UGC/CSIR Net level Maths Question set 2

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These are 20 questions from actual UGC/CSIR Net maths exam for BioScience PhD aspirants. Try this 2nd set first before going through the 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 second full set of 20 Net level questions follow.

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This is a set of 20 questions for practicing UGC/CSIR Net exam: Question Set 2
Answer any 15 out of 20 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. The angles of a right-angled shaped garden are in arithmetic progression and the smallest side is 10.00 m. The total length of the fencing of the garden in m is

1. 60.00

2. 47.32

3. 12.68

4. 22.68

Q2. 25% of 25% of a quantity is x% of a quantity where x is

1. 6.25%

2. 12.5%

3. 25%

4. 50%

Q3. Cucumber contains 99% water. Ramesh buys 100kgs of cucumber. After 30 days of storing, the cucumbers lose some water. They now contain 98% water. What is the total weight of the cucumber now?

1. 99kg

2. 50kg

3. 75kg

4. 2kg

Q4. What is the minimum number of days between one Friday the 13th and the next Friday the 13th? (Assume that the year is a leap year).

1. 58

2. 56

3. 91

4. 84

Q5. A 16.2m long wooden log has a uniform diameter of 2m. To what length the log should be cut to obtain a piece of 22m$^3$ volume?

1. 3.5m

2. 7.0m

3. 14.0m

4. 22.0m

Q6. A bee leaves its hive in the morning and after flying for 30 minutes due south reaches a garden and spends 5 minutes collecting honey. Then it flies for 40 minutes due west and collects honey in another garden for 10 minutes. Then it returns to the hive taking the shortest route. How long was the bee away from its hive? (Assume that the bee flies at constant speed).

1. 85 minutes

2. 155 minutes

3. 135 minutes

4. less than an hour

Q7. What is the last digit of 7$^{73}$?

1. 7

2. 9

3. 3

4. 1

Q8. A bird perched at the top of a 12m high tree sees a centipede moving towards the base of the tree from a distance equal to twice the height of the tree. The bird flies along a straight line to catch the centipede. If both the bird and the centipede move at the same speed, at what distance from the base of the tree will the centipede be picked up by the bird?

1. 16m

2. 9m

3. 12m

4. 14m

Q9. What is the angle between the minute and hour hands of a clock at 7.35?

1. $0^0$

2. $17.5^0$

3. $19.5^0$

4. $20^0$

Q10. A large tank filled with water is to be emptied by removing half of the water present in it every day. After how many days will there be closest to 10% water left in the tank?

1. 1

2. 2

3. 3

4. 4

Q11. The distance between two oil rigs is 6 km. What will be the distance between these two rigs in maps of 1 : 50000 and 1 : 5000 scales respectively?

1. 12 cm and 1.2 cm

2. 2 cm and 12 cm

3. 120 cm and 12 cm

4. 12 cm and 120 cm

Q12. The capacity of the conical vessel shown above is V. It is filled with water up to half its height. The volume of water in the vessel is,

1. $\displaystyle\frac{V}{2}$

2. $\displaystyle\frac{V}{4}$

3. $\displaystyle\frac{V}{8}$

4. $\displaystyle\frac{V}{16}$

Q13. A stream of ants goes from point A to point B and return to A along the same path. All the ants move at a constant speed and from any given point 2 ants pass per second one way. It takes 1 minute for an ant to go from A to B. How many returning ants will an ant meet in its journey from A to B?

1. 120

2. 60

3. 240

4. 180

Q14. A king ordered that a golden crown be made for him from 8 kg of gold and 2kg of silver. The goldsmith took away some amount of gold and replaced it with an equal amount of silver and the crown when made weighed 10kgs. Archimedes knew that under water gold lost 1/20th of its weight while silver lost 1/10th. When the crown was weighed under water it was 9.25 kgs. How much gold was stolen by the goldsmith?

1. 0.5 kg

2. 1 kg

3. 2 kg

4. 3 kg

Q15. A point was chosen at random from a circular disc shown below. What is the probability that the point lies in the sector OAB where Angle AOB = x radians?

1. $\displaystyle\frac{x}{\pi}$

2. $\displaystyle\frac{2x}{\pi}$

3. $\displaystyle\frac{x}{2\pi}$

4. $\displaystyle\frac{x}{4\pi}$

Q16. A ray of light after getting reflected twice from a hemispherical mirror of radius R emerges parallel to the incident ray. The separation between the original incident ray and final reflected ray is,

1. $R$

2. $R\sqrt{2}$

3. $2R$

4. $R\sqrt{3}$

Q17. An ant goes from A to C in the figure crawling only on the lines and taking the least length of path. The number of ways it can do so is,

1. 2

2. 4

3. 5

4. 6

Q18. In the figure below number of circles in the blank rows must be,

1. 12 and 20

2. 13 and 20

3. 13 and 21

4. 10 and 11

Q19. In the figure $\angle ABC = \pi/2$ and $AD = DE = EB$. What is the ratio of the area of the $\triangle ADC$ to that of $\triangle CDB$?

1. 1 : 1

2. 1 : 2

3. 1 : 3

4. 1 : 4

Q20. The area of the shaded region in cm$^2$ is

1. $(\pi - \sqrt{2})$

2. $(\pi - 2)$

3. $\displaystyle\left(\frac{\pi}{4} - \frac{\sqrt{2}}{2}\right)$

4. $(\pi + 2)$