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)

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 sciencespaper part-B, follow link above.

## CSIR NET 2018 December physical sciences

### Part A

Q - 1. A tourist drives20 kmtowards east, turns right and drives6 km, then drives6 kmtowards west. He then turns to his left and drives4 kmand finally turns right and drives14 km. Where is he from his starting point? 1.2.6 kmtowards east20 kmtowards west3.14 kmtowards north4.10 kmtowards 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 examination100questions of1mark each are given. After the examination,20questions are deleted from evaluation, leaving80questions with a total of100marks. Student A had answered4of the deleted questions correctly and got40marks, whereas student B had answered10of the deleted questions correctly and got35marks. 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, each1 mwide. 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? 1.2.6 π3.10 π4.12 π36 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.

The diagram shows that the outer track has an arc length of `S _{outer}` for an angle

`θ`while the inner track has an arc length of

`S`. The diagram shows that

_{inner}`S`is greater than

_{outer}`S`by:

_{inner}*the angle into difference of radii of the tracks*i.e.

`θ × ( r`. Thus for an angle of

_{outer}– r_{inner}= 6 meter )`θ = 2`( the full circle ) the outer track is bigger than the inner track by a distance of

**π**= 360^{0}`2`.

**π**× 6 meter = 12**π**meterHence 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 < mean2.mode < mean < median3.mean < median < mode4.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. IfD = ABC + BCA + CABwhereA,BandCare decimal digits, thenDis divisible by 1.2.37and293.37but not294.29but not37neither29 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 are500 μmand200 μm, respectively. Then the image in camera A will be 1.sharper than in B2.darker than in B3.less sharp and brighter than in B4.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 ofy = 2xand^{2}y = 4xintersect each other at 1.only one point2.exactly two points3.more than two points4.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 = 2x ^{2}` and

`y = 4x`. That means

`4x = 2x`and therefore

^{2 }`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 of1^{2 }- 2? 1.^{2 }+ 3^{2 }- 4^{2 }+ 5^{2 }- ... + 17^{2 }- 18^{2 }+ 19^{2}2.-53.124.95190

**click to see or hide answer to Q – 8**

— the answer is **option: 4**.

Explanation: the summation of the series `1 ^{2 }+ 2^{2 }+ 3^{2 }+ 4^{2 }+ 5^{2 }+ … + n^{2}^{ }`has a value:

`n ( n + 1 ) ( 2n + 1 ) / 6`.

The given sequence can be written as follows:

`1 ^{2 } – 2^{2 }+ 3^{2 }– 4^{2 }+ 5^{2 }– … + 17^{2 }– 18^{2 }+ 19^{2 } `

`= ( 1 ^{2 }+ 2^{2 }+ 3^{2 }+ 4^{2 }+ 5^{2 }+ … + 17^{2 }+ 18^{2 }+ 19^{2 }) –`

`2 ×`

`2`

^{2}`( 1`

^{2 }+ 2^{2 }+ 3^{2 }+ 4^{2 }+ 5^{2 }+ … + 9^{2}^{ })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 gets2chocolates, every mother gets1chocolate while no father gets a chocolate.In total69persons get70chocolates. If the number of children is half of the number of mothers and fathers put together, then how many fathers are there? 1.222.3.23244.69

**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 size30 cm × 40 cmhas a photograph mounted at the center leaving a 5 cm border all around. The area of the border is 1.600 cm^{2 }2.3.350 cm^{2}4.400 cm^{2 }700 cm^{2}

**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 cm ^{2}`. The total area of the frame is

`30 cm × 40 cm = 1200 cm`hence area of the border is

^{2}`600 cm`.

^{2}Hence the answer to this question is **option 1: 600 cm^{2}**

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? 1.2.93.164.257

**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.

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 ofcm. What is the total area of the rectangle?^{2}

1.2.183.244.36108

**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

1.2.18.53.24.04.30.536.0

**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.

**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.

```
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 triangle2.Square3.Regular pentagon4.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. `90 ^{0}` )

Hence the answer to this question is **option 2**

Q - 19. An ideal pendulum oscillates with angular amplitude of300from the vertical. If it is observed at a random instant of time, its angular deviation from the vertical is most likely to be 1.2.0^{0}±3.10^{0}±4.20^{0}±30^{0}

**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*.

Hence the answer to this question is **option 1**

Q - 20. If 'SELDOON' MEANS 'NOODLES' then what does 'SPUOS' mean? 1.SALAD2.SOUPS3.RASAM4.ONION

**click to see or hide answer to Q – 20**

— the answer is **option: 2**.

Explanation: read the letters in the reverse direction. SELDOON reads NOODLES. Hence SPUOS would read SOUPS. Thats option 2.

Hence the answer to this question is **option 2**

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