### (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]

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**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)

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**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

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**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.

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**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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**Questio****n 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 × 10^{9} operations per second

(B) Its clock cycles 2 × 10^{9} times per second

(C) Its RAM stores 2 × 10^{9} bytes per second

(D) Its printer prints 2 × 10^{9} 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) = x^{2} , then the general solution of the differential equation is

(A) 2x^{3} + xy + y^{2} = c

(B) 2x^{3} + 6xy + 3y^{2} = c

(C) 2x + 2xy + y^{2} = c

(D) x^{2} + xy + y^{2} = 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 W_{1}, W_{2}, W_{3}, W_{4} 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 = W_{1} + W_{2} + W_{3} + W_{4}. The vector (W_{1}, W_{2}, W_{3}, W_{4}) 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 x^{2} = 4 – 2y and x^{2} = y + 4 is

(A) 16

(B) 24

(C) 30

(D) 36

**Question: **Let F (x, y, z) = x^{2} + y^{2} + z^{2} + 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: **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: **The order of the permutation (12) (546) (3978) in the symmetric group S_{9} 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, a^{2}), (a^{2}, a)} is NOT a basis of R^{2}, 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 28^{30} −15^{30} 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