# Joint CSIR-UGC NET December 2013: Model Papers: Mathematical Sciences

Council of Scientific & Industrial Research (CSIR) is going to organize Joint CSIR UGC National Eligibility Test (NET) on 22nd December 2013 in six notified subjects. Jagranjosh.com is providing the sample model paper for the candidates preparing for this exam.

CSIR holds the Joint CSIR-UGC NET twice a year, usually in the month of June and December. And, this is the time for CSIR-UGC NET - December 2013, which is going to be held on 22nd December in the subjects - Chemical Sciences; Earth, Atmospheric, Ocean and Planetary Sciences; Life Sciences; Mathematical Sciences; Physical Sciences; Engineering Sciences.

**1. Let x _{n} = n ^{1/n} and y_{n} = (n!)^{1/n}, n > 1 be two sequences of real numbers. Then**

1. (x

_{n}) converges, but (y

_{n}) does not converge

2. (y

_{n}) converges, but (x

_{n}) does not converge

3. Both (x

_{n}) and (y

_{n}) converge

4. Neither (x

_{n}) nor (y

_{n}) converges

**2. The set { x є R : x sin x ≤ 1, x cos x ≤ 1} С R is**

1. A bounded closed set

2. A bounded open set

3. An unbounded closed set.

4. An unbounded open set.

**3. Let f:[0,1]→ R be continuous such that f(t) ≥ 0 for all t in [0, 1]. Define g(x) = f (t) dt then**

1. G is monotone and bounded

2. G is monotone, but not bounded

3. G is bounded, but not monotone

4. G is neither monotone nor bounded

**Joint CSIR-UGC NET December 2013: Model Papers: Mathematical SciencesJoint CSIR UGC NET December 2013: Syllabus for All SubjectsJoint CSIR UGC NET December 2013: Exam Scheme**

CSIR will issue the list of registered candidates on 20 November 2013 for Joint CSIR UGC NET December 2013 scheduled to be held on 22 December.