## Transcript

CA- / 20 i
A
2012 CA
Test Paper Code: CA
Time: 3 Hours Max. Marks: 300
MARKING SCHEME:
(a) For each correct answer, you will be awarded 3 (Three) marks.
(b) For each wrong answer, you will be awarded -1 (Negative one) mark.
(c) Multiple answers to a question will be treated as a wrong answer.
(d) For each un-attempted question, you will be awarded 0 (Zero) mark.
Name
Registration Number
INSTRUCTIONS
A. General:
1. This Booklet is your Question Paper. It contains 20 pages and has 100 questions.
2. The Question Booklet Code is printed on the right-hand top corner of this page.
3. The Question Booklet contains blank spaces for your rough work. No additional
sheets will be provided for rough work.
4. Clip board, log tables, slide rule, calculator, cellular phone or any other
electronic gadget in any form are NOT allowed.
5. Write your Name and Registration Number in the space provided at the bottom.
6. All answers are to be marked only on the machine gradable Objective Response
Sheet (ORS) provided along with this booklet, as per the instructions therein.
7. The Question Booklet along with the Objective Response Sheet (ORS) must be
handed over to the Invigilator before leaving the examination hall.
8. Refer to Special Instruction/Useful Data on reverse of this sheet.
B. Filling-in the ORS:
9. Write your Registration Number in the boxes provided on the upper left-hand-side
of the ORS and darken the appropriate bubble under each digit of your
Registration Number using a HB pencil.
10. Ensure that the code on the Question Booklet and the code on the ORS are the
same. If the codes do not match, report to the Invigilator immediately.
11. On the lower-left-hand-side of the ORS, write your Name, Registration Number,
and Name of the Test Centre and put your signature in the appropriate box with
ball-point pen. Do not write these anywhere else.
C. Marking of Answers on the ORS:
12. Each question has 4 choices for its answer: (A), (B), (C) and (D). Only ONE of
them is the correct answer.
13. On the right-hand-side of ORS, for each question number, darken with a HB
Pencil ONLY one bubble corresponding to what you consider to be the most
appropriate answer, from among the four choices.
14. There will be negative marking for wrong answers.
QUESTION BOOKLET CODE
CA- / 20 ii
A
Special Instructions/ Useful Data
N denotes the set of natural numbers { } 1, 2, 3,
Z denotes the set of integers
¸ denotes the set of rational numbers
R denotes the set of real numbers
C denotes the set of complex numbers
{ }
\ A B x A x B = ∈ ∉ for two sets A and B
LPP denotes Linear Programming Problem
Max f denotes the maximum of f
Min f denotes the minimum of f
x’ denotes the complement of a Boolean variable x
f ′ denotes the first derivative of a function f
x
f denotes the partial derivative of
f
x
∂
∂
of f
y
f denotes the partial derivative of
f
y
∂
∂
of f
f ∇ denotes the gradient of a function f
For all C programs, assume that all standard library functions are
accessible.
CA- / 20 1
A
Who created the first free email service on the Internet?
(A) B. W. Kernighan (B) Bill Gates
Q.1
(C) N. Karmakar (D) Sabeer Bhatia
Let { } { }
2
1, 20, 21 = ∈ ∈ ¸ S x x . Then the number of elements in the set S is
Q.2
(A) 1 (B) 2 (C) 4 (D) 6
The rank of the matrix
1 2 4 1 2
2 3 7 1 2
1 0 2 1 2
1 1 1 2 4
− ⎡ ⎤
⎢ ⎥
−
⎢ ⎥
⎢ ⎥ −
⎢ ⎥
− −
⎣ ⎦
is
Q.3
(A) 1 (B) 2 (C) 3 (D) 4
Mega FLOPS stands for
(A) 10
9
floating point operations per second
(B) 10
5
fixed point operations per second
(C) 10
6
floating point operations per second
Q.4
(D) 10
12
fixed point operations per second
The set ( )
{ }
2
, S x y x or y = ∈ ∉ ∉ R ¸ Z is
Q.5
(A) ( ) ( ) \ \ × R ¸ R Z (B) ( ) ( ) \ × × R R ¸ Z (C) ( ) \ × R ¸ R (D) ( ) \ × R R Z
The number 20
6
– 13
6
is divisible by
Q.6
(A) 11 (B) 5 (C) 13 (D) 6
The inverse of the matrix
1 1 1
2 3 2
3 8 2
⎡ ⎤
⎢ ⎥
⎢ ⎥
⎢ ⎥
⎣ ⎦
is
(A)
10 6 1
2 1 0
7 5 1
− ⎡ ⎤
⎢ ⎥
− −
⎢ ⎥
⎢ ⎥ − − −
⎣ ⎦
(B)
10 6 1
2 1 0
7 5 1
− ⎡ ⎤
⎢ ⎥
− −
⎢ ⎥
⎢ ⎥ − −
⎣ ⎦
Q.7
(C)
10 6 1
2 1 0
7 5 1
− − ⎡ ⎤
⎢ ⎥
−
⎢ ⎥
⎢ ⎥ −
⎣ ⎦
(D)
10 6 1
2 1 0
7 5 1
− ⎡ ⎤
⎢ ⎥
−
⎢ ⎥
⎢ ⎥ − −
⎣ ⎦
CA- / 20 2
A
Let : f → R Rbe defined by
2
( ) 4 5 f x x x = + + . Then which of the following statements is
TRUE?
(A) f is one-one. (B) f is on-to.
Q.8
(C) f is one-one and on-to. (D) f is neither one-one nor on-to.
The number of distinct 3 digit numbers greater than 100 where no digit repeats itself is
Q.9
(A) 504 (B) 648 (C) 326 (D) 210
The digit at the unit place of the number 19
25
is
Q.10
(A) 1 (B) 3 (C) 5 (D) 9
The differential equation
( ) tan cos , ,
2 2
dy
x y x x
dx
π π ⎛ ⎞
+ = ∈ −
⎜ ⎟
⎝ ⎠
has the solution
(A) ( ) cos y x c x = + (B) ( )sec y x c x = +
Q.11
(C) ( )sin y x c x = + (D) ( ) cosec y x c x = +
Consider the function
4 3
( ) 2 1 f x x x = − + − . What is the absolute truncation error for evaluation
of ( ) f x
′
at 0.5 x = by the first order forward difference scheme using a step size, 0.5 h = ?
Q.12
(A)
5
8
(B)
1
2
(C)
1
3
(D)
8
5
Consider the following LPP
Max 5 12
subject to
5 50,
6 3 36,
5, 0, 0
f x y
x y
x y
x x y
= +
+ ≤
+ ≤
≤ ≥ ≥
The number of extreme points of the feasible region are
Q.13
(A) 4 (B) 5 (C) 6 (D) 7
Solution of the initial value problem
( ) ( ) 2cos 3 sin 0, 1 0 y x dx x y dy y + − = =
is
(A)
2 3
cos 1 x y y + = (B)
2 3
sin 0 x y y + =
Q.14
(C)
2 3
cos 2 x y x + = (D)
2 3
sin 0 y x y + =
CA- / 20 3
A
Let α be a real number and { } { }
\ 0 α = ∈ = C G z z . Then G is a group under multiplication
of complex numbers if
Q.15
(A) 0 α = (B) 1 α < (C) 1 α > (D) 1 α =
Order the following processors in the increasing order of speed.
M1: 486, M2: 8085, M3: Dual core, M4: Pentium III
Q.16
(A) M1 M2 M3 M4 (B) M2 M1 M4 M3 (C) M1 M2 M4 M3 (D) M1 M3 M4 M2
Which of the following statements is TRUE?
(A) There exists a field with 1000 elements.
(B) There exists a field with 100 elements.
(C) There exists a field with 500 elements.
Q.17
(D) There exists a field with 9 elements
A particular solution of the differential equation
5 4 3 2
5 4 3 2
3 3 2
x
d y d y d y d y
e
dx dx dx dx
− + − =
is
Q.18
(A)
3
1
3
x
x e (B)
3
1
2
x
x e (C)
3
1
6
x
x e (D)
3
2
3
x
x e
For an LPP, if the constraints are
3,
- 3 5,
0, 0
+ ≤
+ ≤
≥ ≥
x y
x y
y x
then which one of the following point is NOT a feasible point?
Q.19
(A) ( ) 3, 0 (B) ( ) 1, 2 (C) ( ) 2, 4 (D)
5
0,
3
⎛ ⎞
⎜ ⎟
⎝ ⎠
The volume of the tetrahedron bounded by the planes 0, 0, 0 z x y = = = and 1 y z x + − = is
Q.20
(A) 1/6 (B) 6 (C) 1 (D) 1/3
Aadhar Unique Identification (UID) number is of
Q.21
(A) 10 digits (B) 12 digits (C) 14 digits (D) 16 digits
CA- / 20 4
A
The general solution of the nonhomogeneous differential equation
2
2
12 150cos3
d y dy
y x
dx dx
+ − =
is
(A)
3 4
1 2
7cos3 sin3
x x
c e c e x x
−
+ − −
(B)
3 4
1 2
7cos3 sin3
x x
c e c e x x
−
+ − +
(C)
3 4
1 2
7cos3 sin3
x x
c e c e x x
−
+ + +
Q.22
(D)
3 4
1 2
7cos3 sin3
x x
c e c e x x
−
+ − −
Which of the following is/are main memory of a computer?
P: RAM, Q: Hard disk, R: CDROM, S: Pen drive
Q.23
(A) P and Q only (B) Q only (C) P only (D) P, R, and S only
The boundary value problem
( ) ( )
2
2
2
0, 0 0, 1 0
d y
y y y
dx
π + = = =
has
(A) two solutions (B) no solution
Q.24
(C) unique solution (D) infinitely many solutions
Suppose
ˆ ˆ ˆ
2 3 a i j k = − +
,
,
ˆ ˆ
b i k = +
,
and
ˆ ˆ ˆ
3 c i j k = − +
,
. Then
( )
a b c × ×
, , ,
is
Q.25
(A)
ˆ ˆ
8 4 + i j (B)
ˆ ˆ
8 4 − i j (C)
ˆ ˆ
8 8 + i j (D)
ˆ ˆ
8 8 − i j
The Newton-Raphson method is used to find a real root of ( )
3
1 0 f x x x = − + = with initial
approximation
0
1 x = . Then the second approximation
2
x is
Q.26
(A)
1
2
(B)
5
8
(C) 2 (D) 3
SMS stands for
(A) Short Message Service (B) Secured Message Service
Q.27
(C) Short Mail Service (D) Secured mail Service
What is the probability of getting an even number or a number less than 5, in tossing a fair die?
Q.28
(A)
2
3
(B)
1
3
(C)
5
6
(D)
1
6
CA- / 20 5
A
Rabindranath Tagore won the Nobel prize in Literature for his book entitled
(A) War and Peace (B) Malgudi Days
Q.29
(C) Gitanjali (D) Durgeshnandini
Which company is the leader in computer networking?
Q.30
(A) Wipro (B) Cisco (C) Oracle (D) TCS
For the table
x 0 1 2 3
( ) f x
1 2 9 28
the divided difference
[ ]
1, 2, 3 f is
Q.31
(A) 6 (B) 13 (C) 3 (D) 1
Which one of the following is equivalent to 8 Giga bytes?
Q.32
(A) 2
23
bytes (B) 2
33
bytes (C) 2
43
bytes (D) 2
53
bytes
The decimal value of (327)
8
× (25)
8
is
Q.33
(A) 5625 (B) 8175 (C) 3267 (D) 4515
The value of the integral
2
2
0
(1 5 100 ) x x dx + −
∫
by Simpson’s
1
3
rd rule is
Q.34
(A) -288 (B)
764
3
− (C) 288 (D) 289
Which one of the following stands for LAN?
(A) Local Area Network (B) Logical Area Network
Q.35
(C) Large Area Network (D) Least Area Network
The Boolean expression (x + y) (x + y’ ) is equivalent to
Q.36
(A) x + y (B) y (C) xy (D) x
ISP stands for
(A) Internet Security Protocol (B) Intelligent Service Package
Q.37
(C) Internet Service Provider (D) Intelligent Service Provider
CA- / 20 6
A
Let ( , ) ( ) f x y cos xy x cos y = + . Then the value of (2, / 2) (2, / 2)
x y
f f π π + is
Q.38
(A) 0 (B) -2 (C) 2 (D) 4
If
ˆ ˆ ˆ
2 = − +
,
a i j k ,
ˆ ˆ ˆ
2 2 b i j k = − +
,
and
ˆ ˆ ˆ
4 3 2 = − +
,
c i j k , then the projection of a b +
, ,
on the
vector b
,
is
Q.39
(A)
20
3
(B) 20 (C)
20
9
(D)
8
3
For what value of α , the vectors
ˆ ˆ ˆ
2 + + i j k ,
ˆ ˆ ˆ
2 2 α + + i j k and
ˆ ˆ ˆ
i j k + − are coplanar?
Q.40
(A) 1 (B) 2 (C) 4 (D) 8
The next term in the sequence of ternary number 10, 20, 100, 110, … is
Q.41
(A) 120 (B) 111 (C) 112 (D) 101
The 9’ s complement of 123456789 is
Q.42
(A) 876543211 (B) 876543210 (C) 987654321 (D) 012345678
What is the largest unsigned integer that can be expressed with n bits?
Q.43
(A) 2
n – 1
(B) 2
n
– 1 (C) 2
n
+ 1 (D) 2
n + 1
Suppose ( )
3 2
2 1 f x x x x = + + + . Then the polynomial that interpolates the value of f at
1, 0,1 x = − is
(A)
2
4 4 1 x x + + (B)
2
1 x x + +
Q.44
(C)
2
2 2 1 x x + + (D)
2
3 3 1 x x + +
A search engine is
(A) a machine (B) a web site
Q.45
(C) a movie (D) a map used for driving
CA- / 20 7
A
The Lagrange form of the interpolating polynomial that fits the data
x 0 1 2
( ) f x
1 2 5
is
(A) ( )( ) ( ) ( )
1 5
1 2 2 2 1
2 2
x x x x x x − − − + + −
(B) ( )( ) ( ) ( )
1 5
1 2 2 2 1
2 2
x x x x x x − − + + + −
(C) ( )( ) ( ) ( )
1 2
2 1 2 2 1
2 5
x x x x x x − − + + + −
Q.46
(D) ( )( ) ( ) ( )
1 2
2 1 2 2 1
2 5
x x x x x x − − − + + −
The function ( ) , f x y xy = defined on
2 2
1 x y + ≤ has
(A) both maximum and minimum values
(B) only maximum value
(C) only minimum value
Q.47
(D) neither maximum nor minimum value
The area of the region enclosed by the parabola
2
4 x ay = and the line 2 x a = with x -axis is
Q.48
(A)
2
4
3
a (B)
2
3
2
a (C)
2
3
4
a (D)
2
2
3
a
Consider the system of linear equations
2 3
2 2
2 2 1
x y z
x z
x y z
α
α
− + =
+ = −
− + + =
In order to have unique solution to this linear system of equations the value of α should not
be equal to
Q.49
(A)
2
3
− (B)
2
3
(C)
4
3
(D)
4
3
−
CA- / 20 8
A
The quadratic approximation of ( ) , cos cos f x y x y = about the point ( ) 0, 0 is
(A)
( )
2 2
1
1
2
x y + − (B)
( )
2 2
1
1
2
x y + +
Q.50
(C)
( )
2 2
1
1
2
x y − − (D)
( )
2 2
1
1
2
x y − +
Consider the following two lists:
List I List II
1: Mouse P: Input device
2: Modem Q: External memory
3: Pen drive R: Web browser
4: Opera S: Network device
The correct match is
(A) 1 → R, 2 → S, 3 → P, 4 → Q (B) 1 → P, 2 → S, 3 → Q, 4 → R
Q.51
(C) 1 → S, 2 → R, 3 → Q, 4 → P (D) 1 → P, 2 → Q, 3 → S, 4 → R
The matrix
1 2 2
2 2 1
2 1 2
− ⎡ ⎤
⎢ ⎥
−
⎢ ⎥
⎢ ⎥ −
⎣ ⎦
has
(A) all positive eigenvalues
(B) all negative eigenvalues
(C) some positive eigenvalues and some negative eigenvalues
Q.52
(D) one zero eigenvalue
An integrating factor of the differential equation
2sinh cos cosh sin 0 − = x y dx x y dy
is
Q.53
(A) cosh x (B) sinh x (C) sin x (D) cos x
The random variable X follows the Poisson distribution with variance 4. The mean of this
Poisson distribution is
Q.54
(A) 2 (B) 4 (C) 16 (D) 8
Two balls are drawn in succession from a box containing 30 red, 20 white, 10 blue and 15
orange balls; replacement being made after each draw. The probability that neither is orange is
Q.55
(A)
16
25
(B)
9
25
(C)
1
25
(D)
24
25
CA- / 20 9
A
Let the function f has the values
0 1 2
, , f f f at equidistant nodal points
0 1 2
, , x x x where
0
,
i
x x ih = + 1, 2 i = . Then, the divided difference
0 1 2
[ , , ] f x x x is equal to
Q.56
(A)
2
2
f
h
∇
(B)
0
2
f
h
Δ
(C)
2
0
2
2
f
h
Δ
(D)
1
2
f
h
∇
Let ( )( ) 1, 3, 5, 7, 9,10 2, 4, 6, 8 σ = be a permutation in
10
S . Then the smallest positive integer m
such that
m
Id σ = , the identity permutation, is
Q.57
(A) 24 (B) 6 (C) 4 (D) 12
Consider the following two lists:
List I List II
1: TFT P: Visual display unit
2: RAM Q: Volatile memory
3: ROM R: Non-volatile memory
4: CRT S: Non-writable memory
The correct match is
(A) 1 → P, 2 → Q, 3 → S, 4 → R (B) 1 → P, 2 → R, 3 → Q, 4 → S
Q.58
(C) 1 → S, 2 → Q, 3 → S, 4 → P (D) 1 → P, 2 → Q, 3 → S, 4 → P
A base 12 number system is called duodecimal. It uses the symbols 0, 1, 2, ..., 9, A, and B,
where A and B are the symbols used to represent 10 and 11 respectively. What is the
duodecimal equivalent of the decimal number 1594?
Q.59
(A) A09 (B) A0A (C) B0A (D) B0B
A particular solution of the differential equation
2
2
x
d y dy
xe
dx dx
− =
is
(A) ( )
2
1
2
x x
x
e x e − + − (B) ( )
2
1
2
x x
x
e x e
− −
− + −
Q.60
(C) ( )
2
1
2
x x
x
e x e − − (D) ( )
2
1
2
x x
x
e x e
− −
− −
The equation for the tangent plane to the surface
3 2
2 3 − = − x y xz at the point ( ) 1, 1,1 − is
(A) 7 2 2 11 x y z − + = (B) 2 7 2 11 x y z − + =
Q.61
(C) 2 7 2 11 x y z + − = (D) 7 2 2 11 x y z + − =
CA- / 20 10
A
The minimum distance from the origin to the plane
3
3 11 x y z in + − = R is
Q.62
(A) 10 (B) 1
(C) 11
(D) 11
Let σ be a 6-cycle in
12
S . Then
i
σ is also 6-cycle if the value of i is
Q.63
(A) 2 (B) 3 (C) 5 (D) 12
The book entitled, ‘The Discovery of India’ was written by
(A) Abul Kalam Azad (B) Jawaharlal Nehru
Q.64
(C) Rajendra Prasad (D) Sarvepalli Radhakrishnan
Consider the following two lists:
List I List II
1: Functional programming P: C language
2: Logical programming Q: Prolog
3: Procedural programming R: C++
4: Object oriented programming S: Lisp
Which one of the following is correct match?
(A) 1 → P, 2 → Q, 3 → S, 4 → R (B) 1 → P, 2 → Q, 3 → R, 4 → S
Q.65
(C) 1 → P, 2 → R, 3 → S, 4 → Q (D) 1 → S, 2 → Q, 3 → P, 4 → R
What is the octal equivalent of the hexadecimal number ABC?
Q.66
(A) 5674 (B) 5314 (C) 5275 (D) 5274
The fourth order linear differential equation having , , cos 2 , sin 2
x x
e x e x x
− −
as solutions is
(A)
4 3 2
4 3 2
2 5 8 4 0
d y d y d y dy
y
dx dx dx dx
+ + + + =
(B)
4 3 2
4 3 2
2 8 5 4 0
d y d y d y dy
y
dx dx dx dx
+ + + + =
(C)
4 3 2
4 3 2
2 3 4 2 0
d y d y d y dy
y
dx dx dx dx
+ + + + =
Q.67
(D)
4 3 2
4 3 2
2 4 3 2 0
d y d y d y dy
y
dx dx dx dx
+ + + + =
The probability of getting a total of 9 at least once in two tosses of a pair of fair dice is
Q.68
(A)
600
729
(B)
128
729
(C)
601
729
(D)
64
81
CA- / 20 11
A
If the matrix
2
a b
b
⎡ ⎤
⎢ ⎥
⎣ ⎦
has eigenvalues 1 and 3, then the value of ( ) , a b is
Q.69
(A) ( ) 1, 2 (B) ( ) 2,1 (C) ( ) 1, 2 − (D) ( ) 2,1 −
The value of the integral
9
0 1
dy
y y +
∫
is
Q.70
(A) 4
(B) 4( 10 1) −
(C) 8 (D) 12
The truth table of a binary operator ¸ is given below:
x y x ¸ y
0 0 0
0 1 0
1 0 1
1 1 0
Which one of the following is equivalent to x ¸ y?
Q.71
(A) x’ y’ (B) xy (C) x’ y (D) xy’
Suppose
ˆ ˆ ˆ
2 2 3 + = + +
, ,
a b i j k ,
ˆ ˆ ˆ
2 3 a b i j k − = − +
, ,
represent diagonals of a parallelogram whose
sides are a
,
and b
,
. Then the area of the triangle formed by the sides , a b
, ,
and a b +
, ,
is
Q.72
(A)
1
189
4
(B)
1
198
4
(C)
1
179
4
(D)
1
197
4
What is the characteristic equation of the T flip-flop, if Q and Q
+
denote the output during the
current and next clock cycle?
(A) Q
+
= T + Q (B) Q
+
= T’ Q’ + TQ
Q.73
(C) Q
+
= TQ’ + T’ Q (D) Q
+
= T’ + Q’
The integral ( )
1
1
f x dx
−
∫
where f is continuous on [-1,1], is approximated by the formula
( )
1
1
1 1
2 2
f x dx f f α β
−
⎛ ⎞ ⎛ ⎞
− +
⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
∫
= .
Suppose the approximation is exact for all polynomials of degree 1 ≤ . Then the value of α is
Q.74
(A) 1 − (B) 1
(C)
1
2
(D)
1
2
−
CA- / 20 12
A
Let
2
1
( )
1
g x
x x
=
− +
and
2 3
1 2 3
...
o
a a x a x a x + + + + be the Taylor series of the function g
around 0. Then the value of
3
a is
Q.75
(A) 0 (B) 1 (C) -1 (D) 3
Which of the following is/are forbidden input(s) for SR flip-flip?
P: S = 1, R = 1 Q: S = 0, R = 0
Q.76
(A) P only (B) Q only (C) both P and Q (D) neither P nor Q
The iteration formula
( )( )
1
cos sin cos
n n n n n
x x x x R x
+
= − +
where R is a positive constant, is used to find a real root of some function ( ) f x . What is
( ) f x , assuming the iteration method is convergent with an initial approximation
0
x ?
Q.77
(A) tan x R − (B) cot x R − (C) sin x R − (D) cos x R −
The area of the surface generated by rotating the hypocycloid
3 3
cos , sin , 0 x a y a θ θ θ π = = ≤ ≤
about y -axis is
Q.78
(A)
2
12
5
a π (B)
2
5
12
a π (C)
2
6
5
a π (D)
2
5
6
a π
What is the output of a JK flip-flop during next clock cycle, when J = 1, K = 1? Assume, Q is
the output during the current clock cycle.
Q.79
(A) 1 (B) 0 (C) Q (D) Q’
What are the values of the variables i , j , and k after execution of the following program
segment?
i nt i =1, j =2, k=3;
i += j += k;
(A) i = 3, j = 5, k = 6 (B) i = 3, j = 6, k = 5
Q.80
(C) i = 6, j = 3, k = 5 (D) i = 6, j = 5, k = 3
What is the content of the array after execution of the following program segment?
i nt a[ ] = {1, 2, 3, 4}, i ;
f or ( i =1; i <4; ++i ) a[ i ] = a[ i ] + a[ i - 1] ;
(A) {0, 1, 2, 3} (B) {1, 2, 3, 4}
Q.81
(C) {1, 3, 6, 10} (D) {4, 3, 2, 1}
CA- / 20 13
A
The eigenvectors of the matrix
0 0 1
0 0 0
0 0 0
⎡ ⎤
⎢ ⎥
⎢ ⎥
⎢ ⎥
⎣ ⎦
are
(A)
1 0
0 , 1
0 0
⎛ ⎞ ⎛ ⎞
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
(B)
1 0 0
0 , 1 , 0
0 0 1
⎛ ⎞ ⎛ ⎞ ⎛ ⎞
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠ ⎝ ⎠
Q.82
(C)
1 0 1
0 , 1 , 0
0 0 0
⎛ ⎞ ⎛ ⎞ ⎛ ⎞
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠ ⎝ ⎠
(D)
1 0 1
0 , 1 , 1
0 0 1
⎛ ⎞ ⎛ ⎞ ⎛ ⎞
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠ ⎝ ⎠
Consider the following C function:
voi d f un2( i nt n) {
whi l e ( n > 0) {
pr i nt f ( " %d" , n%10) ;
n = n/ 10;
}
}
What is the output of f un2( 475) ?
Q.83
(A) 475 (B) 543 (C) 754 (D) 574
Consider the following algorithm:
(1) f or i = 1 t o p do
(2) f or j = 1 t o q do
(3) f or k = 1 t o r do
(4) c[ i , j ] = c[ i , j ] + a[ i , k] * b[ k, j ] ;
How many times line (4) is executed?
Q.84
(A) 3 (B) p + q + r (C) pqr (D) i j k
CA- / 20 14
A
Consider the following C function:
i nt f un1( i nt n) {
i nt x=0;
whi l e ( n > 1) {
n = n/ 2;
++x;
}
r et ur n ( x) ;
}
What is the return value of f un1( 31) ?
Q.85
(A) 3 (B) 4 (C) 5 (D) 6
Let A be a 3 3 × matrix whose sum of the diagonal elements is
1
2
and the determinant is
1
2
− .
If 1 is an eigenvalue of A, then the eigenvalues of
( )
2
1
A
−
are
Q.86
(A) 1,1, 4 (B)
1
,1,1
4
(C) 1,1, 2 (D)
1
,1,1
2
Let ( )
{ }
3
1
, , 0 S x y z x y z = ∈ + + = R and ( )
{ }
3 2 2 2
2
, , 1 S x y z x y z = ∈ + − ≤ R . Then the set
1 2
S S ∩ is
(A) convex but not bounded.
(B) bounded but not convex.
(C) bounded and convex.
Q.87
(D) neither bounded nor convex.
The number of different Boolean functions with 3 inputs and 4 outputs is
Q.88
(A) 64 (B) 127 (C) 128 (D) 144
What is the output of the following program fragment?
i nt x = 123, y= - 123, z=0;
i f ( x) { i f ( z) pr i nt f ( " aaa\ n" ) ; }
el se i f ( y) pr i nt f ( " bbb\ n" ) ;
el se pr i nt f ( " ccc\ n" ) ;
Q.89
(A) aaa (B) bbb (C) ccc (D) outputs nothing
CA- / 20 15
A
The solution of the following LPP
Max 5
subject to
2 10,
4 3 24,
2 , 0
f x y
x y
x y
y x y
= +
+ ≥
+ ≤
≤ ≥
is
Q.90
(A) 27.5 (B) 26.4 (C) 23 (D) 6
Let : f → R Rbe the function defined by
2
( )
x if x
f x
x if x
⎧ ∈
=
⎨
∉
⎩
¸
¸
. Then the function f is
(A) differentiable on R.
(B) differentiable only at 0.
(C) differentiable only at 1.
Q.91
(D) is continuous at 0 but NOT differentiable at 0.
Consider the following logic circuit:
What is the output F?
Q.92
(A) x + yz (B) y + xz (C) z +xy (D) x + y + z
Suppose
1
φ and
2
φ are two linearly independent solutions of the differential equation
2
1 2 2
0
d y dy
a a y
dx dx
+ + =
where
1
a and
2
a are constants. Then
1
φ and
2
φ have
(A) odd number of common zeros
(B) exactly one common zero
(C) no common zeros
Q.93
(D) at most two common zeros
x
y
z
F
CA- / 20 16
A
Which one is equivalent to xyz + xyz’ + xy’ z + xy’ z’ ?
Q.94
(A) x (B) x’ (C) y + z (D) yz
In the following segment of C program
i nt x;
scanf ( " %d" , &x) ;
i f ( x&1) pr i nt f ( " %s" , STAMENT) ;
STAMENT represents a missing string. Which one of the following is an appropriate string?
(A) “x i s a pr i me number ” (B) “x i s an even number ”
Q.95
(C) “x i s an odd number ” (D) “t he val ue of x i s 1”
Let ( )
{ }
4
1
, , , 0 and 6 7 8 0 = ∈ + + = + + = R W x y z w x y z x y z and
( )
{ }
4
2
, , , 2 3 0 and 2 3 4 0 = ∈ + + = + + = R W x y z w x y z x y z . Then the dimension of the
subspace
1 2
W W + is
Q.96
(A) 1 (B) 2 (C) 4 (D) 3
The composite Trapezoidal rule is used to compute
1
0
−
∫
x
e dx with an error of at most
2
1
10
12
−
× .
How many points should be used?
Q.97
(A) 11 (B) 9 (C) 8 (D) 7
Consider the following C function:
f l oat f ( f l oat x)
{ f l oat sum=1. 0, t er m=1. ;
i nt n=1;
whi l e( n<50)
{ t er m=x*t er m/ n;
sum+=t er m;
n++;
}
r et ur n sum;
}
The return value of the function f ( 1. 0) is the approximate value of
Q.98
(A) 0.0 (B) sin (1.0) (C) cos (1.0) (D) e
CA- / 20 17
A
The length of the one arc of the cycloid
( ) ( ) sin , 1 cos x a t t y a t = − = −
is
Q.99
(A) 8a (B) 4a
(C) 4 2 a (D) 2 2 a
Consider the following C function:
voi d f ( i nt x, i nt y)
{ i nt d;
i f ( x>0)
{ d=x%y;
f ( x/ y, y) ;
pr i nt f ( " %d" , d) ;
}
el se r et ur n;
}
The output for f ( 100, 16) is
Q.100
(A) 11 (B) 64 (C) 82 (D) 110
End of the paper
CA- / 20 18
A
SPACE FOR ROUGH WORK
CA- / 20 19
A
SPACE FOR ROUGH WORK
CA- / 20 20
A
SPACE FOR ROUGH WORK