```The CSIR NET 2018 December 16: Indian Assistant
Professor and PhD scholarship exam solution,
prepared by me. See link below for Part-B (physics).
(this is entirely free stuff: help spread the word)
```

( Physical Sciences Part-B solutions. ) follow link to see solutions for physical sciences paper Part-B

The article aims to make the best attempt at finding the answers for the recently concluded 2018 CSIR NET. Detailed explanatory answers are available to 19 out of  20 questions in Part A. To see solutions for physical sciences paper part-B, follow link above.

## CSIR NET 2018 December physical sciences

### Part A

```Q - 1. A tourist drives 20 km towards east, turns
right and drives 6 km, then drives 6 km towards west.
He then turns to his left and drives 4 km and finally
turns right and drives 14 km. Where is he from his
starting point?

1. 6 km towards east
2. 20 km towards west
3. 14 km towards north
4. 10 km towards south```
click to see or hide answer to Q – 1

— the answer is: option 4.

Explanation: lets refer to the diagram below.

Hence answer is option 4: 10 km towards south.

```Q - 2. In an examination 100 questions of 1 mark
each are given. After the examination, 20 questions
are deleted from evaluation, leaving 80 questions
4 of the deleted questions correctly and got 40
deleted questions correctly and got 35 marks.
In this situation

1. A and B are equally benefited.
2. A and B lost equally.
3. B lost more than A.
4. A lost more than B.```
click to see or hide answer to Q – 2

— the answer is: option 3.

Explanation: questions not deleted: 80. Questions deleted: 20. Old marks per question: 1. New marks per question: 100/80 = 5/4 = 1.25.

A answered correctly ( in old set of questions ) ( 40 / 1.25 ) + 4 = 32 + 4 = 36 but obtained 40 ( in new set of questions ).

Similarly B answered correctly 35 / 1.25 + 10 = 28 + 10 = 38 but obtained 35 ( in the new set of questions).

Clearly B lost more than A.

Hence answer is option 4: B lost more than A.

```Q - 3. A circular running track has six lanes,
each 1 m wide. How far ahead ( in meters )
should the runner in the outermost lane
start from, so as to cover the same distance
in one lap as the runner in the innermost lane?

1. 6 π                    2. 10 π
3. 12 π                   4. 36 π
```
click to see or hide answer to Q – 3

— the answer ( to be reviewed ) is option: 3.

Explanation: lets refer to the diagram below. CSIR NET 2018 December Physical Sciences: answer to question 3, the difference in track length for a given angle depends on the angle as the radii are fixed, for a full circle this is 2π times difference in inner and outer radii. Photo Credit: mdashf.org

The diagram shows that the outer track has an arc length of Souter for an angle θ while the inner track has an arc length of Sinner. The diagram shows that Souter is greater than Sinner by: the angle into difference of radii of the tracks i.e. θ × ( router – rinner  = 6 meter ). Thus for an angle of θ = 2 π = 3600 ( the full circle ) the outer track is bigger than the inner track by a distance of 2 π × 6 meter = 12 π meter.

Hence answer is option 3: 12 π.

```Q - 4. For the following set of observed values
{60, 65, 65, 70, 70, 70, 70, 82, 85, 90, 95, 95,
100, 160, 160}, which of the following
statements is true?

1. mode < median < mean
2. mode < mean < median
3. mean < median < mode
4. median < mode < mean
```
click to see or hide answer to Q – 4

— the answer ( to be reviewed ) is option: none.

Explanation: I am afraid this question does not have an option with the valid answer. Lets see why.

mean: the mean is the total sum of numbers divided by total frequencies of these numbers. Thus mean = ( 1 × 60 ) + ( 2 × 65 ) + ( 4 × 70 ) + ( 1 × 82 ) + ( 1 × 90 ) + ( 2 × 95 ) + ( 1 × 100 ) + ( 2 × 160 ) / ( 1 + 2 + 4 + 1 + 1 + 1 + 2 + 1 + 2 ) = 1337 / 15 = 89.13. The number of times a value occurs in a set of values is known as its frequency. ( here the frequencies add up to 15 )

Thus mean = 89.13.

mode: the mode is the number with the highest frequency ( when the frequency is at-least 2 or more ). Evidently mode is 70 here. ( frequency 4 )

Thus mode = 70.

median: the median of a set of numbers is the one lying in the exact middle of the sequence, for odd number of numbers the middle position refers to the ( “number of numbers” – 1 ) divided by ( 2). So here we need to find the number at the 7th position; ( 15 – 1 ) / 2 = 7. Since the numbers are already in sequence its easy to see that the median is also 70.

Thus median = 70.

Correct option is not given.

```Q - 5. If D = ABC + BCA + CAB where A, B and C
are decimal digits, then D is divisible by

1. 37 and 29
2. 37 but not 29
3. 29  but not 37
4. neither 29 nor 37```
click to see or hide answer to Q – 5

— the answer is option: 2.

Explanation: since the letters A, B and C represent a digit in the decimal system, and each appear once at the 100th, 10th and unity value place, it means D is simply numbers like 111 + 333 + 555 and so on. That means D is always a multiple of 111. 111 is divisible by 37 but not 29.

Hence answer is option 2: 37 but not 29.

```Q - 6. The diameters of the pinholes of two
otherwise identical cameras A and B are 500 μm
and 200 μm, respectively. Then the image in
camera A will be

1. sharper than in B
2. darker than in B
3. less sharp and brighter than in B
4. sharper and brighter than in B
```
click to see or hide answer to Q – 6

— the answer is option: 3.

Explanation: a large aperture ( area that is open to source of light ) in the camera means more light enters the camera ( intensity of light entering is more hence brighter image ). On the other hand light from a single point goes in many different direction, causing blurring of the image, hence a less sharp image is obtained.

Hence the answer is option 3: less sharp and brighter than in B.

```Q - 7. The curves of y = 2x2 and y = 4x intersect
each other at

1. only one point
2. exactly two points
3. more than two points
4. no point at all```
click to see or hide answer to Q – 7

— the answer is option: 2.

Explanation: the curves will intersect at a point (x, y) which satisfies both the equations y = 2x2 and y = 4x. That means 4x = 2xand therefore x = 0 or x = 2. Accordingly y = 0 or y = 8. Thus the two points where the curves intersect are: (0, 0) and (2, 8).

Hence the answer is option 2: exactly two points.

```Q - 8. What is the value of
12 - 22 + 32 - 42 + 52 - ... + 172 - 182 + 192?

1. -5
2. 12
3. 95
4. 190```
click to see or hide answer to Q – 8

— the answer is option: 4.

Explanation: the summation of the series 12 + 22 + 32 + 42 + 52 +  … + n2  has a value: n ( n + 1 ) ( 2n + 1 ) / 6 .
The given sequence can be written as follows:

12 – 22 + 32 – 42 + 52 – … + 172 – 182 + 19

= ( 12 + 22 + 32 + 42 + 52 +  … + 172 + 182 + 19) – 2 × 22 ( 12 + 22 + 32 + 42 + 52 +  … + 92

Thus the sum of this series is [ ( 19 × 20 × 39 ) / 6 ] – [ 8 × ( 9 × 10 × 19 ) / 6 ] = 190

hence the answer to this question is option 4: 190

```Q - 9. At a birthday party, every child gets 2
chocolates, every mother gets 1 chocolate while
no father gets a chocolate.In total 69 persons
get 70 chocolates. If the number of children is
half of the number of mothers and fathers put
together, then how many fathers are there?

1. 22            2. 23
3. 24            4. 69```
click to see or hide answer to Q – 9

— the answer is option: 1.

Explanation: the trick to finding the correct answer to this question is to include the father in all calculations even if they don’t get any chocolates. ( does it remind you of democracy? cos thats what democracy is, even if some don’t get any goodies they are considered an integral part )

Lets denote number of children by C, so the number of mothers is denoted by M and the number of fathers is denoted by F. Now we can write the equations.

total people: C + M + F = 69

total chocolates: 2 C + M = 70

given relation: 2 C = M + F

first and third equations: 3 C = 69 or C = 23

from second equation: M = 70 – 46 = 24

Finally first equation: F = 69 – ( 24 + 23 ) = 22

hence the answer to this question is option 1: 22

```Q - 10. A rectangular photo frame of size 30 cm × 40
cm has a photograph mounted at the center leaving a
5 cm border all around. The area of the border is

1. 600 cm2           2. 350 cm2
3. 400 cm2           4. 700 cm2```
click to see or hide answer to Q – 10

— the answer is option: 1.

Explanation: as the diagram below shows the the photograph occupies an area of 20 cm × 30 cm = 600 cm2. The total area of the frame is 30 cm × 40 cm = 1200 cm2 hence area of the border is 600 cm2. CSIR NET 2018 December Physical Sciences: answer to question 10, the area of the border is the area of the frame minus the area of the photograph. Photo Credit: mdashf.org

Hence the answer to this question is option 1: 600 cm2

```Q - 11. The lift ( upward force due to air )
generated by the wings and engines of an aircraft is

1. positive ( upwards ) while landing and negative
( downwards ) while taking off.

2. negative ( downwards ) while landing and positive
( upwards ) while taking off.

3. negative ( downwards ) while landing as well as
while taking off.

4. positive ( upwards ) while landing as well as
while taking off.```
click to see or hide answer to Q – 11

— the answer is option: 4.

Explanation: the aircraft comes with 4 forces. Lift, Drag, Thrust and Weight. Thrust is aircraft’s own force which comes by burning the fuel. Drag is the resistance or friction on ground or air. Lift is the upward force experienced by the plane which depends upon static as well dynamic pressure ( Bernoulli’s principle ). E.g when the fluid above the aircraft ( air ) is flowing at higher speed, the pressure there is less than the pressure at the bottom. That means there is an upward lift force acting on the plane which would act to raise its height. The reverse is true when the fluid below is moving at faster speeds. This can be controlled by the shape and orientation of the wings and flaps on the plane. The flaps therefore control the drag as well as lift forces. ( This is ensured by using different angles for the flaps )

When we want to take off obviously we need an upward lift force which helps us fly easily. Thus during the take off the lift has to be positive. During landing we need a smooth descent. The weight force is the response of the planes mass to the gravitational force which always pulls it down. Hence having a positive lift will ensure this force is countered and the descent is smoother.

Hence the answer to this question is option 4: positive ( upwards ) while landing as well as taking off

```Q - 12. A student is free to chose only Chemistry,
only Biology or both. If out of 32 students,
Chemistry has been chosen by 16 and Biology by 25,
then how many students have chosen Biology but not
Chemistry?

1. 9                  2. 16
3. 25                 4. 7```
click to see or hide answer to Q – 12

— the answer is option: 2.

Explanation: the Venn diagram shows the problem clearly. The number of students who have chosen chemistry + the number of students  who have chosen biology – the number of students who have chosen both biology and chemistry = the total number of students. CSIR NET 2018 December Physical Sciences: answer to question 12 Venn diagram shows that number of students who took biology but not chemistry is number of students who took biology minus number of students who took both biology and chemistry photo credit: mdashf.org

So the number of students who have chosen both biology and chemistry = 25 + 16 – 32 = 9. Thus the number of students who have chosen biology but not chemistry is the number of students who have chosen biology minus number of students who have chosen both biology and chemistry = 25 – 9 = 16.

Hence the answer to this question is option 2: 16

```Q - 13. Areas of three parts of a rectangle are
given in unit of cm2. What is the total area of
the rectangle?
``` CSIR NET 2018 December Physical Sciences: Question 13 photo credit: mdashf.org
```1. 18                  2. 24
3. 36                  4. 108```
click to see or hide answer to Q – 13

— the answer is option: 3.

Explanation: from the diagram its clear that the area of the 4th part is 18 units. ( right side house is thrice that of left side and bottom house is twice that of the top house ). Thus total area is 53 + 9 + 6 + 18 = 36 units.

Hence the answer to this question is option 3: 36

```Q - 14. In triangle ABC, AB = 11, BC = 61, AC = 60,
and O is the mid-point of BC. Then AO is
``` CSIR NET 2018 December Physical Sciences: Question 14 photo credit: mdashf.org
```1. 18.5                  2. 24.0
3. 30.5                  4. 36.0```
click to see or hide answer to Q – 14

— the answer is option: .

Explanation: at the moment I don’t have an answer. Check back later.

Hence the answer to this question is option

```Q - 15. Find the missing figure in the following
sequence.``` CSIR NET 2018 December Physical Sciences: Question 15, part A photo credit: mdashf.org
click to see or hide answer to Q – 15

— the answer is option: 3.

Explanation: the plus signs are reducing in number: 4, 3, 2, 1 and follow the anti-clockwise pattern for disappearance. Hence the 4th image must have the + sign at the top right, this means only 1 or 3 are the correct option. The dot inside the internal quadrilateral keeps alternating between left and right. So it must be on the right in the 4th ( missing ) image. In option 3 the image has the dot on the right, so we can discard 1 and 3 must be the correct option.

Hence the answer to this question is option 3

```Q - 16. Two solutions X and Y containing ingredients
A, B and C are in proportions a:b:c and c:b:a,
respectively, are mixed. For the resultant mixture
to have A, B and C in equal proportion, it is
necessary that

1. b = ( c - a ) / 2      2. c = ( a + b ) / 2
3. c = ( a - b ) / 2      4. b = ( c + a ) / 2
```
click to see or hide answer to Q – 16

— the answer is option: 4.

Explanation: let the ingredient of A in X is ax, of B in X is bx and that of C in X is cx. Then the ingredient of A in Y is cx,of B in Y is bx and that of C in Y is ax according to the given information. Now X and Y are mixed. So ingredient of A in mixture is ( a + c ) x. Similarly ingredient of B in the mixture is ( 2 b ) x and of C in the mixture is ( a + c ) x. Since they are in equal proportion in the mixture we have 2 b x = ( a + c ) x. This gives b = ( a + c ) / 2. This is given in option 4.

Hence the answer to this question is option 4

```Q - 17. Scatter plots for pairs of observations on
the variables x and y in samples A and B are shown
in the figure.
``` CSIR NET 2018 December Physical Sciences: Question 17 photo credit: mdashf.org
```Which of the following is suggested by the plots?
1. Correlation between x  and y is stronger in A
than in B
2. Correlation between x and y is absent in B
3. Correlation between x and y is weaker in A
than in B
4. y and x have a cause-effect relationship in A,
but not in B
```
click to see or hide answer to Q – 17

— the answer is option: 1.

Explanation: we see that in plot A the scatter data can be fitted to a straight line. In plot A the y variable increases linearly for increase in x variable. This is an example of positive correlation. Whereas in the plot B there is no obvious relation that seems to exist in the data points, this seems to reflect zero correlation among the data points. Hence correlation is stronger in A than in B.

Hence the answer to this question is option 1

```Q - 18. In the context of tiling a plane surface,
which of the following polygons is the odd one out?

1. Equilateral triangle
2. Square
3. Regular pentagon
4. Regular hexagon
```
click to see or hide answer to Q – 18

— the answer ( to be reviewed ) is option: 1.

Explanation: here is a diagram of all the four plane surfaces. Evidently the square is the odd one out ( all its angles are right angle i.e. 900 ) CSIR NET 2018 December Physical Sciences: answer to question 18; 4 different shapes, equilateral triangle, square, regular pentagon and regular hexagon photo credit: mdashf.org

Hence the answer to this question is option 2

```Q - 19. An ideal pendulum oscillates with angular
amplitude of 300 from the vertical. If it is
observed at a random instant of time, its
angular deviation from the vertical is most
likely to be

1. 00                 2. ± 100
3. ± 200              4. ± 300```
click to see or hide answer to Q – 19

— the answer is option: 1.

Explanation: here is a diagram of the simple pendulum exhibiting simple harmonic motion. An ideal pendulum is one where the angular displacement is small enough to be approximated by the sine of the angular displacement itself. i.e. sin θ = θ. But the average of sin θ is zero. Therefore the most likely angular deviation is zero. CSIR NET 2018 December Physical Sciences: answer to question 19; a simple pendulum in simple harmonic motion photo credit: mdashf.org

Hence the answer to this question is option 1

```Q - 20. If 'SELDOON' MEANS 'NOODLES' then what
does 'SPUOS' mean?