IIT JAM MCA 2011 Question Paper PDF Download

(Year 2005)

Question 1:
An abelian group of order 24 has
(A) exactly one subgroup of order 3
(B) exactly two subgroups of order 3
(C) no subgroup of order 3
(D) more than two subgroups of order 3

Question 2:
Which of the following group of statements is correct?
P. Mouse, Key Board, and Plotter are all input devices
Q. Unix, Windows, and Linux are all operating systems
R. Register, Cache, and Hard Disk are all memory modules
S. Monitor, Printer and Scanner are all output devices
(A) P, Q
(B) P, S
(C) R, S
(D) Q,R

Question 3:
A communication system consists of n components. Each of these components functions independently with probability p. The system functions correctly if and only if at least half of its components function. For what range of p, the probability that a five-component system functions correctly is higher than the probability that a three-component system functions correctly?
(A) [0.4, 0.6]
(B) [0, 0.5]
(C) [0, 1]
(D) [0.5, 1]

Question 4:
If A is an n x n matrix, then the system of linear equations Ax = 0
(A) is inconsistent if rank (A) < n
(B) has exactly r solutions if rank (A) = r < n
(C) has infinitely many solutions if rank (A) = n
(D) has infinitely many solutions if rank (A) < n

Question 5:
If an odd function increases for x > 0, then for x < 0 it
(A) increases
(B) decreases
(C) remains constant
(D) oscillates

Question 6:
Which of the following is not true?
(A) The order of the subgroup of a finite group divides the order of the group
(B) Every group of finite order is cyclic
(C) Every cyclic group is abelian
(D) If k is a divisor of the order of a group G, then G must have a subgroup of order k

Question 7:
If the radius of a cylinder is measured with maximum error of 2%, height is measured with maximum error of 0.5%, then the maximum possible error in the computation of volume of the cylinder is
(A) 4.25%
(B) 5%
(C) 4%
(D) 4.5%

Question 8:
Which of the following is true?
(A) The set of all 2 x 2 real matrices forms a group under matrix multiplication
(B) A finite abelian group of order 6 has exactly two non-trivial subgroups
(C) Every finite group is always cyclic
(D) The set of all 2 x 2 real non-singular matrices forms an abelian group under matrix multiplication

Question 9:
For real symmetric matrices A and B, which of the following is true?
(A) AB is a symmetric matrix
(B) AB=BA
(C) All eigen values of AB are real if AB = BA
(D) AB is invertible if either A is invertible or B is invertible

Question 10:
The curves with constant curvature are
(A) circles only
(B) straight lines only
(C) circles and straight lines
(D) ellipse

Question 11:
From the given table

X	1	2	3	4
f(x)	1	7	17	31

the interpolated value of f (1.5) is
(A) 4.5
(B) 4
(C) 3.5
(D) 4.6

Question 12:
The binary representation of the hexadecimal number 125 is
(A) 0000000001111101
(B) 0000000100100101
(C) 0000000111011010
(D) 0000000001111111

Question 13:
For the events A and B to be independent, the probability that both A and Boccur is 1/6 and probability that neither of them occur is 1/3. Then the probability of occurrence of A is
(A) 1/2 or 1/3
(B) 1/4
(C) 1/2 only
(D) 1/3 only

Question 14:
The product of the two binary numbers 00001101 and 00001111 is
(A) 11000011
(B) 00001101
(C) 00010010
(D) 01100011

Question 15:
Which of the following filp-flops use two inputs?
P. JK-Flip-flop
Q. SR-Flip-flop
R. D-Flip-flop
S. T-Flip-flop
(A) P, S
(B) P, Q
(C) R, S
(D) P, R

(IIT JAM MCA 2006 Previous Year Paper)

Question 1:
The differential equation
2ydx − (3y − 2x)dy =0
is
(A) exact and homogeneous but not linear
(B) homogeneous and linear but not exact
(C) exact and linear but not homogeneous
(D) exact, homogeneous and linear

Question 2:
Two teams A and B play a series of four matches. If the probability that team A wins a match is 2/3, then the probability that team A wins three matches, loses one and the third win occurs in the fourth match is
(A) 8/27
(B) 16/27
(C) 8/81
(D) 32/81

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Question 3:
A fair coin is tossed twice. Let A be the event that at least one tail appears and B be the event that both head and tail appear. Then P(A/B), the probability of A given B, is
(A) 1/4
(B) 1/2
|(C) 2/3
(D) 1

Question 4:
Let F be a field. Given below are six statements about F.
1. F is a skew field
2. F is a group with respect to multiplication
3. F is an integral domain
4. F has zero divisors
5. F has no zero divisors
6. Only ideals of F are {0} and itself
In which of the following options all the statements are correct?
(A) 1, 2, 3
(B) 1, 3, 5
(C) 2, 4, 6
(D) 4, 5, 6

Question 5:
Consider the statements
(P) If a linear programming problem has only one optimal solution, then this solution is an extreme point of the feasible region.
(Q) A linear programming problem either is infeasible or has at least one optimal solution.
(R) A linear programming problem can have exactly two optimal solutions.
(S) A feasible linear programming problem has an optimal solution or unbounded solution
Which of the following group of statements is correct?
(A) P, Q
(B) P, R
(C) R, S
(D) P, S

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Question 6:
The sequence 10000, 121, 100, 31, 24, ___ , 20 represent a number x with respect to different bases. The missing number in this sequence is
(A) 22
(B) 21
(C) 16
(D) 10

Question 7:
Which of the following combinations is invalid in SR flip-flops?
(A) S = 0, R = 0
(B) S = 0, R = 1
(C) S = 1, R = 0
(D) S = 1, R = 1

Question 8:
What does the following function print?
void f( )
{
char p;
if((p = getchar()) != ‘n’) f( );
putchar(p);
return;
}
(A) reverse of the given characters
(B) characters in the given order
(C) characters in the given order without the first character
(D) reverse of the given characters without the last character

Question 9:
From the following flip-flops
JK flip-flop
P. SR flip-flop
Q. D flip-flop
R. T flip-flop
The pair of flip-flops which uses only one input is
(A) (P, S)
(B) (Q, R)
(C) (R, S)
(D) (P, R)

Question 10:
ASCII stands for
(A) American Standard Code for International Interchange
(B) American Scientific Code for Information Interchange
(C) American Standard Code for Intelligence Interchange
(D) American Standard Code for Information Interchange

Question 11:
Which of the following is NOT a language processor?
(A) compiler
(B) loader
(C) interpreter
(D) assembler

Question 12:
The sequence that is in ascending order in size is
(A) bit, word, byte, nibble
(B) nibble, byte, bit, word
(C) nibble, bit, word, byte
(D) bit, nibble, byte, word

Question 13:
Which of the following is NOT a internet protocol?
(A) LTP
(B) SMTP
(C) HTTP
(D) ATM

Question 14:
If the word MANMOHANWASHERE corresponds to ZOAABVNBJOFVRFR, then the word that corresponds to LRF is
(A) HEY
(B) MAN
(C) GOT
(D) YES

Question 15:
Which of the following statements in a Boolean algebra is NOT correct?
(A) A + A = A
(B) A . A = A
(C) A + 1 = A
(D) A + AB = A

(IIT JAM MCA Previous year Paper 2007)

Question 1:
Which of the following is a valid C directive?
(A) # include <stdio.h>;
(B) # include <stdio.h>
(C) include <stdio.h>;
(D) include <stdio.h>

Question 2:
Which of the following is NOT a Random Access Storage Device?
(A) Magnetic Tape
(B) Hard Disk
(C) Floppy Disk
(D) CD

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Question 3:
10’s complement of the decimal number 56789 is
(A) 01234
(B) 12345
(C) 43210
(D) 43211

Question 4:
The largest natural number whose base 7 representation has exactly four digits, is
(A) 2400
(B) 6666
(C) 7777
(D) 2401

Question 5:
Which of the following is an 8-bit processor?
(A) Intel 80286
(B) Intel 8086
(C) Intel 8085
(D) Intel Pentium II

Question 6:
BIOS is the acronym for
(A) Binary Input Output Source
(B) Basic Input Output Support
(C) Binary Input Output System
(D) Basic Input Output System

Question 7:
A student computes the sum of squares of the first 40 natural numbers and gives an incorrect answer 22019. By mistake, the student forgot to add the square of one of the numbers. The missed number is
(A) 5
(B) 7
(C) 9
(D) 11

Question 8:
Which of the following is NOT a Software?
(A) Adobe
(B) Browser
(C) Compiler
(D) Device Driver

Question 9:
For which of the following combinations, a JK Flip-Flop will enter into the complement of the present state?
(A) J = 0, K = 0
(B) J = 0, K = 1
(C) J = l, K = 0
(D) J = 1, K = 1

Question 10:
The next term in the series 191, 211, 232, 254, —- is
(A) 267
(B) 276
(C) 277
(D) 287

Question 11:
Match the file extensions in List 1 with the items of list 2.

	List 1		List 2
1.	Operating Systems	P.	Pentium
2.	Application Software	Q.	Linux
3.	Processor	R.	Router
4.	Network	S.	Anti Virus

(A) (1, Q), (2, S), (3, P), (4, R)
(B) (1, Q), (2, R), (3, P), (4, S)
(C) (1, P), (2, S), (3, Q), (4, R)
(D) (1, P), (2, R), (3, S), (4, Q)

Question 12:
For which of the following combinations an SR Flip-Flop is set to 1?
(A) S = 0,    R = 0
(B) S = 0,    R = 1
(C) S = 1,    R = 0
(D) S = 1,    R = 1

Question 13:
The number of ways in which 4 boys and 5 girls can sit in a row so that there is a girl between any two boys is
(A) 4! 5!
(B) 3 (4! 5!)
(C) 5 (4! 5!)
(D) 15 (4! 5!)

Question 14:
A cow is tied with a pole by a 100 meter long rope. What is the probability that at some point of time the cow is at least 60 meters away from the pole?
(A) 9/25
(B) 13/25
(C) 16/25
(D) 18/25

Question 15:
If the Primal Linear Programming Problem is unbounded then which of the following is TRUE?
(A) Dual problem is unbounded
(B) Dual problem has a single bounded optimal solution
(C) Dual problem has multiple bounded optimal solutions
(D) Dual problem is infeasible

(IIT JAM 2008 Question Paper)

Question 1:
The volume of the closed region bounded by the planes
x = 0, y = 0, z = 0 and 2x + 5y + 10z = 10
is
(A) 20/3
(B) 5
(C) 10/3
(D) 5/3

Question 2:
The values of a and b for which the following system of linear equations
ax + y + 3z = a
2x + by – z = 3
5x + 7y + z = 7
has an infinite number of solutions, are
(A) a = l, b = l
(B) a = 1, b = 3
(C) a = 2, b = 3
(D) a = 2,b = 1

Question 3:
Let A and B be any arbitrary square matrices of order 3. Then AB and BA have
(A) the same eigen values and the same eigen vectors.
(B) the same eigen values but may have different eigen vectors.
(C) different eigen values but the same eigen vectors.
(D) different eigen values and different eigen vectors.

Question 4:
G is a group of order 51. Then which one of the following statement is false?
(A) All proper subgroups of G are cyclic.
(B) If G has only one subgroup of order 3 and only one subgroup of order 17, then G is cyclic.
(C) G must have an element of order 17.
(D) If G is abelian then there exists no proper subgroup H of G such that product of all elements of H is identity.

Question 5:
What is the degree of the interpolated polynomial for the data (1, 5), (2, 18), (3, 37), (4, 62) and (5, 93)?
(A) 3
(B) 4
(C) 5
(D) 2

Question 6:
Consider the function f{x) = min{x + 1, |x + l|}. Then f(x) is
(A) always continuous and differentiable.
(B) always continuous but not differentiable at all points.
(C) always continuous but not differentiable at x = -1.
(D) not always continuous.

Question 7:
Out of 120 students, 80 students have taken mathematics, 60 students have taken physics, 40 students have taken chemistry, 30 students have taken both physics and mathematics, 20 students have taken both chemistry and mathematics and 15 students have taken both physics and chemistry. If every student has taken at least one course, then how many students have taken all the three courses?
(A) 5
(B) 25
(C) 15
(D) 10

Question 8:
Consider the experiment of throwing two fair dice. What is the probability that the sum of the numbers obtained in these dice is even?
(A) 1/2
(B) 1/4
(C) 1/3
(D) 1/6

Question 9:
Two dice are rolled until the sum of the numbers appearing on these dice is either 7 or 8. What is the probability that the sum is 7?
(A) 5/11
(B) 6/11
(C) 7/11
(D) 8/11

Question 10:
Let X be the random variable giving the number of heads obtained in 162 successive tosses of a biased coin with probability of getting head in a toss is 1/3. Assume that the tosses are independent. The standard deviation of X is
(A) 6
(B) 8
(C) 7
(D) 9

Question 11:
The maximum value of f(x, y, z) =xyz along all points lying on the intersection of the planes x + y + z = 40 and z = x + y is
(A) 4000
(B) 3000
(C) 2000
(D) 1000

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Question 12:
The following are the same number represented in different bases. 10001, 101, 25, 21,… The next element of the sequence is
(A) 10
(B)17
(C) 22
(D) 33

Question 13:
For which one of the following flip-flops, is the output just the input delayed until the next active clock transition?
(A) SR
(B) T
(C) JK
(D) D

Question 14:
Which one of the following is a valid IP address on a network?
(A) 10.10.256.25
(B) 10.10.25.257
(C) 10.10.25.25
(D) 10.258.25.25

Question 15:
Which of the following connections to the computer is correct for the devices keyboard, mouse and printer respectively.
(A) Parallel port, PS2, serial port
(B) PS2, serial port, PS2
(C) PS2, PS2, parallel port
(D) Serial port, parallel port, PS2

(IIT JAM Paper – Year 2009)

Question 1:

The value of the arithmetic expression -a*b/c+d%k for integers variables a = 5, b=3, c = 2, d = 5, k = 3 is
(A) –5.5
(B) -5
(C) -3
(D) -1

Question 2:
The #include and #define directives are processed at
(A) runtime
(B) compile time and runtime, respectively
(C) compile time
(D) runtime and compile time, respectively

Question 3:
The number of distinct 3 x 3 matrices, constructed using nonnegative integers such that each row sum is 3, is
(A) 1000
(B) 729
(C) 300
(D) 99

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Question 4:
Consider the following statements :
P : If an LPP is infeasible then its dual is unbounded.
Q : An LPP can have more than one optimal solutions.
Which one of the following is TRUE?
(A) Both P and Q are false
(B) Only P is true
(C) Only Q is true
(D) Both P and Q are true

Question 5:
The time taken by a train in going from A to B and coming back to A at a constant speed 90 km/hour is 7 hours less than the time it takes if it runs at a speed of 100 km/hour in going from A to B and runs at a speed of 50 km/hour in coming back from B to A. The distance between A and B is
(A) 720 km
(B) 820 km
(C) 850 km
(D) 900 km

Question 6:
Which of the following sets does not contain any C-keyword?
(A) {intern, global, dynamic, local}
(B) {extern, dynamic}
(C) {extern, intern, local, static}
(B) {global, static, dynamic}

Question 9:
Let P, Q, R be matrices of order 3 x 5, 5 x 7 and 7 x 3, respectively. The number of scalar additions required to compute P(QR) is
(A) 114
(B) 126
(C) 128
(D) 138
Question 10:
Consider the set {l, 3, 7, 9} under the operation of multiplication modulo 10. Which one of the following statements about the given set is FALSE?
(A) It has exactly two elements that are inverses of each other
(B) It is an abelian group
(C) It is a cyclic group
(D) It has a unique generator
Question 11:
Which of the following is TRUE for groups of even order?
(A) Such groups do not have a non-trivial proper subgroup
(B) There is no element which is the inverse of itself
(C) The order of such groups is a power of 2
(D) There are at least two elements whose inverses are the elements themselves

Question 13:
The next element in the sequence 10, 12, 15, 20, 27, … is
(A) 39
(B) 38
(C) 37
(D) 36

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Question 14:
Each student in a class takes at least one elective out of the three available electives. Each one of the electives is taken by 100 students. The number of students who have taken any two electives is either 50 or 51, and the number of students who have taken all three electives is 34. The total number of students in the class is bounded by
(A) 150 and 153
(B) 180 and 183
(C) 181 and 184
(D) 179 and 182

Question 15:
Three persons play a game by tossing a fair coin each independently. The game ends in a trial if all of them get the same outcome in that trial, otherwise they continue to the next trial. What is the probability that the game ends in an even number of trials?
(A) 2/7
(B) 3/7
(C) 1/2
(D) 4/7

(Year 2010)

Question 2:
In the sequence 1, 3, 5, 4, 8, 9,12,17, x,…, …, the value of x is
(A) 19
(B) 20
(C) 21
(D) 29

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Question 3:
Let N be a nilpotent matrix of order 4 with real entries. Then which one of the following statements is true about given values of N?
(A) All given values are non-zero real numbers
(B) All given values are purely imaginary
(C) Zero is the only given value
(D) At least one given value is real and at least one given value has non-zero imaginary part

Question 7:
The average marks of a class of 25 students in a class test is 80. On rechecking of records, it is found that marks of 2 students which were actually 85 and 90 have been wrongly entered as 65 and 55 respectively. The correct average will be
(A) 81.40
(B) 81.70
(C) 83.50
(D) 82.20

Question 8:
Let X = {1, 2, 3, 4}. Then the total number of partitions of the set X is
(A) 5
(B) 12
(C) 15
(D) 16

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Question 9:
Eight couples are participating in a game. Four persons are chosen randomly. The probability that at least one couple will be among the chosen persons is
(A) 5/13
(B) 1/26
(C) 25/26
(D) 2/5

Question 11:
Consider the following table:

X	1	2	3
y	–5	0	7

Then by Lagrange’s interpolation y (1, 5)is
(A) –2.50
(B) –2.75
(C) -2.25
(D) -3.25

Question 13:
With the conversion rate 1 U.S.D. = 48 INR, ten million U.S.D. is equivalent to
(A) 0,48 crores INR
(B) 4.80 crores INR
(C) 48 crores INR
(D) 48,000 lacs INR

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Question 15:
A tap fills a water tank in 20 minutes. Another tap fills the same tank in 30 minutes. If both taps are opened simultaneously, then the time taken (in minutes) to till the tank is
(A) 10
(B) 12
(C) 16
(D) 20

(Year 2011)

Question: Consider the following C program

#include <stdio.h>
int main() {
int x = 01234;
printf(“%d”, x);
return 0;
}
The output of the program will be
(A) 01234
(B) 1234
(C) 567
(D) 668

Question: Consider the following C function

float f(float a, int m) {
float x;
if (m == 0) return 1;
x = f(a, m/2);
if (m%2 == 1) return x * x * a;
else return x * x;
}
What will be the return value of the function f(2,3)?
(A) 20.0
(B) 16.0
(C) 12.0
(D) 8.0

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Question: If the speed of a computer is 2 GHz, then which one of the following statements must be TRUE?
(A) Its processor performs 2 × 10⁹ operations per second
(B) Its clock cycles 2 × 10⁹ times per second
(C) Its RAM stores 2 × 10⁹ bytes per second
(D) Its printer prints 2 × 10⁹ characters per second

Question:
When a computer is switched on, the BIOS is loaded from
(A) Hard Disk
(B) RAM
(C) ROM
(D) CD-ROM

Question:
Let P be a matrix of size 3 × 3 with given values 1, 2 and 3. Then P is
(A) neither invertible nor diagonalizable
(B) both invertible and diagonalizable
(C) invertible but not diagonalizable
(D) not invertible but diagonalizable

Question: If g(x, y)dx + (x +y)dy = 0 is an exact differential equation and if g(x, 0) = x² , then the general solution of the differential equation is
(A) 2x³ + xy + y² = c
(B) 2x³ + 6xy + 3y² = c
(C) 2x + 2xy + y² = c
(D) x² + xy + y² = c

Question:
Consider the following table:

x	1	2	3
y	–10	–6	0

The roots of the corresponding interpolating quadratic polynomial are
(A) −4, 3
(B) 3, 4
(C) −2, 4
(D) −1, 3

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Question:
The value of x in the sequence 2, 4, 10, 28, 82, x, … is
(A) 102
(B) 168
(C) 252
(D) 244

Question: Consider the following segment of a C program

int x = 2;
if (x = 3) printf(“%d”, x++);
else printf(“%d”, –x);

The output of the program segment will be
(A) 0
(B) 2
(C) 3
(D) 4

Question:
In a C program, variables x and y are declared to be of type int. Consider the following four statements
S1: y = x & 1; S2: y = x % 2;
S3: y = x / 2; S4: y = x << 1;
Which of the statements will result in the same value of y for every value of x?
(A) S3 and S4
(B) S1 and S3
(C) S1 and S2
(D) S2 and S4

Question: Four different weights W₁, W₂, W₃, W₄ can take only integral values. They can be used on one or both the pans of a balance to weigh objects having all possible integral weights from unit weight to W, where, W = W₁ + W₂ + W₃ + W₄. The vector (W₁, W₂, W₃, W₄) which maximizes W is
(A) (1, 2, 5, 10)
(B) (1, 3, 9, 27)
(C) (1, 2, 4, 8)
(D) (1, 3, 15, 25)

Question: Suppose the sum and the product of the mean and the variance of a binomial random variable are 10 and 24 respectively. Then the probability of success in a single trial is
(A) 1/4
(B) 3/4
(C) 2/3
(D) 1/3

Question:
An ASCII code contains
(A) 8 bits
(B) 4 bits
(C) 7 bits
(D) 6 bits

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Question:
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is
(A) 255/256
(B) 127/128
(C) 63/64
(D) 31/32

Question:
Three unbiased dice of different colours are rolled. The probability that the same number appears on at least two of the three dice is
(A) 5/36
(B) 1/2
(C) 5/12
(D) 4/9

Question:
Let S be a set with 10 elements. The number of subsets of S having odd number of elements is
(A) 256
(B) 512
(C) 752
(D) 1024

Question: The area bounded by the curves x² = 4 – 2y and x² = y + 4 is
(A) 16
(B) 24
(C) 30
(D) 36

Question: Let F (x, y, z) = x² + y² + z² + xy + yz + zx. The value of F_x + F_y + F_z at (1, 1, 1) is
(A) 12
(B) 10
(C) 16
(D) 8

Question: Three unbiased dice of different colours are rolled. The probability that the same number appears on at least two of the three dice is
(A) 5/36
(B) 1/2
(C) 5/12
(D) 4/9

Question: An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is
(A) 255/256
(B) 127/128
(C) 63/64
(D) 31/32

Question: The order of the permutation (12) (546) (3978) in the symmetric group S₉ is
(A) 6
(B) 9
(C) 12
(D) 24

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Question: Let S be a set with 10 elements. The number of subsets of S having odd number of elements is
(A) 256
(B) 512
(C) 752
(D) 1024

Question: The number of real values of a for which the set {(a, a²), (a², a)} is NOT a basis of R², is
(A) 1
(B) 2
(C) 3
(D) 4

Question: Consider the following statements about terminating (finite number of digits to the right of the point) representations
X: If the binary representation of a number terminates then its corresponding decimal representation also terminates.
Y: If the decimal representation of a number terminates then its corresponding binary representation also terminates.
Then
(A) X is true but Y is false
(B) Y is true but X is false
(C) both X and Y are true
(D) neither X nor Y is true

Question: The octal equivalent of decimal 204 is
(A) 304
(B) 306
(C) 314
(D) 316

Question: The number of three digit numbers greater than 100 in which digits appear in strictly increasing order is
(A) 36
(B) 84
(C) 90
(D) 120

Question: The next number in the sequence of binary numbers 0, 10, 100, 110, … is
(A) 101
(B) 1000
(C) 1001
(D) 1010

Question: The number of reflexive relations on a set with four elements is
(A) 10
(B) 1024
(C) 4096
(D) 8192

Question: When 28³⁰ −15³⁰ is divided by 13, the remainder is
(A) 0
(B) 1
(C) 11
(D) 12

Question: The number of subsets of {1, 2, … , 10} which are disjoint from {3,7,8} is
(A) 128
(B) 1021
(C) 1016
(D) 7

Question: The number of functions taking two Boolean variables as input and providing three Boolean variables as output is
(A) 12
(B) 32
(C) 4096
(D) 65536

Question: Let P, Q, R and S be statements, each of which can be either true or false. It is known that if P is true or Q is true then R is true and S is false. Suppose it is given that R is false. Then which one of the following will certainly be TRUE?
(A) Both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) Both P and Q are false

Question: A JK flip-flop runs on a clock of period 20 KHz. If we set J = K = 1, the output Q is a
(A) constant LOW
(B) constant HIGH
(C) 10 KHz wave
(D) 20 KHz wave

(Year 2012)

Question:
The number of distinct 3 digit numbers greater than 100 where no digit repeats itself is
(A) 504
(B) 648
(C) 326
(D) 210

Question:
Order the following processors in the increasing order of speed.
M1: 486, M2: 8085, M3: Dual core, M4: Pentium III
(A) M1 M2 M3 M4
(B) M2 M1 M4 M3
(C) M1 M2 M4 M3
(D) M1 M3 M4 M2

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Question:
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.
(D) There exists a field with 9 elements

Question:
The volume of the tetrahedron bounded by the planes z = 0, x = 0, y = 0 and y + z – x = 1 is
(A) 1/6
(B) 6
(C) 1
(D) 1/3

Question:
Which of the following is/are main memory of a computer?
P: RAM, Q: Hard disk, R: CDROM, S: Pen drive
(A) P and Q only
(B) Q only
(C) P only
(D) P, R, and S only

Question:
What is the probability of getting an even number or a number less than 5, in tossing a fair die?
(A) 2/3
(B) 1/3
(C) 5/6
(D) 1/6

Question:
The next term in the sequence of ternary number 10, 20, 100, 110, … is
(A) 120
(B) 111
(C) 112
(D) 101

Question:
The 9’s complement of 123456789 is
(A) 876543211
(B) 876543210
(C) 987654321
(D) 012345678

Year 2013

Question 1:
If the function f : R → [0,2] is defined by f(x)=| cosx| + | sinx |, then
(A) f is one-one
(B) f is onto
(C) f is differentiable on R
(D) the minimum value of f is 1

Question 2:
The area of the region bounded by the lines | x | + | y | = 1 is
(A) 1
B) 2
(C) 3
(D) 4

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Question 3:
Consider the table

X	–1	0	1
f (x)	–2	–1	0

Using Lagrange interpolation the value of f (0.6) is
(A) – 0.32
(B) 0.4
(C) – 0.4
(D) 0.32

Question 4:
Consider the following C function
int fun(int n){
int b=0;
while(n! =0){
b = b*10+n%10;
n=n/l0;}
return b;}
The value of fun(7830) is
(A) 7830
(B) 783
(C) 387
(D) 1000

Question 5:
What does the following C program segment display when executed?
int i;
long int k=0;
for(i=1;i<=S0;i++) k+=(i*i);
printf( “%d”, k);
(A) 42075
(B) 42925
(C) 42950
(D) 42750

Question 6:
In general, for a computer which of the following represents the memories in increasing order of their capacities
(A) Register< RAM < Cache < Hard Disk
(B) RAM < Cache < Hard Disk< Register
(C) Register< Cache < RAM < Hard Disk
(D) Cache < RAM < Hard Disk< Register

Question 7:
Suppose two fair dice are rolled. The probability that one face is 4 given that the faces show different numbers is
(A) 5/6
(B) 1/2
(C) 1/3
(D) 1/6

Question 8:
A box contains ten screws out of which four are defective. Six screws are drawn one by one at random, without replacement. The probability that the sixth screw drawn is the last defective one, is
(A) 32/729
(B) 5/21
(C) 1/21
(D) 2/729

Question 9:
The equation of the plane passing through P(O,O,I), Q(l,I,O) and R(O,2,O) is
(A) 2x + y + z = 1
(B) x + y + 2z = 1
(C) x + 2y + z = 1
(D) x + y + 2z = 2

Question 10:
The number of Boolean functions f (x, y) satisfying f (x, y) = f (x’, y’) is
(A) 2
(B) 4
(C) S
(D) 16

Question 11:
The Boolean expression (x + y + z)·(x’+ y + z) · (x + y’+ z) · (x + y + z’) is equivalent to
(A) (x+ y)·(x+z)·(y+z)
(B) (x’+y’)’ (x’+z’)· (y’+z’)
(C) (x+ y’)·(x+z’)·(y+z’)
(D) (x’+y)·(x’+z)· (y’+z)

Question 12:
In a class, each student takes at least one and at most two electives out of three electives namely, DMS, DS and ADA. The table below gives enrollment information of the students in the above courses:

Course	Number of students
DMS	90
DS	70
ADA	90
DMS and DS	30
DS and ADA	30
ADA and DMS	40

Then the total number of students in the class is
(A) 160
(B) 150
(C) 90
(D) 250

Question 13:
The values of k for which the following system of linear equations has non-zero solutions
x + y + z = 0, 2x + ky + 3z = 0, 3x+ 5y + kz = 0 are
(A) 1 and 4
(B) 2 and 4
(C) 3 and 5
(D) 2 and 5

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Question 14:
Suppose a country has coins of denominations 1, 4, and 5. The minimum number of coins required to make the amount 13 is
(A) 2
(B) 3
(C) 4
(D) 5