UGC conducts Jointly with CSIR, the Net exam twice a year for PhD and Lecturership aspirants. For science subjects such as Life Science, Chemical Science etc, the question paper is divided into three parts - Part A, B and C. Part A is on Maths related topics and contains 20 questions any 15 of which have to be answered. The other two parts are on the specific subject chosen by the student.

The questions in Maths are tuned towards judging the problem solving capability of the student using the basic knowledge in maths and not the procedural competence in maths.

The fifth question set of 18 Net level Math questions follows.

This is a set of 15 questions for practicing for UGC/CSIR Net exam: Question Set 5**Answer any 15 out of 18 questions**. Each correct answer will add 2 marks to your score and each wrong answer will deduct 0.5 mark from your score.

Total maximum score 30 marks. Time: 30 mins.

**Q1.** The units digit of $2^{79} + 7^{35}$ is,

- 1
- 3
- 5
- 7

**Q2.** $2^{4x}.4^{10x}=8^{16}$. Find $x$.

- 1
- 2
- 3
- $\frac{1}{2}$

**Q3.** A tank is losing water 50% per hour. The percentage of water left after 2 hour will be,

- 50%
- 0%
- 25%
- 75%

**Q4.** Sumi is 4th from the beginning of a row of girls and 20th from the end of a row while Ruma is 10th from the end of the same row and 14th from the beginning of the row. How many girls are between them?

- 6
- 7
- 9
- 10

**Q5.** The angle between the hour and the minute hands at 30 minutes past 5 is,

- $15^0$
- $20^0$
- $25^0$
- $45^0$

**Q6.** To cover a distance upstream a boat takes 7 hours while to cover half the distance downstream it takes 2 hours. The ratio of still water boat speed and stream speed is,

- 5 : 3
- 11 : 3
- 11 : 7
- 7 : 3

**Q7.** The radius of a solid cylinder is 8 cm and height 20 cm while the diameter of a second cylinder is 16 cm while the height 5 cm. What is the ratio of volumes of the second to the first cylinder?

- 1 : 2
- 7 : 22
- 1 : 4
- 1 : 8

**Q8.** 4 women can do a work in 8 days while 8 men do the same work in 2 days. In how many days 2 men and 4 women working together will finish the work?

- 4
- 3
- 2
- 5

**Q9.** A cycle 2 m long running at 40m per sec overtakes another cycle of same length running at half the speed of the first. How long would it take to overtake?

- 10 secs
- 5 secs
- 4 secs
- 0.2 secs

** Q10.** Probability of a even digit coming up in a six faced die in a single throw is,

- $\displaystyle\frac{1}{2}$
- $\displaystyle\frac{1}{3}$
- $\displaystyle\frac{1}{4}$
- $\displaystyle\frac{1}{6}$

** Q11.** 5 men do a work in 30 days. How many more men are required to finish the job in 25 days?

- 11
- 6
- 2
- 1

**Q12.** A car covers certain distance in 2 hours and 30 minutes. But on a certain day, halfway to the distance it developed a fault and covered the rest of the distance at half its original speed. How much total time it took?

- 3 hours 30 minutes
- 3 hours 45 minutes
- 3 hours 15 minutes
- 4 hours

**Q13.** Manish got 65% marks after announcement of score in 3 subjects. When marks of the fourth subject was announced he found his average to increase to 67%. All subjects having same full marks, how much was his score in the fourth subject?

- 70%
- 72%
- 73%
- 69%

**Q14.** 20 men doing a work can finish a job in 30 days. If after a few days one fourth of the men leave and still they could finish the job in 35 days, for how many days the reduced number of men had to work?

- 20 days
- 18 days
- 15 days
- 25 days

**Q15.** Chord BD subtends an $\angle{BAD}=70^0$ on the circumference above the chord. Then $\angle{BCD}$ subtended by the chord on the lower circumference below the chord is,

- $140^0$
- $120^0$
- $110^0$
- $130^0$

** Q16.** A chord AB of length $3\sqrt{2}$ cm subtends an angle $90^0$ at the centre O of a circle. Area of the sector AOBC is,

- $\displaystyle\frac{9\pi}{4} cm^2$
- $10 cm^2$
- $5\sqrt{2}cm^2$
- $3\sqrt{2}cm^2$

**Q17.** ABCD is a quadrilateral inscribed in a circle with center at O.

If $\angle{COD}=120^0$ and $\angle{BAC}=30^0$, then $\angle{BCD}$ is,

- $75^0$
- $120^0$
- $90^0$
- $60^0$

**Q18.** A die is rolled. If the outcome is an odd number, the probability that it is a prime is.

- $\displaystyle\frac{2}{3}$
- $\displaystyle\frac{1}{3}$
- $\displaystyle\frac{1}{2}$
- $\displaystyle\frac{1}{4}$