INFOMATHS
HCU-2014
that they do not undertake both the activities on any
single day. There were some days when they did
nothing. Out of the days that they stayed at their
grandparent’s house, they involved in one of the two
activities on 22 days. However, their grandmother
while sending an end of vacation report to their
parents stated that they did not do anything on 24
mornings and they did nothing on 12 evenings. How
long was their vacation?
(a) 36 days
(b) 14 days
(c) 29 days
(d) cannot be determined
9. The product of the numbers 1 to 100 (both inclusive)
is a huge number. What is the number of zeros that
this number will have at the right hand end?
(a) 20
(b) 24
c) 100
(d) 22
10. a, b, c, d and e are five consecutive integers in
increasing order of size. Which one of the following
expressions is not an odd number?
(a) ab + c (b) ac + d (c) ab + d (d) ac + e
11. Think of any 3-digi number and write it down twice
side-by-side to form a 6-digit number. Eg: if the
number you think is 123, then 6-digit number is
123123. Which of the following is FALSE about
such 6 digit number?
(a) They are always divisible by 3
(b) They are always divisible by 7
(c) They are always divisible by 11
(d) They are always divisible by 13
12. Yana and Gupta leave from points x and y towards y
and x respectively simultaneously and travel in the
same route. After meeting each other on the way,
Yana takes 4 hours to reach her destination, while
Gupta takes 9 hours to reach his destination. If the
speed of Yana is 48 km/hr, what is the speed of
Gupta?
(a) 72 kmph (b) 32 kmph (c) 20 kmph (d) 30 kmph
13. A car rental agency has the following rental plans.
Plan A: If a car is rented for 5 hours or less the
charge is Rs. 60 per hour or Rs. 12 per kilometer
whichever is more.
Plan B: If the car is rented for more than 5 hours, the
charge is Rs. 50 per hour or Rs. 7.50 per kilometer,
whichever s more.
Atul rented a car from this agency, drove it for 30
kilometers and ended up paying Rs. 300. For how
many hours did he rent the car?
(a)3
(b) 4
(c) 5
(d) 6
Read the following passage and answer the 14-16
based on this passage by choosing the most suitable
answer to the question:
Natural selection cannot possibly produce any
modification in a species exclusively for the good of
another species thought throughout nature one species
incessantly takes advantage of, and profits by, the
structures of others. But natural selection does often
produce structure for the direct injury of other animals, as
we see in the fang of the adder. If it could be proved that
any part of the structure of any one species, had been
formed for the exclusive good of another species, it would
annihilate my theory. It is admitted that the rattle snake
has a poison fang for its own defence, but some authors
suppose that at the same time it is furnished with a rattle,
to warn its prey. I would almost as soon believe that the
cat curls its end of its tail when preparing to spring, in
BOOKLET CODE A
1. A student was asked to add the first few natural
numbers (that is, 1 + 2 + 3 + …) so long as her
patience permitted. As she stopped, she gave the sum
as 575. When the teacher declared the result wrong,
the student discovered that she had missed one
number in the sequence during addition. The number
she missed was:
(a) less that 10
(b) 10
(c) 15
(d) more than 15
2. A five member research group is chosen from
computer scientists (CS) A, B, C and D
mathematicians E, F, G and H. At least 3 CS must be
in the research group. However
A refuses to work with D
B refuses to work with E
F refuses to work with G
D refuses to work with F
If B or C is chosen which of the following is
necessarily true:
I. A is definitely chosen II. D is definitely chosen III.
Either F or G is chosen.
(a) I only (b) II only (c) III only (d) II and III only
3. How many binary strings of length 10 contain at
least three 1’s and at least three 0’s?
(a) 672 (b) 912 (c) 11520 (d) 140
4. The first six Prime Ministers of a country had an
average tenure of 6 years. What is the approximate
tenure of the 7th Prime Minister if the average tenure
of first nine Prime Ministers is 5.25 years and the
duration of the tenure of the 7th, 8th, and 9th Prime
minister are in the ratio 1:2:3?
(a) 1 year 3 months 18 days
(b) 1 year 10 months 15 days
(c) 2 years
(d) 1 year 6 months
5. The three words “MCA SCIS UH” are flashed on a
digital sign board. The world individually are
switched on from a switch-off position at regular
intervals of 4, 7 and 9 seconds respectively. After
they are switched on, the words are switched off
after 2 sec, 3 c and 4 sec respectively. If at time ‘t’
all the words happened to switch off simultaneously,
find the least time at which all three words will
switch on simultaneously.
(a) 252 sec (b) 126 sec (c) 94 sec (d) 38 sec
6. In the following multiplication, each * represents a
digit. What is the multiplier?
2
3
5

*
*
*
*
*
*
*
*
*
*
*
*
5
6
*
(a) 24
(b) 96
(c) 48
(d) 12
7. Now the time is 4 O’ clock. By 5 O’ clock, the
minute hand overtakes the hour hand between 4 and
5. In 24 hours, that is by 4 O’ clock tomorrow, how
many times does the minute hand overtake the hour
hand?
(a) 24
(b) 12
(c) 23
(d) 22
8. Ram and Shyam take a vacation at their
grandparents’ house. During the vacation, they do
any activity together. They either played tennis in the
evening or practiced Yoga in the morning, ensuring
1
INFOMATHS/MCA/MATHS/
INFOMATHS
“Either I or B belong to a different family from the
other two”, which of the following is definitely true?
(a) A belongs to TRUE family
(b) B belongs to TRUE family
(c) C belongs to FALSE family
(d) B belongs to FALSE family
25. How many ordered pairs of integers (a, b) are needed
to guarantee that there are two ordered pairs (a 1, b1)
and (a2, b2) such that a1 mod 5 = a2 mod 5 and b1
mod 5 = b2 mod 5?
(a) 13
(b) 16
(c) 26
(d) 25
PART B
1
1
26. Let f  x  

1 x
x3
Then the domain of the real function f is
(a) (-, -3)  (1, )
(b) (1, )
(c) (-, -1)  (-3, )
(d) x  1, x  - 3
27. Consider x2 – 3x – 2 < 10 – 2x. This inequality holds
when
(a) x > 4 and x < – 3
(b) x < 4 and x > – 3
(c) x < 2 and x > – 3
(d) x < 2 and x > – 3
order to warn the doomed mouse. It is a much more
probable view that the rattle snake uses its rattle, in order
to alarm the many birds and beasts which are known to
attack even the most venomous species. (-Charlces
Darwin in The Origin of Species).
14. What, according to the author is a contradiction to
the theory of Natural selection?
(a) Natural selection creates changes in a species so
that it helps other species.
(b) Natural selection creates changes in a species so
that it helps other species.
(c) Natural selection creates changes in a species so
that it can defend itself
(d) None of these
15. Why, according to the author, does the rattle snake
have a rattle?
(a) To warn its prey
(b) I self defence
(c) to scare any attacker (d) for no reason
16. From the passage give an example of a structure that
is produced to cause direct harm to other animals.
(a) rattle of a rattle snake (b) curl of a cat’s tail
(c) poison fang of a snake
(d) fang of the adder
17. There are 6 coins in a purse whose value is Rs. 1.15.
The possible denominations of the coins are Rs. 1,
50ps, 25ps, 10 ps, 5ps. Which denomination cannot
be in the purse, if from the 6 coins, no change can be
given for Rs. 1, 50ps, 25ps or 10ps?
(a) 5ps
(b) 10ps (c) 25ps (d) 50ps
18. Let X be a four-digit number that is a multiple of 9
with exactly three consecutive digits being same.
How many such X s are possible??
(a) 12
(b) 16
(c) 19
(d) 20
19. Find 9 integers from 1 to 20 (both inclusive) such
that no combination of any 3 of the nine integers
form an arithmetic progression
(a) 1, 2, 6, 7, 9, 14, 15, 18, 20
(b) 1, 2, 4, 7, 9, 14, 16, 19, 20
(c) 2, 3, 6, 8, 12, 15, 17, 18, 20
(d) 2, 3, 5, 8, 12, 15, 16, 19, 20
20. A hundred apples have to divided between 25 people
so that nobody gets an even number of apples. In
how many ways can this be done?
(a) 100 (b) 25
(c) 1
(d) 0
21. Let X = {1, 2, 3, ….. 3000}. What is the number of
elements of X which are divisible by 3 or 11 but not
by 33?
(a) 1182 (b) 1092 (c) 1272 (d) 191
22. How many words can be made with letters of the
word INTERMEDIATE if the positions of the
vowels and consonants are preserved?
(a) 151200
(b) 21600 (c) 43200 (d) 7200
23. There are 51 houses on a street. Each house has an
address between 1000 to 1099 (both inclusive).
Which one of the following is definitely true?
I.
At least one house has an odd numbered address
II. At least one house has an even numbered address
III. There will be at least two houses with consecutive
addresses
IV. There will be more than two houses with consecutive
addresses
(a) I and III
(b) II and III
(c) I, II and III
(d) I, II and IV
24. Each of the three persons A, B and C belong to either
TRUE family whose members always speak truth or
FALSE family whose members always lie. If A says
28.
lim
x 4
x 2
?
4 x
(a) -1/2
29.
(b) -1/4
(c) 0
(d) 1/ 2
f  x    n1  x  n  has a minimum at x0. Then x0
m
2
=?
m  m  1
1 1
1
  ...... 
(b)
2
2 3
m
m 1
1 1 1
1
(c)
(d) 1    ......  
2
m 2 3
m
30. The number of surjections from A = {1, 2, 3, …..n},
n  2 onto B = {a, b} is
(a)  n2 
(b) nP2
(c) 2n – 2 (d) 2n – 1
(a) 1 
31. Let  denote the null set and P(S) denote the power
set of S. Then how many elements does P(P())
have?
(a) 0
(b) 1
(c) 2
(d) 3
32. In a town of 10,000 families, it ways found that 40%
families buy newspaper A, 20% buy newspaper B,
10% buy newspaper C, 5% buy A and B, 3% buy B
and C, and 4% buy A and C. If 2% buy all the
newspapers, then the number of families who do not
buy any of the newspapers A, B, C is
(a) 3300 (b) 1400 (c) 4000 (d) 1200
n
 1
33. Suppose f  n   1   , n  N , n  2 . Then
 n
(a) 1 < f(n) < 2
(b) 2 < f(n) < 3
(c) 3 < f(n) < 4
(d) 0 < f(n) < 1
34. The number of relations on a set of n elements is
equal to
2
(a) n2
(b) 2n
(c) 2n
(d) n
35. If [x] denotes the integer part of x, then
3
2
1   x  dx is equal to
(a) 4
n
36.
(b)
1
 k  k  1
2 1
(c) 1
(d) 3
is equal to
k 1
2
INFOMATHS/MCA/MATHS/
INFOMATHS
1
n
(a)
37. If


(b)
10
12
5
100
46. From the top of a mountain of 60m height, the angles
of depression of the top and the bottom of a tower
are observed to be 30 and 60 respectively. Find the
height of the tower.
(a) 40m (b) 50m (c) 55m (d) 30m
47. In a convex pentagon ABCDE, the sides have
lengths 1, 2, 3, 4 and 5, though not necessarily in that
order. Let F, G, H and I be the mid-points of the
sides AB, BC, CD and DE respectively. Let X be the
mid-point of segment FH, and Y be the midpoint of
segment FH, and Y be the mid-point of segment GI.
The length of segment XY is an integer. Find all the
possible values for the length of side AB.
(a) 1 or 2 (b) 2 or 4 (c) 3 only (d) 4 only
48. Find the minimum and maximum values of the
function (10 cos  + 24 sin )
(a) -10, 24 (b) -25, 25 (c) -26, 26 (d) 10, 24
49. Find a value of
1
n
1
(c)
(d)
n 1
n 1
n  n  1
f  x  dx  6, 
10
f  x  dx  2 and
100
f  x  dx  4 then
(a) 0
(b) -12
dx
38. Find 
3 x
(a) log2 – log3
(c) undefined

12
5
f  x  dx  ?
(c) 4
(d) -2
2
39. The value of the integral
(b) log3 – log2
(d) 1
 /9 sec3 x tan 3 x
  2  sec3x 
1/3
0
dx
is equal to
2/3
1
1 2/3
4  2 2
(a)
(b)  42/3  32/3 
2
2
2/3
1 2/3
1
42/3  3
4   22/3 
(c)
(d)
2
2
40. Derivative of sinx2 with respect to 2x2 is
 x2 
1
(a) cos 2 x
(b) cos  
2
 2 


(c) 2 cos x2





(d)
 

50.
51.
1
cos x 2
2
x2
dy
if y   1  t  dt
sin x
dx
2
(a) 2x (1 + x ) – cos x (1 + sinx)
(b) x2 – sin x
 x2 
(c) x 2 1    sin x 1  sin 2 x / 2 
2

52.
41. Find
53.
(d) 2x – cos x
42. Determine the set of all the values of  for which the
point (, 2) lies inside the triangle formed by the
lines
2x + 3y – 1 = 0
x + 2y – 3 = 0
5x – 6y – 1 = 0
 3
 1 
 3 1   1 
(a)  , 1   ,1
(b)  ,    ,1
2
2

 

 2 3  2 
 3 
(c)  ,1
(d) (-1, 1)
 2 
43. A ray of light is sent along the line x – 2y – 3 = 0.
On reaching the line 3x – 2y – 5 = 0, the ray is
reflected from it. Find the equation of the line
containing the reflected ray.
(a) 29x – 2y – 31 = 0
(b) 2x + y – 3 = 0
(c) 2x + 3y – 5 = 0
(d) 2x + 29y – 31 = 0
44. In a triangle ABC, where A = (-4, 2), B = (2, 1) and
C = (-4, -5), find ACB.
(a) 30
(b) 45
(c) 25
(d) 60
45. The length and bread of a rectangle formed by the
lines
x + y = 5, x – y = 0,
x + y = 10 and x – y = 4 is
(a) 2 2, 12.5
(b) 4, 5
(c) 1, 10
(d)
54.
2  2  2 cos 4
(a) 2 cos 2
(b) cos 2 (c) 2 cos  (d) sin 2
The value of sin (2sin-1 (0.6))
(a) 0.96
(b) sin (1.2)
(c) 0.48 (d) sin (1.6)
6
If  is a non-real root of x = 1, then evaluate
 5   3   1
 2 1
(a) 2
(b) 0
(c) 
(d) -2
The solution set of
(5 + 4cos) (2cos  +1) = 0
In the interval [0, 2] is
(a) {/3, }
(b) {/3, 2/3}
(c) {2/3, 4/3}
(d) {2/3, 5/3}
If cos  - 4sin = 1, find sin + 4 cos.
(a)  1
(b) 0
(c)  2
(d)  4

2
2 3


Consider the matrix A   2 1 6 
 1 2 0 
Which of the following vectors are eigen vectors of
A with respect to the eigen value -3?
1
 2
 3




x1   2  , x2   1  , x3  0
 1
 0 
1 
(a) x1 x2 (b) x2 only (c) x2, x3 (d) x1, x2 and x3
55. If the system of equations
ax + y + z = 0.
x + by + z = 0
and x + y + cz = 0, (a, b, c  0) has a non-trivial
a
1
1


solution, then the value of
1 a 1 b 1 c
(a) a
(b) 1
(c) 0
(d) -1
 1 4 2 2 
 4 7 3 5 

56. For the matrix A  
3 0 8 0


 5 1 6 9 
The co-factor A31 is
(a) 14
(b) -14
(c) 204 (d) 250
1 2 2 
57. Consider the matrix A  0 2 0 
1 1 3 
12.5, 20.5
3
INFOMATHS/MCA/MATHS/
INFOMATHS
Then A3 – 9A is
(a) an identity matrix
(b) a matrix with all entries 10
(c) a diagonal matrix
(d) a matrix with all entries 0
58. The determinant of the matrix
 a2

a
1


cos
nx
cos
n

1
x
cos
n

2
x
 

 
  
 sin  nx  sin  n  1 x sin  n  2  x 


is independent of
(a) n
(b) a
x 8 8
59.
(c) x
1 1
64 48
(b)
,
,
175 175
4 4
3 1
64 48
(c) ,
(d)
,
255 255
4 4
68. A normal 8  8 chess-board is made up of 64 black
and white cells. A smaller square is being cut
randomly such that the cut is made only along the
boundaries of the cells. What is the probability of
getting a 4  4 square?
(a) 16/204 (b) 16/203 (c) 4/64 (d) 4/16
27
69. Representation of
in 2’s complement form
32
assuming 8 bits are used to represent is
(a) 0.1101100
(b) 1.0010100
(c) 0.0010100
(d) 1.0010100
70. The value of (FAC)16 – (786)16 in base 8 is
(a) 4046 (b) 2076 (c) 726 (d) 4166
71. If the equation x2 - 25x + 256 = 0 has roots (9)10 and
(10)10, in which base is the equation represented?
(a) 11
(b) 7
(c) 8
(d) 9
72. An n-digit decimal number is encoded in binary form
as follows: every odd numbered digit from the most
significant digit is encoded using binary Coded
Decimal (BCD) form and the rest of the even
numbered digits are encoded using 4-bit Gray Code.
What is encoded form for the decimal number 8743?
(a) 1000 0100 0010 0010 (b) 1000 0101 0010 0010
(c) 1000 0101 0100 0010 (d) 1000 0100 0100 0010
Consider the flowchart given in figure 1 and answer
the questions 73-75
The function reverse (N) reverses the digits of the number
N
(a)
(d) None of these
f  x   2 x 8 has local maximum at?
2 2 x
60.
61.
62.
63.
64.
65.
66.
67.
(a) 4
(b) - 4
(c) 16
(d) 82  22
The general solution of the differential equation
d2y
dy
 2  y  e2 x is
2
dx
dx
(a) (c1 + c2x) ex + e2x
(b) c1ex + e2x
x
2x
(c) c1xe + e
(d) (c1 + c2x)ex + 2e2x
The differential equation for all circles passing
through the origin and having centres on the x-axis is
dy
dy
 0 (b) x 2  y 2  2 xy
0
(a) x 2  y 2  2 xy
dx
dx
dy
dy
 0 (d) x 2  y 2  2 xy
0
(c) x 2  y 2  2 xy
dx
dx
Let A and B be two events such that the probabilities
Pr (A'  B) = 0.20 and Pr(A  B) = 0.15. Find Pr
(A|B).
(a) 3/4
(b) 1/4
(c) 4/7
(d) 3/7
A purse contains a 1-rupee coin and three 1-dollar
coins, a second purse contains two 1-rupee coins and
four 1-dollar coins, and a third purse contains three
1-rupee coins and a 1-dollar coin. If a coin is taken
out from one of the purses selected at random, find
the probability that it is a rupee.
(a) 4/9
(b) 1/12 (c) 1/3
(d)1/9
A box contains 50 bolts and 150 nuts, half of the
bolts and half of the nuts are rusted. If one item is
chosen at random, then the probability that it is
rusted or is bolt is
(a) 2/4
(b) 3/4
(c) 5/8
(d) 5/6
Suppose M is the mode of S2 the variance of n
observations. If a positive constant 'a' is added to all
the observations, the mode and variance of these
observations will be respectively
(a) M, S2
(b) M – a, S2
2
(c) M + a, S + a
(d) M + a, S2
Using only the probabilities Pr (A  B) and Pr (A 
B), which of the following probabilities cannot be
calculated?
(a) Pr (A  B)
(b) Pr (A'  B')
73. If N = 255 what is the value of A when the algorithm
(c) Pr (A'  B')
(d) Pr(B)
halts?
A, B, C and D are playing a card game which has
(a) 1515 (b) 6666 (c) 5151 (d) 5555
many rounds. In each round A, B, C and D cut a
74. If N = 75 what is the sum of the digits of N when the
pack of 52 cards successively in the given order.
algorithm halts?
What is the probability that A cuts a spade first in the
(a) 6
(b) 12
(c) 18
(d) 24
game? What is the probability that B cuts a spade
75. If N = 255, how many times is the statement A = N
first?
executed?
(a) 3
(b) 2
(c) 5
(d) 4
4
INFOMATHS/MCA/MATHS/
INFOMATHS

i.e. let tennis = t
Yoga = t + 12
t + t + 12 = 22
 2t = 10
t=5
HCU-2014 SET-A
1
A
11
A
21
A
31
C
41
A
51
D
61
A
71
B
2
C
12
B
22
C
32
C
42
A
52
C
62
D
72
D
3
B
13
D
23
C
33
B
43
A
53
D
63
A
73
B
4
B
14
B
24
D
34
C
44
B
54
C
64
C
74
B
5
A
15
A
25
B
35
D
45
A
55
C
65
D
75
D
6
B
16
D
26
C
36
C
46
A
56
A
66
D
7
D
17
A
27
A
37
B
47
C
57
NOT
67
B
8
C
18
D
28
B
38
A
48
C
58
A
68
A
9
B
19
C
29
C
39
B
49
C
59
B
69
B
10
C
20
D
30
C
40
D
50
A
60
A
70
A
9.
11. Ans. (a) Eg. 221221
Not divisible by 3.
12. Ans. (b)
2 S2

3 48
 S2 = 32 km/h
13. Ans. (d) For 6 hours.
6 hours  50 per hour = Rs. 300
14. Ans. (b)
15. Ans. (a)
16. Ans. (d)
C.S.
Mathematics
B, C, A
F, G
B, C, D
E, G
So, either F. or G is chosen.
3.
Ans. (b) 912
4.
Ans. (b) 9  5.25 – 6  6
= 47.25 – 36.
= 11.25 yrs
1x + 2x + 3x = 11.25
 6x = 11.25
 x = 1.875
875
 1yrs 
 12
1000
1 yrs + 10 month
15 days
5.
Ans. (a) LCM of 4, 7, 9
= 252 s Ans.
6.
Ans. (b)
*
*
*
*
*
*
*
5
3
*
*
*
6
17. Ans. (a)
8.
1 coin = 25 p
1 coin = 50 p
4 coin = 10p  4 = 40
Total = 1.15
Coins = 6
So, 5Ps
18. Ans. (d) Total 20 possibilities are possible.
19. Ans. (c) 2, 3, 6, 8, 12, 15, 17, 18, 20.
No, combination forms an Arithmetic progression.
20. Ans. (d) Zero way because even number of apples
can’t be distributed
21. Ans. (a)
22. Ans. (c)
23. Ans. (c) Since total hours = 5
At least one house has on odd numbered address
At least one hour has an even numbered address
There will be at least two houses with consecutive
addresses.
5
*
*
24. Ans. (d) From option
Either statement (B) or (D) is definitely true
Sina A says “Either I or B belong to a different
family from the other two’ So A must be from true
family.
So B  false family
25. Ans. (b)
*
Hence, multiple is 96.
7.
T1 S2
4 S2



T2 S1
9 48

Ans. (c)
2
100 100
 2
5
5
= 20 + 4 = 24 Ans.
Ans. (b)
10. Ans. (c) a, b, c, d, e are five con____ integer.
Case I.
12345
Case II 2, 3, 4, 5, 6
ab + d = odd
HCU-2014 CODE-A SOLUTIONS
1. Ans. (a) 1 + 2 + 3 + …… + 575 + x
n  n  1
 575  x
2
 n(n + 1) = 1050 + 2x
Substituting = n = 34
34  35 = 1190
 2x = 1190 – 1150
 2x = 40
 x = 20
So, Greater then 15.
2.
So, holidays
= 24 + 5
= 29 days
Ans. (d) 22 times in 12 hours it coincides 11 times so
24 hours = 22 times.
Ans. (c) Tennis – evening
Yoga – Morning i.e. diffence between Tennis and
Yoga is 12
5
INFOMATHS/MCA/MATHS/
INFOMATHS
PART-B
1
26. Ans. (c) f  x  
1 1 1 1
1
1
     
1 2 2 3
n n 1
1
n
 1

n 1 n 1
1

1 x
x3
x+3>0
x>-3
1–x>0
1>x
 (-3, 1)
37. Ans. (b)
12

27. Ans. (a) x2 – x – 12 < 0
(x – 4) (x + 3) < 0  -3 < x < 4
10
12
10
5

10
12

f  x  dx 
100
 f  x  dx  4
12
 f  x  dx  12
5
2
dx
 log x
x
3


3
sec t tan t dt
1
0 2  sec t 3

 3
2 + sec t = z
sec t tan t dt = dz

n
 x 2  dx 
2

1
5
 
8
3
 
2 dx
2
 

 7 dx 
 
 
7  6 2
1
40. Ans. (d) y = sinx2
dy
 cos x 2  2 x 
dx
z = 2x2
dz
 4x
dx
5 dx
1

9
 
8
8 dx
 
6 5 2
 
8 7 2
n
1

5 2 2 3

2
2
dy cos  x  2 x cos  x 


dz
4 x2
2
9  8  3  6  3
1 
cos x 2
 k  k  1    k  k  1 
k 1

2

z 3 1  32

  4  33 
2

3 2
3
5
7
n
 1 dx 
 
6
4 dx 
2
 2 1  3  2  2
36. Ans. (c)
4
dz
z 3
3 z1/3  3 3
2
   6 dx 

4
2
1
2
3
39. Ans. (b) 3x = t
3dx = dt
 1
33. Ans. (b) 2 < f(n) < 3 as lim 1    e
n 0
 n
6
2
2
 log 2  log 3  log  
3
32. Ans. (c) 100 – [40 + 20 + 10 – 5 – 3 – 4 + 2]
100 – [70 – 12 + 2]
40%
40

 10000
100
 4000
7
…(iii)
 f  x  dx  8  4
31. Ans. (c) 2
5 dx 
…(ii)
12
38. Ans. (a)
3
 f  x  dx  2
5
30. Ans. (c) 2 – 2
 
12
12
n
4
5
 f  x  dx  2  6  8
So minima

100
12
m  m  1 

 2  mx 
0
2


m 1
x
2
f " x   2  m = + ve
3
12
…(i)
100
f '  x   2  x  1   x  2   .....   x  n  
35. Ans. (d)
 f  x dx  4
From (i) and (ii)
2
n 1
34. Ans. (c) 2n
100
5
f  x  dx   f  x  dx 
5
m

f  x  dx  2,
10
5
5

29. Ans. (c) f  x     x  n 
100
 f  x  dx   f  x  dx  6
x 2
x 2

28. Ans. (b) lim
x4 4  x
x 2
x4
1
1
lim
 lim

x 4
 4  x  x  2 x 4 x  2 4

f  x  dx  6,
41. Ans. (a) y 
k 1
 1  t  dt
sin x
6
INFOMATHS/MCA/MATHS/
INFOMATHS
dy
 1  x 2   2 x   1  sin x  cos x
dx
= 2x (1 + x2) – (1 + sinx) cos x
AM tan 60

3
BM tan 30
AM
3
AM  AB
3AB = 2AM
2
AB   60  40 m
3
42. Ans. (a)
47. Ans. (c)
(5/4, 7/8)
48. Ans. (c) 10cos + 24sin
(1/3, 1/9
 102  242 , 102  242
 100  576, 100  576
 676, 676
- 26, 26
43. Ans. (a) m1 
1
2
m
3
2
49. Ans. (c)
1 3
3

 m2
2 2  2
1 3
3
1 
1  m2
2 2
2
3
21 7
1  m2 
 m2
2
8 4
18
29
m2 
4
8
29
m2 
2
Pt. of intersection is?
x = 1, y = - 1
29
 y  1   x  1
2
29x – 2y – 31 = 0
2  2  2cos2 2 
2  2cos2 
2  2 cos 2  
= 2 cos 
50. Ans. (a) sin (2sin-1(0.6)
= 2.  0.6   1   0.6
51. Ans. (d)
1 5
1
24
ACB = 45
b
5
2
4
2
 5   3   1
 2 1
[6 = 1]
1, , 2, 3, 4, 5  G.P. with c.r.
 2  4
=  2
  2
 1
m2 
45. Ans. (a) L 
2
= 2  0.6  0.8
= 0.96
25

4  4
44. Ans. (b) m1 
2  2  2 cos 4
52. Ans. (c) (5 + 4cos) (2cos + 1) = 0
5
1
cos    or cos   
4
2
1
cos   
2
 2 4 
 3 , 3 


2 2
 2.5 2  12.5
53. Ans. (d) cos - 4sin = 1
sin + 4cos = ?
cos = 1 + 4sin
1  cos   1  cos 
4sin  
1  cos 
2
sin 
4sin  
1  cos 
-4cos - 4 = sin
4cos + sin = - 4
or sin = 0
4cos + sin = 4
46. Ans. (a)
AM
 tan 60
CM
BM
 tan 30
CM
7
INFOMATHS/MCA/MATHS/
INFOMATHS
= a2 [-sinx] – a[sin (n + 2)x] + sinx
= (1 – a2) sinx – a sin2x
Independent of n.
 1 2 3
54. Ans. (c)  A  3I    2 4 6


 1 2 3 
(A + 3I) x1  0
(A + 3I) x2 = 0
(A + 3I) x3 = 0
x2 & x3 are eigen vectors.
1 0 0 x 8 8 x 8 8
59. Ans. (b) f '  x   2 x 8  0 1 0  2 x 8
2 2 x 2 2 x
= x – 16 + x – 16 + x2 – 16 = 0
= 3(x2 = 16)
x=4
f" (x) = 3(2x)
f" (-4) = - 24 < 0
so f(x) is maximum at x = - 4
2
a 1 1
55. Ans. (c) 1 b 1  0
1 1 c
C2  C2 – C1 C3  C3 – C1
a 1 a 1 a
1 b 1
1
0
0
60. Ans. (a) y" – 2y' + y = e2x
 It’s solutions are C.F. + P.I.
m2 – 2m + 1 = 0
m=1
C.F. = C1ex + C2xex
To find PF : (D2 – 2D + 1)y = e2x
e2 x
e2 x
y 2
 2
 e2 x
D  2D  1 2  2.2  1
So solution is
= C.F + PI
= c1ex + c2xex + e2x
0
c 1
a
1 a
1
1  a 1  b 1  c 
1 b
1
1 c
R1  R1 + R2 + R3
1
1
1
0 =0
0
1
a
1
1


1 a 1 b 1 c
1
1  a 1  b 1  c 
1 b
1
1 c
0
0
1
0 0
0
1
61. Ans. (a) (x – h)2 + y2 = h2  x2 + h2 – 2xh + y2 = h2
x2  y 2
h
2x
dy
0
Diff  2  x  h   2 y
dx
dy
xh y
0
dx
a
1
1


0
1 a 1 b 1 c
56. Ans. (a) A31   1
31
4
2
2
7
3
5
0 0 1
2
 x2  y 2
x 
 2x

dy
0
 y
dx

dy
2 x 2  x 2  y 2  2 xy
0
dx
dy
x 2  y 2  2 xy
0
dx
1 6 9
= - 4[-27 – 30] – 2[63 + 5] – 2[42 – 3]
= 57  4 – 2  68 – 2  39 = 57  4 – 2  107 = 14
62. Ans. (d) P(A'  B) = 0.20] P(A  B) = 0.15
 P(B) = 0.20 + 0.15 = 0.35
1 2 2
57. Ans. (n.o.t) A  0 2 0 
1 1 3
3
2
A – 9A = A[A - 9I]
= A[A - 3I] [A + 3I]
1 2 2  2 2 2  4 2 2
0 2 0   0 1 0  0 5 0 




1 1 3  1 1 0  1 1 6 
0 2 2  4 2 2  2 12 12
0 2 0 0 5 0  0 10 0 


 

1 0 2 1 1 6 6 0 14
 A
P   .P  B   P  A  B 
B
 A  0.15 3
P  

 B  0.35 7
1 1 1 2 1 3
    
3 4 3 6 3 4
1 1 3
4 1 4
    
12 9 12 12 9 9
63. Ans. (a)
64. Ans. (c) P(rusted or bolts) = P(rust) + P(bold) – P(r
 b)
1 50
25
 

2 200 200
58. Ans. (a) a2 [cos(n + 1)x sin(n + 2)x – cos(n + 2)x
sin(n+ 1)x] –a [cosnx sin(n + 2)x – sin(nx)
cos(n+2)x]
+1 [cos(nx) sin (n+1)x – sin(nx) cos(n+1)x]
8
INFOMATHS/MCA/MATHS/
INFOMATHS
69. Ans. (b)
1 1 1
 
2 4 8
3 1 5
  
4 8 8

70. Ans. (a)
71. Ans. (b)
65. Ans. (d)
72. Ans. (d)
66. Ans. (d)
73. Ans. (b)
67. Ans. (b)
13

52
39
C4 13
 
52
C4 48
39
C8 13

52
C8 44
39
52
74. Ans. (b)
C12 13
C12 40
75. Ans. (d)
68. Ans. (a) Total squares are
8  9  17
  82 
 204
6
No. of 4  4 square = 25 and no. of 4  4 on edges =
16
16 so probability of 4 4 square on edges 
204
MY PERFORMANCE ANALYSIS
No. of Questions
Attempted (=A)
No. of Right
Responses (=R)
No. of Wrong
Responses (=W)
9
Net Score
(NS = R – 0.25W)
Percentage Accuracy
(= PA= 100R/A)
INFOMATHS/MCA/MATHS/