[nilesh]

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Hello sir is there any one can provide me here old question papers for Tata Institute of Fundamental Research?

[prince karak]

The Tata Institute of Fundamental Research is a public research institution in Mumbai and Hyderabad, India, dedicated to basic research in mathematics and the sciences.

TIFR GS is conducted by the Tata Institute of Fundamental Research for Graduate School Admissions.

The Graduate programmes at TIFR are Chemistry, Mathematics, Physics, Biology, Computer Systems Sciences and Science Education.

Get download all TIFR old question paper:



Important dates:

Online registration start from 09 Sep 2016
Last date to submit application form of Physics, Chemistry, Maths and Computer & Systems Science 17 Oct 2016
Last date for Online Payment 21 Oct 2016
Download Hall ticket 10 Nov 2016
Date of Entrance Examination 11 Dec 2016
GATE Scored based applications to Systems Science
(including Communications and Applied Probability) Opens : January 19, 2017
Closes : Two weeks after GATE 2017 results declared.
Declaration of Result (shortlist for interview) 31 Jan 2017



TIFR old question paper computer and science:

Part A: Common Part
1. A suitcase weighs one kilogram plus half of its weight. How much does the suitcase weigh?
(a) 1.333... kilograms
(b) 1.5 kilograms
(c) 1.666... kilograms
(d) 2 kilograms
(e) cannot be determined from the given data

2. For vectors x, y in Rn, define the inner product x, y = n i=1 xiyi, and the length of x to be x = x, x. Let a, b be two vectors in Rn so that b = 1. Consider the following statements:
(i) a, b≤ b
(ii) a, b≤ a
(iii) a, b = a b
(iv) a, b≥ b
(v) a, b≥ a

Which of the above statements must be TRUE of a, b? Choose from the following options.
(a) (ii) only
(b) (i) and (ii)
(c) (iii) only
(d) (iv) only
(e) (iv) and (v)

3. On planet TIFR, the acceleration of an object due to gravity is half that on planet earth. An object on planet earth dropped from a height h takes time t to reach the ground. On planet TIFR, how much time would an object dropped from height h take to reach the ground?
(a) t/√2
(b) √2t
(c) 2t
(d) h/t
(e) h/2t
CSS 2017 Common Part Page 2 of 17

4. Which of the following functions asymptotically grows the fastest as n goes to infinity?
(a) (log log n)!
(b) (log log n)log n
(c) (log log n)log log log n
(d) (log n)log log n
(e) 2
√log log n

5. How many distinct ways are there to split 50 identical coins among three people so that each person gets at least 5 coins?
(a) 335
(b) 350 − 250
(c) 35 2
(d) 5015 • 335
(e) 372

6. How many distinct words can be formed by permuting the letters of the word ABRACADABRA?
(a) 11! 5! 2! 2!
(b) 11! 5! 4!
(c) 11! 5! 2! 2!
(d) 11! 5! 4!
(e) 11!

7. Consider the sequence S0, S1, S2,... defined as follows: S0 = 0, S1 = 1, and Sn = 2Sn−1 + Sn−2 for n ≥ 2. Which of the following statements is FALSE?
(a) for every n ≥ 1, S2n is even
(b) for every n ≥ 1, S2n+1 is odd
(c) for every n ≥ 1, S3n is a multiple of 3
(d) for every n ≥ 1, S4n is a multiple of 6
(e) none of the above
CSS 2017 Common Part Page 3 of 17

8. In a tutorial on geometrical constructions, the teacher asks a student to construct a right-angled triangle ABC where the hypotenuse BC is 8 inches and the length of the perpendicular dropped from A onto the hypotenuse is h inches, and offers various choices for the value of h. For which value of h can such a triangle NOT exist?
(a) 3.90 inches
(b) 2√2 inches
(c) 2√3 inches
(d) 4.1 inches
(e) none of the above

9. Consider the majority function on three bits, maj : {0, 1}3 → {0, 1}, where maj(x1, x2, x3) = 1 if and only if x1+x2+x3 ≥ 2. Let p(α) be the probability that the output is 1 when each input is set to 1 independently with probability α. What is p
(α) = d dαp(α)?
(a) 3α
(b) α2
(c) 6α(1 − α)
(d) 3α2(1 − α)
(e) 6α(1 − α) + α2

10. For a set A, define P(A) to be the set of all subsets of A. For example, if A = {1, 2}, then P(A) = {∅, {1, 2}, {1}, {2}}. Let f : A → P(A) be a function and A is not empty. Which of the following must be TRUE?
(a) f cannot be one-to-one (injective)
(b) f cannot be onto (surjective)
(c) f is both one-to-one and onto (bijective)
(d) there is no such f possible
(e) if such a function f exists, then A is infinite

11. Let f ◦ g denote function composition such that (f ◦ g)(x) = f(g(x)). Let f : A → B such that for all g : B → A and h : B → A we have f ◦ g = f ◦ h ⇒ g = h. Which of the following must be TRUE?
(a) f is onto (surjective)
(b) f is one-to-one (injective)
(c) f is both one-to-one and onto (bijective)
(d) the range of f is finite
(e) the domain of f is finite
CSS 2017 Common Part Page 4 of 17

12. Consider the following program modifying an n × n square matrix A:
for i = 1 to n:
for j = 1 to n:
temp = A[i][j] + 10
A[i][j] = A[j][i]
A[j][i] = temp - 10
end for end for
Which of the following statements about the contents of the matrix A at the end of this program must be TRUE ?
(a) the new A is the transpose of the old A
(b) all elements above the diagonal have their values increased by 10 and all values below have their values decreased by 10
(c) all elements above the diagonal have their values decreased by 10 and all values below have their values increased by 10
(d) the new matrix A is symmetric, that is, A[i][j] = A[j][i] for all 1 ≤ i, j ≤ n
(e) A remains unchanged

13. A set of points S ⊆ R2 is convex if for any points x, y ∈ S, every point on the straight line joining x and y is also in S. For two sets of points S, T ⊂ R2, define the sum S +T as the set of points obtained by adding a point in S to a point in T. That is, S + T := {(x1, x2) ∈ R2 : x1 = y1 + z1, x2 = y2 + z2, (y1, y2) ∈ S, (z1, z2) ∈ T}.
Similarly, S −T := {(x1, x2) ∈ R2 : x1 = y1−z1, x2 = y2−z2, (y1, y2) ∈ S, (z1, z2) ∈ T} is the set of points obtained by subtracting a point in T from a point in S. Which of the following statements is TRUE for all convex sets S, T?
(a) S + T is convex, but not S − T
(b) S − T is convex, but not S + T
(c) exactly one of S + T and S − T is convex, but it depends on S and T which one
(d) neither S + T nor S − T is convex
(e) both S + T and S − T are convex

Here is PDF of TIFR old question paper computer and science: