CS 1. This question" consists of TWENTY FIVE sub-questions, 1.1 to 1.25, of ONE mark each. For each of the sub-questions, four alternatives, A, B, C, and D are provided. Choose the most appropriate alternative and darken its bubble on the OBJECTIVE RESPONSE SHEET (ORS) against the corresponding sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. Do not use the ORS for any rough work. You may use the Answer Book (last few pages) for any rough work.
The rank of the matrix
is
4
2
1
O
1.2 The trapezoidal rule for integration gives exact result when the integrand is a polynomial of degree
0 but not 1,
1 but not 0
0 or 1
2
1.3 The solution to the recurrence equation T(2 k ) = 3 T(2 k-l) + 1, T(1) = 1 is:
2k
(3 k+1 - 1)/2
3 log 2 k
2 log 3 k
1.4 The minimum number of colours required to colour the vertices of a cycle with n nodes in such a way that no two adjacent nodes have the same colour is:
2
3
4
n – 2 ë n/2 û + 2
1.5 In the worst case, the number of comparisons needed to search a singly linked list
of length n for a given element is
log 2 n
n/2
log 2 n – 1
n
1.6 Which of the following is true?
The set of all rational negative numbers forms a group under multiplication.
The set of all non-singular matrices forms a group under multiplication.
The set of all matrices forms a group under multiplication.
Both B and C are true.
1.7 The language accepted by a Pushdown Automaton in which the stack is limited to 10 items is best described as
Context Free
Regular
Deterministic Context Free
Recursive
1.8 If X then Y unless Z" is represented by which of the following formulas in
propositional logic ? (" Ø " is negation, " Ù " is conjunction, and " ® " is implication)
(X Ù Ø Z) ® Y
(X Ù Y) ® Ø Z
X ® (Y Ù Ø Z)
(X ® Y) Ù Ø Z
1.9 A device employing INTR line for device interrupt puts the CALL instruction on the data bus while
INTA is active
HOLD is active
READY is active
None of the above
1.10 In 8085 which of the following modifies the program counter?
Only PCHL instruction
Only ADD instructions
Only JMP and CALL instructions
All instructions
1.11 In serial data transmission, every byte of data is padded with a '0' in the beginning
and one, or two ‘1's at the end of byte because
Receiver is to be synchronized for byte reception
Receiver recovers lost '0's and '1's from these padded bits
Padded bits are useful in parity computation
None of the above.
1.12 . Minimum sum of product expression for f(w,x,y,z) shown in Karnaugh-map below is
wx ®
yz ¯
00
01
11
10
00
0
1
1
0
01
X
0
0
1
11
X
0
0
I
10
0
I
1
x
A. xz +y'z
B. xz' + zx'
C. x'y + zx'
D. None of the above
1.13 Which of the following is not a form of memory?
instruction cache
instruction register
instruction opcode
translation look aside buffer
1.14 The decimal value 0.25
is equivalent to the binary value 0.1
is equivalent to the binary value 0.01
is equivalent to the binary value 0.00111…
cannot be represented precisely in binary
1.15. The 2's complement representation of the decimal value -15 is
1111
11111
111111
10001
1.16. Sign extension is a step in
floating point multiplication
signed 16 bit integer addition
arithmetic left shift
converting a signed integer from one size to another
In the C language
At most one activation record exists between the current activation record and the activation record for the main
The number of activation records between the current activation record and the activation record for the main depends on the actual function calling sequence.
The visibility of global variables depends on the actual function calling sequence.
Recursion requires the activation record for the recursive function to be saved on a different stack before the recursive function can be called.
1.18 The- results returned by functions under value-result and reference parameter passing conventions
Do not differ
Differ in the presence of loops
Differ in all cases
May differ in the presence of exceptions
Relation R with an associated set of functional dependencies, F, is, decomposed into BCNF. The redundancy (arising out of functional dependencies) in the resulting set of relations is
Zero
More than zero but less than that of an equivalent 3NF decomposition
Proportional to the size of P+
Indeterminate
1.20 With regard to the expressive power of the formal relational query languages, which of the following statements is true?
Relational algebra is more powerful than relational calculus
Relational algebra has the same power as relational calculus
Relational algebra has the same power as Safe relational calculus
None of the above
1.21 In 2's complement addition, overflow
is flagged whenever there is carry from sign bit addition
cannot occur when a positive value is added to a negative value
is flagged when the carries from sign bit and previous bit match
None of the above
1.22 Which of the following scheduling algorithms is non-preemptive?
Round Robin
First-In First-Out
Multilevel Queue Scheduling
Multilevel Queue Scheduling with Feedback
1.23 The optimal page replacement algorithm will select the page that
Has not been used for the longest time in the past.
Will not be used for the longest time in the future .
Has been used least number of times.
Has been used most number of times.
1.24 In the absolute addressing mode
the operand is inside the instruction
the address of the operand is inside the instruction
the register containing the address of the operand is specified inside the instruction
the location of the operand is implicit
1.25 Maximum number of edges in a n - node undirected graph without self loops is
n 2
n (n-1)/2
n-1
(n+1)(n)/2
CS2. This question consists of TWENTY FIVE sub-questions, 2.1 to 2.25, of TWO marks each. For each of the sub-questions, four alternatives, A, B, C, and D are provided. Choose the most appropriate alternative and darken its bubble on the OBJECTIVE RESPONSE SHEET (ORS) against the corresponding sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. Do not use the ORS for any rough work. You may use the Answer Book (last few pages) for any rough work.
2.1 Consider the following logic circuit whose inputs are functions f 1, f 2, f 3 and output is f.
f 1(x,y,z)
f 2(x,y,z)
f3 (x,y,z)= ?
Given that
f 1(X,Y,Z) = å (0,1,3,5),
f 2(X,Y,Z) = å (6,7), and
f(x,y,z) = å (I,4,5),
f3 is
A. å (1,4,5)
B. å (6,7)
C. å (0,1,3,5)
D. None of the above
2.2 Consider the following multiplexor where I0, I1, I2, I3 are four data input lines
selected by two address line combinations AIAO =00,01,10,11 respectively and f is
the output of the multiplexor. EN is the Enable input.
The function f (x, y ,z) implemented by the above circuit is
xyz’
xy+z
x+y
None of the above
2.3. Let f(A,B} = A' +B . Simplified expression for function f (f(x+y.y),z) is
x' +z
xyz'
xy' + z
None of the above.
2.4. What are the states of the Auxiliary Carry (AC) and Carry Flag (CY) after executing the following 8085 program?
MVI H, 5DH
MVI L , 6BH
MOV A, H
ADD L
AC= 0 and CY =0
AC= 1 and CY= 1
AC= 1 and CY=O
AC = 0 and CY = 0
2.5 The Finite state machine described by the following state diagram with A as
starting state, where an arc label is x/y and x stands for I-bit input and y stands for
2-bit output
Outputs the sum of the present and the previous bits of the input.
Outputs 01 whenever the input sequence contains 11
Outputs 00 whenever the input sequence contains 10
None of the above
2.6 The performance of a pipelined processor suffers if
the pipeline stages have different delays
consecutive instructions are dependent on each other
the pipeline stages share hardware resources
all of the above
2.7 Horizontal microprogramming
does not require use of signal decoders
results in larger sized microinstructions than vertical microprogramming
uses one bit for each control signal
all of the above.
2.8 Consider the following declaration of a 'two-dimensional array in C:
char a[100][100];
Assuming that the main memory is byte-addressable and that the array is stored starting from memory address 0, the address of a[40][50] is
4040
4050
5040
5050
2.9. The number of leaf nodes in a rooted tree of n nodes, with each node having 0 or 3 children is:
n/2
(n-1)/3
(n-1)/2
(2n+1)/3
2.10. Consider the following algorithm for searching for a given number x in an unsorted - array A[1..n] having n distinct values:
Choose an i uniformly at random from 1..n;
If A[i] = x then Stop else Goto 1;
Assuming that x is present in A, what is the expected number of comparisons made by the algorithm before it terminates?
n
n-l
2n
n/2
2.11. The running time of the following algorithm
Procedure A(n)
If n <= 2 return(1) else return (A ( é Ö n ù ));
is best described by
O(n)
O(log n)
O(1og log n)
O(1)
2.12. A weight-balanced tree is a binary tree in which for each node. The number of nodes
in the left sub tree is at least half and at most twice the number of nodes in the right
sub tree. The maximum possible height (number of nodes on the path from the root to the farthest leaf) of such a tree on n nodes is best described by which of the following?
log 2 n
log 4/3 n
log 3 n
log 3/2 n
2.13. The smallest finite automaton which accepts the language
{x | length of x is divisible by 3} has .
A. 2 states
B. 3 states
C. 4 states
D. 5 states
2.14. Which of the following is true?
The complement of a recursive language is recursive.
The complement of a recursively enumerable language is recursively enumerable.
The complement of a recursive language is either recursive or recursively enumerable.
The complement of a context-free language is context-free.
The Newton-Raphson iteration X n+l == (X n/2) + 3/(2X n)
can be used to solve the equation
X 2 =3
X 3=3
X 2=2
X 3=2
2.16 Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is
1/16
1/8
7/8
15/16
2.17 The binary relation S = f (empty set) on set A = { 1,2,3} is
Neither reflexive nor symmetric
Symmetric and reflexive
Transitive and reflexive.
Transitive and symmetric
2.18 The C language is.
A context free language
A context sensitive language
A regular language
Parsable fully only by a Turing machine
2.19. To evaluate an expression without any embedded function calls
One stack is enough
Two stacks are needed
As many stacks as the height of the expression tree are needed
A Turing machine is needed in the general case
2.20 Dynamic linking can cause security concerns because
Security is dynamic
The path for searching dynamic libraries is not known till runtime
Linking is insecure
Cryptographic procedures are not available for dynamic linking
Which combination of the following features will suffice to characterize an OS as a multi programmed OS?
More than one program may be loaded into main memory at the same time for execution.
If a program waits for certain events such as I/O. another program is immediately scheduled for execution.
If the execution of a pr ogram terminates, another program is immediately scheduled for execution.
a
a and b
a and c
a, b, and c
2.22 In the index allocation scheme of blocks to a file, the maximum possible size of the file
depends on .
the size of the blocks, and the size of the address of the blocks.
the number of blocks used for the index, and the size of the blocks.
the size of the blocks, the number of blocks used for the index, and the size of the
address of the blocks.
d. None of the above
2.23 A B + -tree index is to be built on the Name attribute of the relation STUDENT. Assume that all student names are of length 8 bytes, disk blocks are of size 512 bytes, and index pointers are of size 4 bytes. Given this scenario, what would be the best choice
of the degree (i.e. the number of pointers per node) of the B+ -tree? .
16
42
43
44
2.24 Relation R is decomposed using a set functional dependencies, F, and relation S is decomposed using another set of functional dependencies, G. One decomposition is definitely BCNF, the other is definitely 3NF, but it is not known which is which. To make a guaranteed identification, which one of the following tests should be used on the decompositions? (Assume that the closures of F and G are available).
Dependency-preservation
Loss less-join
BCNF definition
3NF definition
2.25 From the following instance of a relation schema R (A,B,C), we can conclude that:
A
B
C
1
1
1
1
1
0
2
3
2
2
3
2
A functionally determines B and B functionally determines C
A functionally determines B and B does not functionally determine C
B does not functionally determine C
A does not functionally determine B and B does not functionally determine C