Download pune university , 2001

INFOMATHS
PUNE UNIVERSITY , 2001
NUMBER OF QUESTIONS : 50
1.
There are 400 students, out of which 200 passed in
Physics, 280 passed in Maths. 80 failed in both How
many passed in both?
a. 80 b. 100
c. 120
d. 160
e. 240
x
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
x
16.
Limit of
e
x
2 2 2 ........ 
a. 2
17.
18.
19.
(1  tan x )  tan 2 x ) dx  ?
a. e x tan 2 x
b. e x tan x sec x
c. e x sec x
d. e x tan x e. e x sec 2 x
The equation of tangent to the parabola : y2 = 4x at (1, 2)
is .
a. x + y = 3
b. x – y = 3
c. x – y + 1 = 0
d. x + y – 1 = 0
e. x + y – 2 = 0
Coefficient of x16 in (x2 + x3 + x4 + …..)5 is .
a. 10C6
b. 10C5
c. 10C2
d. 10C3
e. N.O.T
If P and Q are logical statements, then "P implies (P
implies Q)" has truth value.
a. P
b. Q
c. False
d. True
e. N.O.T
1 x 2 x 3 x 4 + …….+ 18 x 19 x 20 = .
a. 21190 b. 42260 c. 35910 d. 15200 e. 17780
The equation of a plane which is parallel to X – Y plane
and is 5 units below is .
a. x + y + 5 = 0
b. z + 5 = 0
c. x + y – 5 = 0
d. –z + 5 = 0 e. xy + 5 = 0
Negative of the statement. Either 1 win or you lose “is .
a. I do not win ad you lose.
b. I win or you lose
c. I do not win and you do not lose
d. I do not win and you lose.
e. None of these.
An ant crawls from a point (-6, 24, -8) to another point
whose coordinates are (9, 35, 12). When it has crawled 52
units, What is the shortest distance from X – Z plane?
120
24
a. 8
b. 9
c.
d.
e. N.O.T
153
10
What is the angle (in radians) between the hour and minute
hand when 20 minutes have elapsed after 7 o'clock?
7
2
7

5
a.
b.
c.
d.
e.
18
9
9
3
9
b.
3
20.
21.
22.
23.
24.
c.
54
d.
3
2
e.
y =
9
3
a. tan 1
b. tan 1
13
13
14
1
c. tan 1
d. tan 1
5
6
3
e. tan 1
2
If (3 + i) x + (1 – 2i) y + 7' = 0, then the value of x and y
is.
a. 2, -6
b. 3, -1
c. 1, -3
d. –3 , -1 e. –1,3

Express P = 5i + 3j + 4k as a linear combination of the
three vectors.



a i ;b i  j :c i  j k.
 

 

a. 2 a  b  4 c
b. 5 a  b  0 c
 

1  3  5 
c. a  b  c
d. 2 a  4 b  c
2
2
2



e. 4 a  3 b  2 c
There is a group of 16 persons including three : A, B and
C.A committee of 4 is be made from these 16 persons
such that A is always included and B C are always
excluded ? In how many ways can this be done?
a. 186
b. 286
c. 264
d. 306
e. 364
A room has three lamps from a group of 10 lamps out of
which 4 are working and 6 are burnt out, 3 are selected
and put n sockets . The probability that there will be light
is .
1
2
1
5
a.
b.
c.
d.
e. N.O.T
6
3
2
6
If 0 < p< 2, the roots of p(x + 1) (x + 3) + 2 = 0 are .
a. Real and equal b. Imaginary and unequal
c. Pure complex and equal
d. Pure Complex and unequal
e. Pure Complex and equal .
There are 15 stations on a route. What is the number of
different kinds of tickets Ist and IInd class ?
a. 360
b. 420
c. 480
d. 540
e. 600.
Which of the following means the logical statement. For
every N, there is a successor " where N is it . set of natural
numbers and s(x) define the successor function ?
a. x  N, y  N, y = s(x)
b.  x  N, y  N, y = s(x)
c. x N, y  N, y = s(x)
d. x N, (y  N, y = s(x)
e. x N,( y  N y = s(x))
3  5i
Complex conjugate of
is .
3  4i
29
3
3
29
11 27

i

i

i
b.
c.
25 25
25 25
25 25
11 27
3
29

i

i
d.
e.
25 25
25 25
How many integer solution are there for x1 + x2 + x3 + x4 =
12, where x1 > 0.
a. 240
b. 360
c. 455
d. 675
e. N.O.T
If 3rd and 7th term of an arithmetic progression is 17 and
37 , What is the sum of first 20 terms of this progression ?
a. 2010
b. 1090
c. 1140
d. 1940
e. 2140
The series 1 + 2(x - -2)+ 3(x - 2)2 + 4(x - 2)3 +….
Converges in the range .
a. –1 < x < 1
b. –2 < x <2
c. –2 < x < -1
d. 1 < x < 3
e. 3<x < 4
a.
25.
26.
27.
1
acute angle between 27y = x2 and
8x at (18,12) is.
x
10  2  5  1
as x tends to 0 is .
x sin x
a. Log 7
b. Log 10
5
2
c. Log
d. (Log 2)(log 5) e. Log
2
5
Sin 600 cos 330 - cos 120 sin (-390) =
1
1
a. 2
b. 1
c.
d. –1
e. 
2
2
Find the value of k which will make the following system
of equations consistent.
5x – y + 3 = 0: 2x – y – 3 = 0 : kx – y – 1 = 0
a. 2
b. 3
c. 4
d. 5
e. 6
Find the sum to 10 terms of the series
3 3 3 3
3   
........ .
2 4 8 16
1
1
a. 2 
b. 2 
1024
512
1
1
1
c. 2 
d. 2 
e. 2 
556
128
64
The
5
2
– (1) –
INFOMATHS
28.
dy

dx
x  2y
b.
y  3x
43.
c. 6x2 + 12x – 100 = 0
d. 5x2 - 6x + 2 = 0
e. 6x2 - 100x + 13 = 0
A pyramid which has square base of dimensions 8cm x
8cm and whose height is 4 cm is cut at a height of 3 cm
from base parallel to it. Volume of the part containing the
base is :
a. 104
b. 92
c. 84
d. 64
e. 32
44.
If
If x2 + y2 + 4x – 6y – 3 = 0, then
a.
2x  2 y  2
xy
c.
2x  3
4y  5
d.
y3
x2
e.
x2
3 y
8
29.
30.
31.
32.
33.

a 
 is 112 .
The constant term in the expansion of  x 
3
x


Find the value of a .
3
7
a.  2 b. 
c.  5 d. 4
e.
2
2
1
x2
If y = F(x) =
where x  , then for What value of
2
2x  1
x is F(y – 1) = -2 .
a. 3
b. 2
c. 3
d. 6
e. 8
If one root of x2 – 6x + k = 0 is twice the other root then k
=?
a. 3
b. 5
c. 4
d. 6
e. 8
What is the area of a parallelogram whose sides are 3i + 2j
– k and 2i – j + 3K ?
a. 190
b. 191
c. 193
d. 195
e. 197
What are the number of permutations of the word
CALCUTTA ?
a. 5!
b. 6!
c. 7!
d. 8!
e. N.O.T
45.
35.

1 
 ?
Find the constant term in  2x 
x2 

a. 200
b. 220
c. 240
d. 260
e. 216
A particle follows a path where distance s is travelled in
time
i
governed
by
the
equation
t3 t 2

 6t  5. What is the acceleration of the
3
2
particle at a time when the speed of the particle is zero ?
a. 5
b. 6
c. 7
d. 8
e. 9
2
7?
What real value of x satisfies : 1 
x
a. {-3, 4}
b. {-4, 3}
1
1
1 1 
c.  ,  
d.  , 
e. {7 , 0}
4
3
3 4 
In how many ways can 5 letters be placed in 5 envelopes if
letters are too lange for one of the envelopes ?
a. 72
b. 84
c. 95
d. 105
e. 125
A bag contains 4 white and 6 black balls . 2 balls are
drawn at random. What is the probability that both are of
the same color ?
1
2
3
2
7
a.
b.
c.
d.
e.
5
5
5
15
15
How many numbers of 4 different digits are possible such
that the numbers are more than 5000 and digits 1, 2, 4, 5, 7
and 8 only are used?
a. 180
b. 210
c. 240
d. 450
e. 500
A staircase has 8 steps. A boy can take either 1 or 2 steps
in one stride. What is the number of ways in which the boy
can get to the top of the staircase ?
a. 82
b. 28
c. 32
d. 34
e. 42.
Shadow of a tree reduces by 20 feet when the sun rises
from 30o to 45o above horizon . What is the height of the
tree ?
10
a. 10 b. 10 3 c.
d.10 ( 3  1)
e. 20 3
3
If P and Q are roots of : 2x2 + 6x – 5 – 0 , then P3 and Q3
are the roots of .
a. 8x2 + 396x – 125 = 0
b. 8x2 + 216x – 125 = 0
46.
47.
37.
38.
39.
40.
41.
42.
7  320  125
a. (4, -9)
c. (-9, -4)
As n  
 a  b 5 , then (a , b)  .
b. (-3, 5)
d. (9, -4) e. (3, -5)
5 n 1  3n 1
2 n 1  5 n 1
converges to.
25
3
5
25
b.
c.
d.
e. 25
4
2
3
g
Two unbiased dice are thrown. Probability that the sum of
the number s appearing on the Upper face is at least 11 is .
3
2
5
3
a.
b.
c.
d.
e. N.O.T
11 11
12
12
o
o
o
Cos 24 + cos 55 + cos + 125 + cos 204o + cos 300o =
3
1
c.
d.
e. 1
2
2
2
Volume of the solid formed by revolution about X axis the
region bounded by the parabola. y2 = x and the straight
line x = 1 is .




a. 
b.
c.
d.
e.
2
3
4
4
Angle of elevation of a cloud from a height of 100 feet
above lake is 30o and the angle of depression of the
reflection of the cloud in the lake from the same point is
60o . What is the height of the cloud ?
100
a. 200 3 b. 200
c.
d. 100 3 e. 100
3
Find the area between the curves: 4y2 = 9x: 3x2 = 16y.
a. 6
b. 3
c. 8
d. 4
e. 5
a. 0
48.
49.
s
36.
45
a.
6
34.
3  20 
50.
– (2) –
b.
1
Answers the Question. Pune University 2000
1
D
11
B
21
D
31
E
41
D
2
D
12
C
22
B
32
D
42
A
3
D
13
E
23
C
33
C
43
C
4
B
14
E
24
C
34
C
44
D
5
B
15
A
25
C
35
A
45
E
6
D
16
A
26
B
36
C
46
E
7
C
17
e
27
D
37
A
47
C
8
A
18
a
28
E
38
E
48
B
9
E
19
B
29
A
38
A
49
B
10
C
20
D
30
C
40
D
50
D