#1
July 1st, 2014, 08:03 AM
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JNU University Pre Ph.d Mathematics Exam Question Papers
Provide me question paper for Jawaharlal Nehru University Pre PHD mathematics science examination ?
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#2
July 1st, 2014, 11:08 AM
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Re: JNU University Pre Ph.d Mathematics Exam Question Papers
Here I am giving question paper for Jawaharlal Nehru University Pre PHD mathematics science examination in a file attached with it so you can get it easily. Which of the following rings is a field? (a) Z / 57Z (b) (Z/3Z)x(Z/3Z) (c) R[x] /(x2 -2) (d) Q[x]+2+2) 2. For a finite group G (a) there does not exist any group homomorphism 9: G -* Z (b) there is a unique group homomorphism 9: G -> Z (c) there are infinitely many group homomorphisms 9: G -> Z (d) there are exactly [ G I group homomorphisms cp : G -3 Z 3. Let R be a subring of C containing Q. Suppose it, 4-3 e R. Which of the following is not necessarily true? (a) J/neR (b) n/Je R (c) [(n+1)2 - (n-1)21/(n15)e R (d) (,/n2-7)/(-13- +1)eR 4. Let X be a set and let B and C be some fixed subsets of X. If for any subset A of X, A c C implies A c B, which of the following statements is true? (a) C * B (b) Bc C (c) Cc B (d) B c C /91 7 [ P.T.O. 5. Let f : X -> Y be a surjective map. Which of the following is necessarily true? (In the following, Ids stands for the identity map on the set S) (a) There exists g : Y -> X such that g o f = Idx (b) There exists a unique g : Y -> X such that g o f = IdX (c) There exists g : Y -a X such that f o g = Idy (d) There exists a unique g : Y -* X such that f o g = Idy 6. Let - be some equivalence relation on R. We are told that under this relation , r - (r + 1) for every r e R. We can now definitely conclude that (a) the number of equivalence classes is infinite the number of equivalence classes is finite ( 7T) 7C (it -2)- (it +2) 7. Let V be a non-trivial inner product space over R. For vectors v, WE V we say v - w if (v, w) = 0. Then the relation - is (a) symmetric but neither reflexive nor transitive (b) transitive but neither reflexive nor symmetric (c) an equivalence relation (reflexive , symmetric and transitive) (d) symmetric and transitive , but not reflexive 8. Let A e SL3 (lIt) be a matrix such that Av = v for some v * 0 in lit3. Which of the following statements about A is necessarily true? (a) A is a rotation (b) A is the identity map (c) A is diagonalizable (d) None of the above 9. A box contains 4 blue and 3 green balls. Two balls are drawn out together at random from the box. What is the probability that the two balls are of different colours? (a) 5/7 (b) 4/7 (c) 3/7 (d) 2/7 |
#3
September 12th, 2015, 09:56 PM
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Re: JNU University Pre Ph.d Mathematics Exam Question Papers
i want to ph.d. entrance paper
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