HI,
TODAY NO FIST HOUR ALL ARE REQUESTED TO REACH OUR CLASS BY 7.15 ( SECOND HOUR)
"Whatever We Do We Should Always Rememeber Our Aim"------------------------------- "Each work has to pass through these stages—ridicule, opposition, and then acceptance. Those who think ahead of their time are sure to be misunderstood." - VIVEKANANDHA-
PUBLIC PROVIDENT FUND - 1968
Scheme introduced by Central Government in 1968. The Scheme enables the members of the public to make contributions to the Fund and obtain Income Tax rebate under the relevant provisions of the Income Tax.
Eligibility
Minimum Rs.500/- per annum in multiples of Rs.5/-
Maximum Rs.70,000/- per annum
Duration
Rate of Interest
8% per annum credited in account on 31st March every year calculated on the minimum balance between 5th day and end of the month.
Loans
Loan upto 25% of balance at the end of first financial year from third to sixth year. Second loan can be taken on full payment of first loan.
Withdrawals
Only one withdrawal allowed during any one year from sixth year. Withdrawal limited to 50% of the balance at the credit at the end of 4th year preceding the year in which the amount is withdrawn or the end of the preceding year whichever is lower.
The account extended beyond 15 years; partial withdrawal allowed up to 60% of the balance to the credit at the commencement of the extended period.
Tax Benefits
Other Facilities
PART B
1. Explain Towers of Hanoi problem and solve it using recursion.
2. Find the time complexity and space complexity of the following problems.
1) Factorial using Recursion.
2) Compute nth Fibonacci Number.
3) Compute xn or exponentiate (x,n).
4) mxn matrix multiplication
5) nxn matrix multiplication
6) mxn matrix addition.
7) Sequential/linear search.
3. Describe best, worst and average case analysis with an example.
1. What is divide and conquer technique?
2. Give the control abstraction for divide and conquer technique.
3. Write the recurrence relation for DandC.
4. Timecomplexity of Binary search is O(logn). Justify.
5. Write a straight forward max min algorithm.
6. Explain the greedy method.
7. Define feasible and optimal solution.
8. Write the control abstraction for greedy method.
9. What are the constraints of knapsack problem?
10. What is a minimum cost spanning tree?
11. Specify the algorithms used for constructing Minimum cost spanning tree.
12. State single source shortest path algorithm (Dijkstra's algorithm).
13. Calculate the T(n) for the given recurrence form
T(n) = T(1) if n=1
T(n) = aT(n/b)+f(n) if n>1
where a=2,b=2, T(1)=2, f(n)=n;
PART-B
1. Explain the binary search algorithm with an example.
2. Explain mimmax problem using Divide and conquer technique. Compute its time complexity.
3. Explain merge sort with an example. Compute its time complexity.
4. Explain Quick sort with an example. Give its time complexity.
5. Solve the knapsack problem using greedy technique.
6. Explain Prim's algorithm to construct Minimum cost spanning tree.
7. Explain Kruskal's algorithm to construct Minimum cost spanning tree.
8. Explain Optimal Randomized algorithm to construct Minimum cost spanning tree.
9. Explain single source shortest path algorithm (Dijkstra's algorithm).
1. What are explicit constraints and implicit constraints?
2. Explain 8-Queen problem in brief.
3. What are static trees and dynamic trees?
4. Give any 4 problems that could be solved by backtracking.
5. What are the constraints of 8-Queens problem
6. Define m-colorability optimization problem.
7. What is a Hamiltonian cycle?
8. What are the 2 methods of Branch and bound techniques?
9. Compare and contrast LC-BB and FIFO BB.
10. What is a reduced cost matrix?
PART – B
1. Explain N-Queens problem using Backtracking.
2. Explain Graph Coloring.
3. Explain sum of subsets.
4. Explain Hamiltonian cycles.
5. Solve Knapsack problem using backtracking.
6. Explain Traveling Salesperson problem using branch and bound techniques.
1. What is P and NP?
2. What is deterministic algorithm?
3. What is Non-Deterministic Algorithm?
4. Draw the relationship between P, NP, NP complete and NP-hard.
5. What is the property of NP-Complete problem?
6. What is the property of NP-Hard problem?
7. What are the two most famous unsolved problems in Computer science?
PART – B