Gate (CS) 2000 Paper without Solution | GATE Computer Science Engineering(CSE) 2025 Mock Test Series - Computer Science Engineering (CSE) PDF Download

 Page 1


GATE CS - 2000
  
SECTION - A 
1. This question consists of TWENTY-THREE multiple questions of ONE mark each.
For each question (1.1 – 1.23), four possible alternatives (A, B, C and D) are
given, out of which ONLY ONE is correct. Indicate the correct answer in the boxes
corresponding to the questions only on the FIRST sheet of the answer book.
1.1 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 
cards to guarantee that three cards are from some same suit is  
(a) 3 (b) 8 (c) 9 (d) 12 
1.2 An n × n array v is defined as follows: 
, for all , , ,1 i j i j i j i i n j n ? = - = = = = ? ?
? ?
The sum of the elements of the array v is 
(a) 0 (b) n -1 (c) 
2
3 2 n n - + (d) 
( )
2
1
2
n
n
+
1.3 The determinant of the matrix 
2 0 0 0
8 1 7 2
2 0 2 0
9 0 6 1
? ?
? ?
? ?
? ?
? ?
? ?
? ?
is: 
(a) 4 (b) 0 (c) 15 (d) 20 
1.4 Let S and T be language over S={a,b} represented by the regular expressions 
(a+b*)* and (a+b)*, respectively. Which of the following is true? 
(a) S ? T (b) T ? S (c) S = T (d) S nT = f 
1.5 Let L denotes the language generated by the grammar S 
 0S0/00. 
Which of the following is true? 
(a) L = 0
+
 (b) L is regular but not 0
+
(c) L is context free but not regular (d) L is not context free 
1.6 The number 43 in 2’s complement representation is 
(a) 01010101 (b) 11010101 (c) 00101011 (d) 10101011 
1.7 To put the 8085 microprocessor in the wait state 
(a) lower the HOLD input (b) lower the READY input  
(c) raise the HOLD input (d) raise the READY input 
Page 2


GATE CS - 2000
  
SECTION - A 
1. This question consists of TWENTY-THREE multiple questions of ONE mark each.
For each question (1.1 – 1.23), four possible alternatives (A, B, C and D) are
given, out of which ONLY ONE is correct. Indicate the correct answer in the boxes
corresponding to the questions only on the FIRST sheet of the answer book.
1.1 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 
cards to guarantee that three cards are from some same suit is  
(a) 3 (b) 8 (c) 9 (d) 12 
1.2 An n × n array v is defined as follows: 
, for all , , ,1 i j i j i j i i n j n ? = - = = = = ? ?
? ?
The sum of the elements of the array v is 
(a) 0 (b) n -1 (c) 
2
3 2 n n - + (d) 
( )
2
1
2
n
n
+
1.3 The determinant of the matrix 
2 0 0 0
8 1 7 2
2 0 2 0
9 0 6 1
? ?
? ?
? ?
? ?
? ?
? ?
? ?
is: 
(a) 4 (b) 0 (c) 15 (d) 20 
1.4 Let S and T be language over S={a,b} represented by the regular expressions 
(a+b*)* and (a+b)*, respectively. Which of the following is true? 
(a) S ? T (b) T ? S (c) S = T (d) S nT = f 
1.5 Let L denotes the language generated by the grammar S 
 0S0/00. 
Which of the following is true? 
(a) L = 0
+
 (b) L is regular but not 0
+
(c) L is context free but not regular (d) L is not context free 
1.6 The number 43 in 2’s complement representation is 
(a) 01010101 (b) 11010101 (c) 00101011 (d) 10101011 
1.7 To put the 8085 microprocessor in the wait state 
(a) lower the HOLD input (b) lower the READY input  
(c) raise the HOLD input (d) raise the READY input 
GATE CS - 2000
  
1.8 Comparing the time T1 taken for a single instruction on a pipelined CPU with time 
T2 taken on a non-pipelined but identical CPU, we can say that 
(a) T1 = T2 (b) T1 = T2 (c) T1 < T2 
(d) T1 is T2 plus the time taken for one instruction fetch cycle 
1.9 The 8085 microprocessor responds to the present of an interrupt 
(a) as soon as the TRAP pin becomes ‘high’ 
(b) by checking the TRAP pin for ‘high’ status at the end of each instruction each 
(c) by checking the TRAP pin for ‘high’ status at the end of the execution of each 
instruction. 
(d) by checking the TRAP pin for ‘high’ status at regular intervals. 
1.10 The most appropriate matching for the following pairs 
X: Indirect addressing 1: Loops 
Y: Immediate addressing 2: Pointers 
Z: Auto decrement addressing 3. Constants
is 
(a) X – 3  Y – 2  Z - 1 (b) X – 1  Y – 3  Z - 2 
(c) X – 2  Y – 3  Z - 1 (d) X – 3  Y – 1  Z - 2 
1.11 The following C declarations 
struct node{ 
int i: 
float j; 
}; 
struct node *s[10]; 
define s to be 
(a) An array, each element of which is a pointer to a structure of type node  
(b) A structure of 2 fields, each field being a pointer to an array of 10 elements 
(c) A structure of 3 fields: an integer, a float, and an array of 10 elements 
(d) An array, each element of which is a structure of type node 
1.12  The most appropriate matching for the following pairs 
X: m=malloc(5); m= NULL; 1: using dangling pointers 
Y: free(n); n->value=5; 2: using uninitialized pointers 
Z: char *p; *p=’a’; 3. lost memory
Page 3


GATE CS - 2000
  
SECTION - A 
1. This question consists of TWENTY-THREE multiple questions of ONE mark each.
For each question (1.1 – 1.23), four possible alternatives (A, B, C and D) are
given, out of which ONLY ONE is correct. Indicate the correct answer in the boxes
corresponding to the questions only on the FIRST sheet of the answer book.
1.1 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 
cards to guarantee that three cards are from some same suit is  
(a) 3 (b) 8 (c) 9 (d) 12 
1.2 An n × n array v is defined as follows: 
, for all , , ,1 i j i j i j i i n j n ? = - = = = = ? ?
? ?
The sum of the elements of the array v is 
(a) 0 (b) n -1 (c) 
2
3 2 n n - + (d) 
( )
2
1
2
n
n
+
1.3 The determinant of the matrix 
2 0 0 0
8 1 7 2
2 0 2 0
9 0 6 1
? ?
? ?
? ?
? ?
? ?
? ?
? ?
is: 
(a) 4 (b) 0 (c) 15 (d) 20 
1.4 Let S and T be language over S={a,b} represented by the regular expressions 
(a+b*)* and (a+b)*, respectively. Which of the following is true? 
(a) S ? T (b) T ? S (c) S = T (d) S nT = f 
1.5 Let L denotes the language generated by the grammar S 
 0S0/00. 
Which of the following is true? 
(a) L = 0
+
 (b) L is regular but not 0
+
(c) L is context free but not regular (d) L is not context free 
1.6 The number 43 in 2’s complement representation is 
(a) 01010101 (b) 11010101 (c) 00101011 (d) 10101011 
1.7 To put the 8085 microprocessor in the wait state 
(a) lower the HOLD input (b) lower the READY input  
(c) raise the HOLD input (d) raise the READY input 
GATE CS - 2000
  
1.8 Comparing the time T1 taken for a single instruction on a pipelined CPU with time 
T2 taken on a non-pipelined but identical CPU, we can say that 
(a) T1 = T2 (b) T1 = T2 (c) T1 < T2 
(d) T1 is T2 plus the time taken for one instruction fetch cycle 
1.9 The 8085 microprocessor responds to the present of an interrupt 
(a) as soon as the TRAP pin becomes ‘high’ 
(b) by checking the TRAP pin for ‘high’ status at the end of each instruction each 
(c) by checking the TRAP pin for ‘high’ status at the end of the execution of each 
instruction. 
(d) by checking the TRAP pin for ‘high’ status at regular intervals. 
1.10 The most appropriate matching for the following pairs 
X: Indirect addressing 1: Loops 
Y: Immediate addressing 2: Pointers 
Z: Auto decrement addressing 3. Constants
is 
(a) X – 3  Y – 2  Z - 1 (b) X – 1  Y – 3  Z - 2 
(c) X – 2  Y – 3  Z - 1 (d) X – 3  Y – 1  Z - 2 
1.11 The following C declarations 
struct node{ 
int i: 
float j; 
}; 
struct node *s[10]; 
define s to be 
(a) An array, each element of which is a pointer to a structure of type node  
(b) A structure of 2 fields, each field being a pointer to an array of 10 elements 
(c) A structure of 3 fields: an integer, a float, and an array of 10 elements 
(d) An array, each element of which is a structure of type node 
1.12  The most appropriate matching for the following pairs 
X: m=malloc(5); m= NULL; 1: using dangling pointers 
Y: free(n); n->value=5; 2: using uninitialized pointers 
Z: char *p; *p=’a’; 3. lost memory
GATE CS - 2000
  
is: 
(a) X – 1  Y – 3  Z - 2 (b) X – 2  Y – 1  Z - 3 
(c) X – 3  Y – 2  Z - 1 (d) X – 3  Y – 1  Z - 2 
1.13 The most appropriate matching for the following pairs 
X: depth first search 1: heap 
Y: breadth-first search 2: queue 
Z: sorting 3: stack 
is: 
(a) X – 1  Y – 2  Z - 3 (b) X – 3  Y – 1  Z - 2 
(c) X – 3  Y – 2  Z - 1 (d) X – 2  Y – 3  Z - 1 
1.14 Consider the following nested representation of binary trees: (X Y Z) indicates Y 
and Z are the left and right sub stress, respectively, of node X. Note that Y and Z 
may be NULL, or further nested. Which of the following represents a valid binary 
tree? 
(a) (1 2 (4 5 6 7)) (b) (1 (2 3 4) 5 6) 7)  
(c) (1 (2 3 4)(5 6 7))  (d) (1 (2 3 NULL) (4 5)) 
1.15 Let s be a sorted array of n integers. Let t(n) denote the time taken for the most 
efficient algorithm to determined if there are two elements with sum less than 
1000 in s. which of the following statements is true? 
(a) t (n) is 0(1) (b) n = t(n) = n log
2 
n 
(c) n log
2
 n = t(n) < 
2
n ? ?
? ?
? ?
(d) t(n) = 
2
n ? ?
? ?
? ?
1.16 Aliasing in the context of programming languages refers to 
(a) multiple variables having the same memory location 
(b) multiple variables having the same value 
(c) multiple variables having the same identifier 
(d) multiple uses of the same variable 
1.17 Consider the following C declaration 
struct { 
short s [5] 
union { 
float y; 
long z; 
} u; 
}t; 
Page 4


GATE CS - 2000
  
SECTION - A 
1. This question consists of TWENTY-THREE multiple questions of ONE mark each.
For each question (1.1 – 1.23), four possible alternatives (A, B, C and D) are
given, out of which ONLY ONE is correct. Indicate the correct answer in the boxes
corresponding to the questions only on the FIRST sheet of the answer book.
1.1 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 
cards to guarantee that three cards are from some same suit is  
(a) 3 (b) 8 (c) 9 (d) 12 
1.2 An n × n array v is defined as follows: 
, for all , , ,1 i j i j i j i i n j n ? = - = = = = ? ?
? ?
The sum of the elements of the array v is 
(a) 0 (b) n -1 (c) 
2
3 2 n n - + (d) 
( )
2
1
2
n
n
+
1.3 The determinant of the matrix 
2 0 0 0
8 1 7 2
2 0 2 0
9 0 6 1
? ?
? ?
? ?
? ?
? ?
? ?
? ?
is: 
(a) 4 (b) 0 (c) 15 (d) 20 
1.4 Let S and T be language over S={a,b} represented by the regular expressions 
(a+b*)* and (a+b)*, respectively. Which of the following is true? 
(a) S ? T (b) T ? S (c) S = T (d) S nT = f 
1.5 Let L denotes the language generated by the grammar S 
 0S0/00. 
Which of the following is true? 
(a) L = 0
+
 (b) L is regular but not 0
+
(c) L is context free but not regular (d) L is not context free 
1.6 The number 43 in 2’s complement representation is 
(a) 01010101 (b) 11010101 (c) 00101011 (d) 10101011 
1.7 To put the 8085 microprocessor in the wait state 
(a) lower the HOLD input (b) lower the READY input  
(c) raise the HOLD input (d) raise the READY input 
GATE CS - 2000
  
1.8 Comparing the time T1 taken for a single instruction on a pipelined CPU with time 
T2 taken on a non-pipelined but identical CPU, we can say that 
(a) T1 = T2 (b) T1 = T2 (c) T1 < T2 
(d) T1 is T2 plus the time taken for one instruction fetch cycle 
1.9 The 8085 microprocessor responds to the present of an interrupt 
(a) as soon as the TRAP pin becomes ‘high’ 
(b) by checking the TRAP pin for ‘high’ status at the end of each instruction each 
(c) by checking the TRAP pin for ‘high’ status at the end of the execution of each 
instruction. 
(d) by checking the TRAP pin for ‘high’ status at regular intervals. 
1.10 The most appropriate matching for the following pairs 
X: Indirect addressing 1: Loops 
Y: Immediate addressing 2: Pointers 
Z: Auto decrement addressing 3. Constants
is 
(a) X – 3  Y – 2  Z - 1 (b) X – 1  Y – 3  Z - 2 
(c) X – 2  Y – 3  Z - 1 (d) X – 3  Y – 1  Z - 2 
1.11 The following C declarations 
struct node{ 
int i: 
float j; 
}; 
struct node *s[10]; 
define s to be 
(a) An array, each element of which is a pointer to a structure of type node  
(b) A structure of 2 fields, each field being a pointer to an array of 10 elements 
(c) A structure of 3 fields: an integer, a float, and an array of 10 elements 
(d) An array, each element of which is a structure of type node 
1.12  The most appropriate matching for the following pairs 
X: m=malloc(5); m= NULL; 1: using dangling pointers 
Y: free(n); n->value=5; 2: using uninitialized pointers 
Z: char *p; *p=’a’; 3. lost memory
GATE CS - 2000
  
is: 
(a) X – 1  Y – 3  Z - 2 (b) X – 2  Y – 1  Z - 3 
(c) X – 3  Y – 2  Z - 1 (d) X – 3  Y – 1  Z - 2 
1.13 The most appropriate matching for the following pairs 
X: depth first search 1: heap 
Y: breadth-first search 2: queue 
Z: sorting 3: stack 
is: 
(a) X – 1  Y – 2  Z - 3 (b) X – 3  Y – 1  Z - 2 
(c) X – 3  Y – 2  Z - 1 (d) X – 2  Y – 3  Z - 1 
1.14 Consider the following nested representation of binary trees: (X Y Z) indicates Y 
and Z are the left and right sub stress, respectively, of node X. Note that Y and Z 
may be NULL, or further nested. Which of the following represents a valid binary 
tree? 
(a) (1 2 (4 5 6 7)) (b) (1 (2 3 4) 5 6) 7)  
(c) (1 (2 3 4)(5 6 7))  (d) (1 (2 3 NULL) (4 5)) 
1.15 Let s be a sorted array of n integers. Let t(n) denote the time taken for the most 
efficient algorithm to determined if there are two elements with sum less than 
1000 in s. which of the following statements is true? 
(a) t (n) is 0(1) (b) n = t(n) = n log
2 
n 
(c) n log
2
 n = t(n) < 
2
n ? ?
? ?
? ?
(d) t(n) = 
2
n ? ?
? ?
? ?
1.16 Aliasing in the context of programming languages refers to 
(a) multiple variables having the same memory location 
(b) multiple variables having the same value 
(c) multiple variables having the same identifier 
(d) multiple uses of the same variable 
1.17 Consider the following C declaration 
struct { 
short s [5] 
union { 
float y; 
long z; 
} u; 
}t; 
GATE CS - 2000
  
Assume that objects of the type short, float and long occupy 2 bytes, 4 bytes and 
8 bytes, respectively. The memory requirement for variable t, ignoring alignment 
considerations, is 
(a) 22 bytes (b) 14 bytes (c) 18 bytes (d) 10 bytes 
1.18 The number of tokens in the following C statement 
printf(“i=%d, &i=%x”,i,&i); 
is 
(a) 3 (b) 26 (c) 10 (d) 21 
1.19. Which of the following derivations does a top-down parser use while parsing an 
input string? The input is assumed to be scanned in left to right order. 
(a) Leftmost derivation 
(b) Leftmost derivation traced out in reverse 
(c) Rightmost derivation  
(d) Rightmost derivation traced out in reverse 
1.20. Which of the following need not necessarily be saved on a context switch 
between processes? 
(a) General purpose registers (b) Translation look-aside buffer 
(c) Program counter   (d) All of the above 
1.21. Let m[0]…m[4] be mutexes (binary semaphores) and P[0] …. P[4] be processes. 
Suppose each process P[i] executes the following: 
wait (m[i];wait (m[(i+1) mode 4]); 
……… 
release (m[i]); release (m[(i+1)mod 4]); 
This could cause 
(a) Thrashing (b) Deadlock 
(c) Starvation, but not deadlock (d) None of the above 
1.22. B
+
 -trees are preferred to binary trees in databases because 
(a) Disk capacities are greater than memory capacities 
(b) Disk access is much slower than memory access 
(c) Disk data transfer rates are much less than memory data transfer rates 
(d) Disks are more reliable than memory  
1.23. Given the relations 
employee (name, salary, deptno), and 
department (deptno, deptname, address) 
Page 5


GATE CS - 2000
  
SECTION - A 
1. This question consists of TWENTY-THREE multiple questions of ONE mark each.
For each question (1.1 – 1.23), four possible alternatives (A, B, C and D) are
given, out of which ONLY ONE is correct. Indicate the correct answer in the boxes
corresponding to the questions only on the FIRST sheet of the answer book.
1.1 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 
cards to guarantee that three cards are from some same suit is  
(a) 3 (b) 8 (c) 9 (d) 12 
1.2 An n × n array v is defined as follows: 
, for all , , ,1 i j i j i j i i n j n ? = - = = = = ? ?
? ?
The sum of the elements of the array v is 
(a) 0 (b) n -1 (c) 
2
3 2 n n - + (d) 
( )
2
1
2
n
n
+
1.3 The determinant of the matrix 
2 0 0 0
8 1 7 2
2 0 2 0
9 0 6 1
? ?
? ?
? ?
? ?
? ?
? ?
? ?
is: 
(a) 4 (b) 0 (c) 15 (d) 20 
1.4 Let S and T be language over S={a,b} represented by the regular expressions 
(a+b*)* and (a+b)*, respectively. Which of the following is true? 
(a) S ? T (b) T ? S (c) S = T (d) S nT = f 
1.5 Let L denotes the language generated by the grammar S 
 0S0/00. 
Which of the following is true? 
(a) L = 0
+
 (b) L is regular but not 0
+
(c) L is context free but not regular (d) L is not context free 
1.6 The number 43 in 2’s complement representation is 
(a) 01010101 (b) 11010101 (c) 00101011 (d) 10101011 
1.7 To put the 8085 microprocessor in the wait state 
(a) lower the HOLD input (b) lower the READY input  
(c) raise the HOLD input (d) raise the READY input 
GATE CS - 2000
  
1.8 Comparing the time T1 taken for a single instruction on a pipelined CPU with time 
T2 taken on a non-pipelined but identical CPU, we can say that 
(a) T1 = T2 (b) T1 = T2 (c) T1 < T2 
(d) T1 is T2 plus the time taken for one instruction fetch cycle 
1.9 The 8085 microprocessor responds to the present of an interrupt 
(a) as soon as the TRAP pin becomes ‘high’ 
(b) by checking the TRAP pin for ‘high’ status at the end of each instruction each 
(c) by checking the TRAP pin for ‘high’ status at the end of the execution of each 
instruction. 
(d) by checking the TRAP pin for ‘high’ status at regular intervals. 
1.10 The most appropriate matching for the following pairs 
X: Indirect addressing 1: Loops 
Y: Immediate addressing 2: Pointers 
Z: Auto decrement addressing 3. Constants
is 
(a) X – 3  Y – 2  Z - 1 (b) X – 1  Y – 3  Z - 2 
(c) X – 2  Y – 3  Z - 1 (d) X – 3  Y – 1  Z - 2 
1.11 The following C declarations 
struct node{ 
int i: 
float j; 
}; 
struct node *s[10]; 
define s to be 
(a) An array, each element of which is a pointer to a structure of type node  
(b) A structure of 2 fields, each field being a pointer to an array of 10 elements 
(c) A structure of 3 fields: an integer, a float, and an array of 10 elements 
(d) An array, each element of which is a structure of type node 
1.12  The most appropriate matching for the following pairs 
X: m=malloc(5); m= NULL; 1: using dangling pointers 
Y: free(n); n->value=5; 2: using uninitialized pointers 
Z: char *p; *p=’a’; 3. lost memory
GATE CS - 2000
  
is: 
(a) X – 1  Y – 3  Z - 2 (b) X – 2  Y – 1  Z - 3 
(c) X – 3  Y – 2  Z - 1 (d) X – 3  Y – 1  Z - 2 
1.13 The most appropriate matching for the following pairs 
X: depth first search 1: heap 
Y: breadth-first search 2: queue 
Z: sorting 3: stack 
is: 
(a) X – 1  Y – 2  Z - 3 (b) X – 3  Y – 1  Z - 2 
(c) X – 3  Y – 2  Z - 1 (d) X – 2  Y – 3  Z - 1 
1.14 Consider the following nested representation of binary trees: (X Y Z) indicates Y 
and Z are the left and right sub stress, respectively, of node X. Note that Y and Z 
may be NULL, or further nested. Which of the following represents a valid binary 
tree? 
(a) (1 2 (4 5 6 7)) (b) (1 (2 3 4) 5 6) 7)  
(c) (1 (2 3 4)(5 6 7))  (d) (1 (2 3 NULL) (4 5)) 
1.15 Let s be a sorted array of n integers. Let t(n) denote the time taken for the most 
efficient algorithm to determined if there are two elements with sum less than 
1000 in s. which of the following statements is true? 
(a) t (n) is 0(1) (b) n = t(n) = n log
2 
n 
(c) n log
2
 n = t(n) < 
2
n ? ?
? ?
? ?
(d) t(n) = 
2
n ? ?
? ?
? ?
1.16 Aliasing in the context of programming languages refers to 
(a) multiple variables having the same memory location 
(b) multiple variables having the same value 
(c) multiple variables having the same identifier 
(d) multiple uses of the same variable 
1.17 Consider the following C declaration 
struct { 
short s [5] 
union { 
float y; 
long z; 
} u; 
}t; 
GATE CS - 2000
  
Assume that objects of the type short, float and long occupy 2 bytes, 4 bytes and 
8 bytes, respectively. The memory requirement for variable t, ignoring alignment 
considerations, is 
(a) 22 bytes (b) 14 bytes (c) 18 bytes (d) 10 bytes 
1.18 The number of tokens in the following C statement 
printf(“i=%d, &i=%x”,i,&i); 
is 
(a) 3 (b) 26 (c) 10 (d) 21 
1.19. Which of the following derivations does a top-down parser use while parsing an 
input string? The input is assumed to be scanned in left to right order. 
(a) Leftmost derivation 
(b) Leftmost derivation traced out in reverse 
(c) Rightmost derivation  
(d) Rightmost derivation traced out in reverse 
1.20. Which of the following need not necessarily be saved on a context switch 
between processes? 
(a) General purpose registers (b) Translation look-aside buffer 
(c) Program counter   (d) All of the above 
1.21. Let m[0]…m[4] be mutexes (binary semaphores) and P[0] …. P[4] be processes. 
Suppose each process P[i] executes the following: 
wait (m[i];wait (m[(i+1) mode 4]); 
……… 
release (m[i]); release (m[(i+1)mod 4]); 
This could cause 
(a) Thrashing (b) Deadlock 
(c) Starvation, but not deadlock (d) None of the above 
1.22. B
+
 -trees are preferred to binary trees in databases because 
(a) Disk capacities are greater than memory capacities 
(b) Disk access is much slower than memory access 
(c) Disk data transfer rates are much less than memory data transfer rates 
(d) Disks are more reliable than memory  
1.23. Given the relations 
employee (name, salary, deptno), and 
department (deptno, deptname, address) 
GATE CS - 2000
  
Which of the following queries cannot be expressed using the basic relational 
algebra operations (s,p,×,   ,?,n,-)? 
(a) Department address of every employee  
(b) Employees whose name is the same as their department name 
(c) The sum of all employees’ salaries 
(d) All employees of a given department 
2. This question consists of TWENTY-SIX multiple questions of TWO marks each.
For each question (2.1 – 2.26), four possible alternatives (A, B, C and D) are
given, out of which ONLY ONE is correct. Indicate the correct answer in the boxes
corresponding to the questions only on the SECOND sheet of the answer book.
2.1 X,Y and Z are closed intervals of unit length on the real line. The overlap of X and 
Y is half a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and 
Z be k units. Which of the following is true? 
(a) k must be 1 (b) k must be 0 
(c) k can take any value between 0 and 1 (d) None of the above 
2.2. E
1
 and E
2
 are events in a probability space satisfying the following constraints: 
• Pr(E
1
) = Pr(E
2
)
• Pr(E
1
 ? E
2
) = 1
• E
1
 and E
2 
are independent
The value of Pr(E
1
), the probability of the event E
1
, is 
(a) 0 (b) 
1
4
(c) 
1
2
(d) 1 
2.3. Let 
100
2
3
log
l
i
S i
=
=
?
and 
and T=
100
2
2
log x xdx
?
Which of the following statements is true? 
(a) S > T (b) S = T 
(c) S < T and 2S > T  (d) 2S = T 
2.4. A polynomial p(x) satisfies the following: 
p(1) = p(3) = p(5) = 1 
p(2) = p(4) = -1 
The minimum degree of such a polynomial is 
(a) 1 (b) 2 (c) 3 (d) 4