This is the actual questions set 3 appearing in UGC/CSIR Net math exams for PhD aspirants. After going through the test refer to its solutions.

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 third set of 15 Net level questions follow. This must be answered first before referring to its paired solution set.

This is a set of 15 questions for practicing UGC/CSIR Net exam: Question Set 3

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: Proportionate (35 mins).

**Q1. **Rainfall is measured in mm. One day there was a rainfall of 4mm at Kolkata. To collect the rainwater a hemispherical glass bowl of radius 1cm was kept in an open area. How much percent of the bowl was filled up by rainwater?

- 40
- 50
- 60
- 75

**Q2.** Two friends decided to start a race on a bright sunny day. Friend A with usual speed of 8m/sec ran faster than his friend B, whose usual speed was 6m/sec and so it was agreed that the race would be run with a handicap of 40m to A. How much distance would B cover before A overtook him?

- 120m
- 160m
- 80m
- 100m

**Q3.** One day Minti started down in a lift from the 10th floor of a building at the same time as her friend Pinki started up from the ground floor in another lift. They had decided to meet in between rather than wait longer. If Minti's lift covered 3 floors by the time Pinki's covered 2 floors and if they knew it, on which floor will they meet wasting minimum time?

- 3
- 4
- 5
- 2

**Q4.** At the end of a year in a business, profit decreased by 15% with cost price remaining the same. If the previous year profit was 20% what is the percent decrease in sale price this year?

- 12.5%
- 15%
- 10%
- 20%

**Q5.** $\left(\frac{1}{5}\right)^{3x} = 0.008.$ The value of $(0.25)^x$ is,

- 22.5
- 0.25
- 0.0625
- 0.5

**Q6.** Five boys are sitting in a row. Pintu is to the left of Khokon. Kalua is to the right of Apu. Sunny is in the middle of Kalua and Pintu. Who is to the extreme right of the row?

- Khokon
- Apu
- Pintu
- Kalua

**Q7.** A can do a work in 3 days while B can do the same work in in 4 days. If they work together for a total wage of Rs. 2800 how much does A get?

- Rs. 1200
- Rs. 1900
- Rs. 1300
- Rs. 1600

**Q8.** Remainder of $7^{57}$ divided by 10 is,

- 7
- 9
- 3
- 1

**Q9.** In $\triangle{PQR}$, S and T are two points on the sides PR and PQ respectively. $\angle{PQR}=\angle{PST}$. If PT = 5 cm, PS = 3 cm and TQ= 3 cm, the length of line SR is,

- $\frac{31}{3}$ cm
- 5 Cm
- 3 cm
- $\frac{41}{3}$ cm

**Q10.** Growth of a type of fungus was monitored at regular intervals of time and is shown in the graph below. Around which time is the rate of growth zero?

- Near day 1
- On day 3
- Between days 3 and 5
- Between days 5 and 7

**Q11.** There are seven sisters in a house in a village where there is no electricity or any gadget. The activities of the seven sisters in one day are,

- Sister-1: Reading Novel
- Sister-2: Cooking
- Sister-3: Playing Chess
- Sister-4: Playing Sudoku
- Sister-5: Washing clothes
- Sister-6: Gardening

What is Sister-7 doing?

- Sleeping
- Taking bath
- Out marketing
- Playing chess

**Q12.** How many squares are there in the following figure?

- 13
- 10
- 4
- 5

**Q13.** In a bicycle wheel if there were 10 more spokes, the angle between them would have reduced by six degrees. Can you find out the number of spokes in the wheel?

- 10
- 20
- 30
- 40

** Q14.** How many numbers are there from 20 to 40 that have no factor among the numbers from 2 to 10?

- 3
- 4
- 5
- 6

**Q15.** If $2^{4x} + 2^{5x} = 1280$, then x is,

- 4
- 5
- 3
- 2