My experience and interview at IITK (Kanpur) – Part II – The written test

Continuing from my previous post,

I finally reached Kanpur at around 11am, I took a taxi (actually a 6 seater auto kind of vehicle, popularly known as chakdi) to rawatpur from station, the rates of these taxis are unbelievably cheap, I paid 8 bucks for nearly 15kms!  I took another taxi from rawatpur to IIT, again paid only 2 bucks for abt 3kms…After reaching the main gate, I reported at the security post, who directed me to allocated hosted, Hall of Residence – 5, a fellow interviewee was kind enough to offer me a ride from security post to hostel in his auto(the actual 3 wheeler one 😉 ). The campus was really big, recently found out that its more than 4 sq. Kms., the department was atleast half kilometer away from hostel. I was totally exhausted and decided to rest for a while and slept throughout the afternoon, later in the evening, I purchased the mobile charger and a LAN cable(in hopes of connecting to IITK network – a different story for some other time) from the incampus shopping center.

I also befriended couple of guys that evening, Pankaj and Piyush, we decided to report together at the department for the written test the next day. I spent last couple of hours before sleep trying to recall what I had studied throughout my journey and made a small summary. I had a great sleep that night, even though I had to sleep on hard cot, without bedding.

Atlast, the time had come for us to give the written test, I was kinda nervous, but it didn’t really show on my face, all three of us were in different categories, Piyush had applied for Ph.D and Pankaj was not in General category, we were led to lecture hall complex to give the test.

The way the invigilators and professor gave an intro to the test seemed like they repeated the same set of questions every year and did not want anyone to take back the question paper, but dear reader, to your luck, I managed to remember quite a lot of them, and here are the questions:

1.bird flies @ 100mph two vehicles a – 30mph, b – 20mph, dist – 100miles, find total dist bird travels
2. xy(z^)+(x^)yz+xyz (minimize)
3. 10 steps, monkey can take either 1 or 2 steps, total ways?
4. 10 houses in a row, red or blue, no consecutive blue (same as above), total ways?
5. master theorm,
t(n)=sqrt(n)t(sqrt(n))+n
6. master theorm,
t(n)=2t(n/2)+n/log n
7. 90% boys participated, 80% of successful were boys, in total 5% successed, what % of actual passed are boys?
8. 9 houses, 6 persons – 3 boys, 3 girls, various conditions, answer 3 questions based on that
a. e & k dont occupy rooms next to occupied
b. J was next to p & a
c. t takes one next to last
d. all girls are non – consecutive
9. r – z are 9 candidates, to serve in 3 committees, a,b n c,
each should serve only one committee
a. a should have exactly one more than b
b. c can be empty
d. r,s,t cannot serve for c
e. u,v,w cannot serve for b
f. x,y,z cannot serve for a
… various questions on assertion ( 3 )
10.pyramid with equilateral base, has a infinite circle centered same as pyramid, what is the probability(to which it tends) of seeing two faces of pyramid for infinite radius circle
11. smallest number with mod 10 =9, mod 9 = 8 so on…
12. no.of zeroes in fact(30)
13. last digit of 7^2009
14. using rand() generate a number with expected value k
options: while(rand()<1/k)v++; return v
while(rand()<(1-1/k))v++; return v
while(rand()>(1-1/(k+1)))v++; return v
15. insertion sort can be performed in O(nlog n) n selection sort can be performed in O(nlog n) using
heap, red-black
red-black, heap
heap, heap
heap, queue
16. given a sorted array A, a sum of two terms, x, find if two terms are present in A,the algo for this can be done in
O(n)
O(log n)
cannot be done
O(sqrt(n))
17. given a singly linked list a->b->c->d and address of node to delete, say address of c, a->b->d, can be done in
O(n)
O(log n)
cannot be done
O(1)
18. Two binary search trees, t1 and t2 are to be merged into new bst T, wat is the time efficiency
19. ways of arranging k rooks on a nxn board
20. no. of rectangles in 8×8 board
21. u can cut only 1 piece at a time, with no change of motion, no rotation etc. u want to have 8×8 board, how many cuts do u require ( 63 cuts)
22. 40 edges, 40 vertices in an undirected graph, probability of having cycle? (1.00)
23. u chances of winning against nadal is 0.00001% n against gopilal is 10%, you win 2 matches to win series, which of following match sequence will have higher prob of u winning series.
nadal-nadal-nadal
nadal-nadal-gopilal
gopilal-nadal-gopilal
nadal-gopilal-nadal
24. n bit strings with k – alterations (10 or 01)
25. f(x) is number of 1’s in binary representation of x, what is value of f(4x)-f(2x+1)

There were totally some 50 questions(all objective), I could manage to recall some 33 questions above (incl. some extra questions which are based on common data, thats why numbering above reads only till 25), there was negative marking too, so I attempted only those in which I had high confidence, which resulted in me attempting about 40 questions, which was way above many others, most of the fellow candidates had attempted around 25~35 questions, this got me into worry, thinking that I might have gone wrong in many questions. I refrained myself from discussing the answers, we all went back to hostel to have lunch, the results were awaited by evening… More on this in my next post.

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