Twice a year UGC Jointly with CSIR conducts the Net exam 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 ability of the student using basic concepts in maths rather than procedural competence in maths.

The fourth set of 15 Net level questions follow. To gain maximum benefits from this resource, the student must first answer this set before referring to the corresponding 15 question solution set.

This is a set of 15 questions for practicing UGC/CSIR Net exam: Question Set 4

Answer all 15 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: 25 mins.

**Q1.** The unit's digit of the product $(693\times{694}\times{695}\times{698})$ is,

- 2
- 8
- 0
- 4

**Q2.** In a city average age of men and women are 72.4 years and 67.4 years respectively, while the average of the total number of citizens is 69.4 years. The percentage of men in the city is,

- 40
- 50
- 60
- 66.7

**Q3.** Two angles of a triangle are 40% and 60% of the largest angle. The largest angle is,

- $120^0$
- $90^0$
- $80^0$
- $100^0$

**Q4.** A bird sitting at the top of a pole spots a centipede 36m away from the base of the pole. If the bird catches the centipede at 16m from the base of the pole both moving at the same speed, the height of the pole is,

- 18m
- 15m
- 12m
- $12\sqrt{2}$m

**Q5.** In the circle with centre at $O$, $AB$ is a chord. $\angle{ACB} + \angle{OAB}$ =

- $120^0$
- $60^0$
- $90^0$
- $180^0$

**Q6.** A car travels uphill to a point at a speed of 20km/hr and returns back to its original position at a speed of 60km/hr. The average speed in which the car covered the whole distance is,

- 30km/hr
- 40km/hr
- 45km/hr
- 35km/hr

**Q7.** If $5^{\sqrt{x}} + 12^{\sqrt{x}} - 13^{\sqrt{x}} = 0$, then x is,

- $\displaystyle\frac{25}{4}$
- 4
- 9
- 6

** Q8.** The angle between the hour and minute hands of a clock at 10 past 10 is,

- $120^0$
- $115^0$
- $65^0$
- $55^0$

**Q9.** In a river, a boat travelling at a still water speed of 6m/sec overtook a second boat travelling in the same direction and of same length at a still water speed of 4m/sec in 10secs. The length of each boat is,

- 100m
- 5m
- 10m
- Cannot be determined

**Q10.** 16 men can do a piece of work in 20 days. How many extra percentage of men will have to be brought in to complete the work in 40% of the original time?

- 50%
- 250%
- 80%
- 150%

**Q11.** A cube of ice of volume $100cm^3$ floats in water with $\frac{9}{10}$ths of its volme under water. If its portion above water melts at a rate of $10{\%}$ per minute, what will be its approximate volume above water after 3 minutes?

- $7cm^3$
- $7.29cm^3$
- $9.7cm^3$
- $7.3cm^3$

**Q12.** The minimum value of $2p^2 + 3q^2$, where $p^2 + q^2=1$ and $-1 {\leq} p,q {\leq} 1$ is,

- 0
- 2
- 1
- 2.5

** Q13.** From a bag containing 1 green, 4 blue and 5 red balls, if a ball is picked up blindfolded, what is the probability of picking up a blue ball?

- $\frac{1}{4}$
- $\frac{2}{5}$
- $\frac{1}{10}$
- $\frac{2}{3}$

** Q14.** A rubber mat of thickness 1cm is rolled tightly with no gaps between layers into a solid cylindrical shape that stood on ground with a base area of $1m^2$ and height 1m. The total surface area of the sheet is,

- $2.02m^2$
- $202.02m^2$
- $101.01m^2$
- $200.02m^2$

**Q15.** In a queue of girls Lakshmi stood at the 5th position from the front and 15th position from the end. In another queue girls Veeny stood at the 18th position from the front and 7th from the end. The total number of girls in two queues together is,

- 20
- 38
- 40
- 43