lim An  B  A
e
1
C
x
2
3
1
1  x  2  C
3
Solve
(b) ln x  tan 1 x 
 x 1  x dx
(a)
(c) lim  An  Bn   A lim Bn  B lim An
22.
5
2
(c)  ln 2  
18 
3
(d) 1,4,7,9,12 ,...... 27
(a) lim  An  Bn   lim Bn  lim An  B  A
21.
3
5
(b)  ln 2  
2
 18
(e) ln x  tan 1 x  x  C
(e) none of the above
19.
5
3
(a)  ln 2  
18 
2
3
n
(c) 1, 1 3 , 1 5 , 1 7 ,.........
Thursday 8th March, 2012.
2
 x  1 ln xdx
(b) y 2  A tan 2 x  4  C
(d) None
(d) y  A sin x  1  C
1
Mock checks readiness for the real exam
2
Join us for the Revision Classes.
Aje Taiwo Tutor
28.
GEG101 (Engineering Pure Mathematics)
 2 cos
(a) Mix graph
(c) Curvy graph
dx
Solve
x 1
2
x
C
2
(a) tan 1
2
tan x  C
3
(b)
33.
 tan x 
  C (d) None
(c) tan 1 

 2 
(e)
29.
tan x 
C
tan 

3
 3 
Evaluate
 tan
2
2
x sec xdx
1 3
tan x  C
3
(b)
(c) 2 tan x  C
1
2
(d) tan x  C (e) 3 tan x  C
Solve
(a)

sin4 x  2dx
1
cos4 x  2  C
4
1
(b)  cos3 x  5  C
3
1
(c)  cos2 x  5  C
2
1
(e) cos4 x  2  C
4
31.
35.
(a) sec x  C
2
30.
34.
1 

1
Thursday 8th March, 2012.
1
(d)  cos4 x  2  C
4
36.
Two set A and B are equal if
(a) They contain the same number of elements
(b) They have equal number of and the same nature of
elements
(c) No element of A could be found in B
(d) No member of B could be found in A but those of
B are in A
37.
(b) Digraph
(d) Multi graph
The sink in fig. 2 is
(a) E7
(b) E1 (c) E4
(d) E3
The source in fig. 2 is
(a) E7
(b) E1 (c) E4
(d) E3
The Adj Matrix is
0

1
0
(a) 
0

0
0

0
1 0 0 0 0 0

1 1 0 1 1 1
1 1 1 0 1 1

0 1 0 0 0 0

1 0 0 1 0 0
0 1 0 0 0 0

1 1 0 0 0 0 
0

1
0
(b) 
0

0
0

0
1 0 0 1 0 0

1 1 0 1 1 1
1 1 1 0 1 1

0 1 1 0 1 0

1 0 0 1 0 0
0 1 0 0 0 0

1 1 0 1 0 0 
0

1
0
(c) 
0

1
0
 1

1 0 1 0 0 0

1 0 0 1 1 1
1 1 1 0 1 1

0 1 0 0 0 0

1 0 0 1 0 0
0 1 0 0 1 0

1 1 0 0 1 0 
0

1
0
(d) 
0

0
0
 0

1 1 0 0 0 0

1 1 0 1 1 1
1 1 0 0 1 1

0 1 0 0 0 0

1 0 1 1 0 0
0 1 0 0 0 0

1 1 0 0 0 0 
The order of the graph is
(a) 7
(b) 12 (c) 19
(d) 5
Which of the following expression is not a possible
partition of set S  x, f ( x) 9  x  25
(a) 1,2,3,5
(b) 7  x  7
(c) All positive integers between 0 and 25
(d) All numbers - ∞ to + ∞
38.
Use for Questions 32 to 36
In expressing a logic function in product of sum form
we consider the point where the function is
(a) zero
(b) one
(c) undetermined (d) complemented variable only
Use for questions 39-41
Given the relation z  x, y 5x  y 2  9,14,19,31,45,61,79
39.
The set of order pairs of Z is
(a) 1,2, 2,2, 3,2, 3,4, 4,5, 5,6, 6,7
(b) 0,0
(c) 1,3, 2,3, 4,5, 8,9, 1,2, 4,5, 7,8, 6,3
Fig 2
32.
(d) 7,8, 5,6, 3,6, 3,6, 2,3, 1,9, 0,4, 5,7
Fig 2 is a:
Mock checks readiness for the real exam
3
Join us for the Revision Classes.
Aje Taiwo Tutor
40.
GEG101 (Engineering Pure Mathematics)
111
The domain of Z is
(a) 1,2,3,4,5,6
(b) 2,5,8,9,6,3
(c) 1,4,6,8,4,9
(d) 3,4,5,6,9
47.
41.
The range is
42.
If X, Y and Z are logic variables such that the
(a) 2,3,4,9(b) 2,4,5,6
Thursday 8th March, 2012.
0
If X  Y  0 then which of these is not true:
(a) some elements of X can be found in Y
(b) All elements of X are found in Y
(c) X is an element of Y
(d) X and Y are disjoint sets
(c) 0 (d) 1,3,5,7,9
48.
In fig Q48, the output Y equals:
F  x  yz
expression
is a valid Boolean expression
then which of these is not true of F
(a) xy  xz
(b) x  y  x  z
(c) x  y  z 
(d) x  y  z
0; if X  Y  0
Y

 1; otherwise 
43.
The expression
describes an
(a) AND operation (b) Exclusive -OR
(c) NOT operation (d) OR operation
44.
If
Y  ab  c  bc  a reduces to
(a) a b  c  (b) ab  c  (c) ab  c
45.
(d) a  b
49.
Which of these is a function:
(a) y  x 3
(c) y  sin x
46.
(a) abcd
(c) a  b  c  d
4,15,25,65,1
(c) 3,23,64,2 (d) 2,26,11,3
(d) x  y  3
2
 
 
If X  3,4,5 and Y  2,6 , then which is not a binary
relation
(a) 3,14,6
(b) x  y 2  yx  3
1
(b) 0
(d) ab  cd  ac  bd
2
Given the truth table
abc
f
000
0
001
11
f could be expressed as
010
0
(a) b  c a  c  (b) bc
011
1
100
1
101
0
(c) abc  abc  abc
110
1
50.
(b)
Any Class of objects in which at least two sets of binary
operation are possible is called:
(a) a Ring (b) a Path
(c) a Close (d) an Exit
(d) a  b  c 
Mock checks readiness for the real exam
4
Join us for the Revision Classes.