P. f(x) is continuous for all real values of x
Q. f(x) is differentiable for all real values of x

  int j, n;
  j = 1;
  while (j <= n)
        j = j*2;

     Group I                          Group II
(P) Gang Scheduling              (1) Guaranteed Scheduling
(Q) Rate Monotonic Scheduling    (2) Real-time Scheduling
(R) Fair Share Scheduling        (3) Thread Scheduling

[A  I]
[I  A]

Consider the following expressions P, Q and R.
P: X = Y⋆Z 
Q: Y = X⋆Z 
R: X⋆Y⋆Z=1

Pi = Ai ⨁ Bi and Gi = AiBi

Si = Pi ⨁ Ci and Ci+1 = Gi + PiCi , where C0 is the input carry.

IF: Instruction Fetch
ID: Instruction Decode and Operand Fetch
EX: Execute
WB: Write Back

ADD R2, R1, R0       R2 <- R0 + R1
MUL R4, R3, R2       R4 <- R3 * R2
SUB R6, R5, R4       R6 <- R5 - R4

8 2 3 ^ / 2 3 * + 5 1 * -

A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. If L = 41, and I = 10, what is the value of n?

S --> iCtSS1|a
S1 --> eS|ε
C --> b

P: Every regular grammar is LL(1)
Q: Every regular set has a LR(1) grammar

Process  Execution time  Arrival time
P1             20            0
P2             25            15
P3             10            30
P4             15            45

P: Increasing the number of page frames allocated to a 
   process sometimes increases the page fault rate.
Q: Some programs do not exhibit locality of reference.

 
    alloc           request
    X Y Z            X Y Z
P0  1 2 1            1 0 3
P1  2 0 1            0 1 2
P2  2 2 1            1 2 0

  /* P1 */
while (true) {
  wants1 = true;
  while (wants2 == true);
  /* Critical
    Section */
  wants1=false;
}
/* Remainder section */       


/* P2 */
while (true) {
  wants2 = true;
  while (wants1==true);
  /* Critical
    Section */
  wants2 = false;
}
/* Remainder section */

Q1 : Select e.empId
     From employee e
     Where not exists
        (Select * From employee s where s.department = “5” and 
                                        s.salary >=e.salary)
Q2 : Select e.empId
     From employee e
     Where e.salary > Any
    (Select distinct salary From employee s Where s.department = “5”)

(P) SMTP     (1) Application layer
(Q) BGP      (2) Transport layer
(R) TCP      (3) Data link layer
(S) PPP      (4) Network layer
             (5) Physical layer

S --> aB        S --> bA
B --> b         A --> a
B --> bS        A --> aS
B --> aBB       A --> bAA

S --> aB        S --> bA
B --> b         A --> a
B --> bS        A --> aS
B --> aBB       A --> bAA

A process has been allocated 3 page frames. Assume that none of the pages of the process are available in the memory initially. The process makes the following sequence of page references (reference string): 1, 2, 1, 3, 7, 4, 5, 6, 3, 1 If optimal page replacement policy is used, how many page faults occur for the above reference string?