Download quintessence

INFOMATHS
PUNE-2014
What is the correct negation of statement (“2 is even
dy
13. If ey = sinx and 0 < x <  then find
in terms of x
and – 3 is negative”)
dx
(a) 2 is odd and – 3 is not negative
(a) tan x
(b) cot x
(b) 2 is odd and – 3 is negative
(c) – tan x
(d) – cot x
(c) 2 is odd or – 3 is not negative
4
(d) 2 is odd or – 3 is negative
14. If f  x  
and g(x) = 2x and f[g(x)] = g[f(x)]
x 1
2. Which of the following polynomial best
then find the value of x
ex 1  x2
approximately equals the function
1 
 1
x
(a)  
(b) 2, 
 3
3
(a) 1 + x + x2
(b) x + 2x2 + x3
2
3
2
1

3x x
3x x
x
(c) 0,1, 
(d) N.O.T
(c) 1   
(d)
  x3
3

2 6
2 6 24
15. Find the square root of – 7 – 24i
 i 0
4n
3. If A  
and
n

N
then
the
value
of
A
2i
7  i
7  i

(a) 3 + 4i (b)
(c)
(d)
0 i 
4i
1 i
1 i
1 0 
 i 0 
(a) 
(b) 
2  x2


16. Find coefficient of x4 in the expansion of
 0 i 
0 1 
1  x  x2
0 i 
0 1 
in ascending power of x
(c) 
(d) 


(a) 12
(b) - 2
(c) – 4
(d) 6
i
0
1
0




 0 2  
1 2 
4. If A  
then find the value of |A2009 – 5 A2008| 17. Given

A      and its transpose of A is
3 5 
    
is
(a) – 6
(b) – 4
(c) – 5
(d) N.O.T
equal to its inverse then
2
1
1
3

x


(a)   
(b)   
5. The minimum value of the
if x  0
2
2
1 x
(a) 0
(b) 1
(c) 9
(d) 2
1
(c)   
(d) All of these
6. Find the 4th term in the expansion of (1 – x)3/2
3
1 3
3 3
x (c)
x (d) N.O.T
(a) 0
(b)
a
 x3 sin x 
18. If f  x   
16
8
 find  a f  x   ?
2 
1
7. If [ ] denotes the greatest integer less then or equal to
(a) 0
(b) – 2a3
(c) 3
(d) 4
x & - 1  x < 0, 0  y < 1, 1  z < 2 then the value of
19.
Students
in
college _____ laptops to do their work
determinant
(a) are given
(b) are gave
[ z] 
[ x]  1 [ y]
(c)
given
(d) were used
 [ x] [ y ]  1 [ z ] 
20. Sachin will ______ degree next year.


 [ x]
[ y ] [ z ]  1
(a) finish
(b) finishes
(c)
finished
his
(d) finish his
(a) [x]
(b) [y]
(c) [z]
(d) None of these
21. Lectures sometimes _____ Saturday.
8. The cube root of 9 3  11 2 is
(a) hold on
(b) hold at
(a) 3  2
(b) 3 3  2
(c) held on
(d) held at
22.
Dinesh
had
purchased
four
pair of shirts even though
(c) 3 3  3 2
(d) 3  2
he
has
short
of
money.
Choose the appropriate
f  x
9. If  xf  x  
find f(x)
punctuation.
2
(a) Shirts, Even though he
2
ex
(b) Shirts, even though he
x
-x
(a) e
(b) e
(c) log x (d)
(c) shirts, even though, he
2
(d) shirts, even though, he
10. Find the area bounded by the curve y = e2x &
between x axis and y axis and line x = 0 to x = 2
1 3 2   1 
1 4
1 4
23. 11 0 5 1  1   0
(a)  e  e 
(b)  e  1
2
2
0 3 2   x 
e4 e
e4  1
then the best approximation of x

(c)
(d)
4 2
4
(a) - .8599 (b) -.8597
(c) -.8595 (d) -.8588
11. If f(x) = |x|3 then find f’(0)
24. One hundred identical coins, each with probability p
(a) 1
(b) 0
(c) 1/2
(d) 1/3
of showing heads are tossed once. If 0 < p < 1 and
12. The differential equation xdy – ydx = 0 represents
the probability of heads showing on 50 coins is equal
(a) parabola
(b) straight line
to that heads showing on 51 coins, the value of p is
(c) circle
(d) hyperbola
(a) 1/2
(b) 50/101
(c) 51/101
(d) 49/101
1.
1
INFOMATHS/MCA/PUNE-2014
INFOMATHS
25. Find the value of m for which the given equations 3x
 3n  4 n 
+ my = m and 2x – 5y = 20 has solution satisfying
(c) 
(d) N.O.T
n
 4  1 
the condition x > 0, y > 0
15 

34. Ram and Shyam have equal number of daughters.
(a)  ,
(b) (30, )

There are three cinema tickets which are to be
2


distributed among the daughters of Ram and Shyam.
15 

(c)  ,
The probability that the two tickets goes to the
   30,   (d) N.O.T
2 

daughter of one and one ticket goes to another
26. Find the value of x for which the equation
daughters is 6/7. Then the number of daughter each
2
2
of Ram and Shyam have
x  5x  3  2 x  5x  3  15 has real solution
(a) 3
(b) 4
(c) 8
(d) N.O.T
(a) 6
(b) 1
35. An ordinary cube has 4 blank faces, one face marked
5  113
5  113
2 and another face marked 3. Then the probability of
(c)
(d)
2
2
obtaining 12 in 5 throw is
27. For three events A, B and C, P (exactly one of the
5
5
5
(a)
(b)
(c)
(d) N.O.T
events A or B occurs) = P (exactly one of the events
1296
1944
2592
B or C occurs) = P (exactly one of the events C or A
occurs) = p and P (all the three events occurs 36. 3 z  1  z , where z is complex number, then
z
3z  4
simultaneously) = p2 where 0 < p < ½. Then the
probability of at least one of the three events A, B
find the number of solution of z satisfying the
and C occurring is
equation
2
2
(a) zero
(b) atmost 2
3p  2p
p  3p
(a)
(b)
(c)
atleast
2
(d) Infinite solution
2
2
37.
Satish
had
stopped
car
at
petrol
pump because there
3 p  p2
3 p  2 p2
_____ petrol in the tank
(c)
(d)
2
4
(a) isn’t much
(b) wasn’t much
28. A point (p, q) lies on the curve 2y = x2 is nearest to
(c) isn’t many
(d) wasn’t many
the point (4, 1) then the point (p, q) satisfy the 38. There are 120 students in a class, the students opted
condition
physics are even numbered, and the students opted
(a) p < 1, q > 3
(b) p > 1, q < 3
mathematics are divisible by 5 and the students opted
(c) p < 3, q < 3
(d) N.O.T
chemistry are divisible by 7. Then find the number of
29. Evaluate limit lim n sin  2 n !e  equal
students which had taken none of the above subjects.
x 
(a) 9
(b) 41
(c) 84
(d) N.O.T
(a) 
(b) /2
(c) 2
(d) N.O.T
39. Three of the six vertices of a regular hexagon are
30. If z = a + ib, the the points z, z and origin (0, 0)
chosen of random. The probability that the triangle
form
with these three vertices is equilateral triangle is
(a) Equilateral
equal to
(b) Isosceles
(a) 1/2
(b) 1/5
(c) 1/10 (d) 1/20
(c) right angle
40. All + ve number that are multiple of 3 are put in just
(d) Triangle with all three acute angle
a position forming an infinite string of digit for
31. India plays two matches each with West Indies and
example
Australia. In any match the probabilities of India
Multiple of 3 : 369121518212427….
getting points 0, 1 and 2 are 0.45, 0.05 and 0.5
in just a position of multiple of 3
respectively. Assuming that the outcomes are
8th digit from the left of string 1
independent, the probability of India getting at least
9th digit from the left of string 8. Then
seven point is
200th digit from the left of string
(a) 0.8750
(b) 0.0875
(a) 1
(b) 3
(c) 7
(d) N.O.T
(c) 0.0625
(d) 0.0250
41. According to above question
32. A students appears for test I, II and III. The student
2000th digit from the left of string
is successful if he passes either in tests I and II or
(a) 3
(b) 7
(c) 9
(d) N.O.T
tests I and III. The probabilities of the students 42. Find the locus of a point which divides the line AB
passing in tests I, II and III are p, q and 1/2
1
externally in the ratio :1 . Where A is a point on
respectively. If the probability that students is
2
successful is 1/2 then
2
parabola
y
–
2y
–
4x
+
5 = 0 from which tangent is
(a) p = q = 1
drawn
which
meets
the
directrix
at B.
(b) p = q = 1/2
Then
find
the
locus
(c) p = 1, q = 0
(a) (x + 1) (y – 1)2 = - 4 (b) (x –1) (y – 1)2 = - 4
(d) there are infinite values of p and q
(c) (x – 2) (y – 1)2 = - 4 (d) N.O.T
 3 4 
n
43. If AAT = I & det A = 1 then which is correct
33. If X  
 then X is equal to
1

1
(a) A – I = 0
(b) A + I = 0


(c) A – 2I = 0
(d) N.O.T
3n 4n 
 2  n n 
(a) 
(b)
44.
If
f(x)
=
1
for
x
is
a
rational
number and f(x) = 0 x is

 n
5  n 
 n n 

irrational number then lim f  x  is
x 0
(a) 0
2
(b) 1
(c) 1/2
(d) N.O.T
INFOMATHS/MCA/PUNE-2014
INFOMATHS
1
45.
lim 1  3x  x
x 0
(a) e-3
(b) e3
(c) 3
(d) -3
46. For the real value of (a, b) the function
x
lies in (a, b)
f  x  2
x  5x  9
(a) a = 0, b = 0
(b) a = - , b = 0
1
1
,b  2
(c) a 
(d) a  , b  1
20
11
47. There were three logistician peoples name Galelio,
Newton, Einstein and the anther man Archimeds
who challenged them to play a game to check their
reasoning ability. Archimeds had 4 blue tickets and 4
yellow tickets. Out of these eight tickets he posted
two tickets on the forehead of each of them and put
the remaining two in his pocket after that they were
asked to guess the colours of tickets on their
foreheads. But in terms he saw only the ticket of
others but not see the colour of ticket on their own
forehead Their replies are
Galelio : No
Newton : No
Einstein : No
Galelio : No
Newton : Yes
then what was the colour of tickets on Newtons
forehead
(a) both blue
(b) both yellow
(c) cannot be determined (d) N.O.T
48. If
 f  x  c  dx  5
2
1
(a) 1/n
(b) 1/k
(c) k/n
(d) N.O.T
55. A particle, moves along a straight line with velocity
v(t) = t2 displacement between t = 1 & t = 2
(a) 7/3
(b) 8/3
(c) 9
(d) N.O.T
56. A2 + A + 2I = 0 then which s incorrect
(a) A is non-singular
(b) A  0
1
(c) A is symmetric
(d) A1   A  I 
2
57. For 3  3 matrix A where all the elements are either
0 or 1. Then the maximum value of |A| cannot
exceeds
(a) 4
(b) 2
(c) 1
(d) N.O.T
58. If it is, given that the value of a + b = 100 then
maximum value of ab is
(a) less than 2601
(b) great than 2601
(c) greater than 2601 and less than 2800
(d) less than 2400
59. k persons are distributed over n cells then find the
probability that k person are sitting in adjacent to
each other in cells
 n  k  1!
 n  k !
(a)
(b)
n!
nk
 n  k  1 k !
(c)
(d) N.O.T
n!
60. Determinant of A = 11 then determinant of matrix
formed by cofactor of the value lie between
(a) between 101 to 161
(b) between 200 to 300
(c) between 50 to 100
(d) greater than 150
61. Find volume of y = sec x in first quadrant between 0
then what will be the value of
<x<
2c
 f  x  dx 
(a) 

.
4
(b) 2
(c)  - 2
(d)  - 1
1 c
(a) 5 + c (b) 5 – c (c) c
(d) 5
49. Three numbers are choosen randomly from 1 to 100
then find the probability of getting number which are
divisible by 2 and 3
4
4
9
(a)
(b)
(c)
(d) N.O.T
25
1155
1024
50. The probability of obtaining 6 first time in repeatedly
throw of cube. Then find the probability that six
obtained for first time in n  3
(a) 25/36 (b) 1/36 (c) 5/36 (d) N.O.T
The standard analogue clock will having the hour hand
and minute hand and second hand
51. If we start counting at 00 : 01 then the second hand
shown ‘xx’ seconds after that minute hand just
passed over the hour hand 5 time, then ‘xx’ equals
(a) 5
(b) 16
(c) 27
(d) N.O.T
52. If we start counting at 00 : 01 then the second hand
shown ‘xx’ second after that the minute hand just
passed over the found hand 8 times, then ‘xx’ equals
(a) 16
(b) 28
(c) 26
(d) N.O.T
53. In equation 2x3 + x + n = 0 roots lies between [0, 1]
then the value of n
(a) lies between 0 & 1
(b) lies between -1 & 1
(c) lies between 2 & 3
(d) N.O.T
54. There are n differents keys find the probability that
the particular lock is opened at the kth time when it is
given that each key is tried only once
ANSWERS
1
C
11
B
21
C
31
B
41
B
51
D
61
A
3
2
C
12
B
22
C
32
C
42
A
52
C
3
A
13
B
23
A
33
D
43
A
53
D
4
A
14
A
24
C
34
B
44
D
54
C
5
X
15
B
25
C
35
C
45
B
55
A
6
B
16
A
26
A
36
B
46
D
56
D
7
C
17
A
27
A
37
B
47
D
57
B
8
D
18
A
28
C
38
A
48
D
58
A
9
D
19
A
29
D
39
C
49
B
59
B
10
D
20
D
30
B
40
B
50
A
60
A
INFOMATHS/MCA/PUNE-2014