Part A: CSIR - NET Solution (Bio Group):Dec 2015

1. A shopkeeper purchased a product for Rs.$100$ and sells it making a profit of $10$%. The customer resells it to the same shopkeeper incurring a loss of $10$%. In these dealings the shopkeeper makes
1. no profit, no loss

2. Rs. $11$
3. Re. $1$
4. Rs. $20$

Solution: CP for the customer: $100+10=110$

and $10$% of $110=11$ So customer sells shopkeeper at $99$. SO Shopkeeper makes a profit of Rs $10+1=11$.

$2$nd option is correct.

2. A vessel is partially filled with water. More water is added to it at a rate directly proportional to time. Which of the following graphs depicts correctly the variation of total volume $V$ of water with time $t$?

Solution: $\frac{dv}{dt}=kt$ Integrating we get : $v= kt^2/2+c$ Since it is given that intially there was some liquid. So, $2$ option is correct.

3. The triangle formed by the lines $y=x$ $y=1-x$  and $x=0$ in a two dimensional plane is (x and y axes have the same scale)
1. isosceles and right-angled
2. isosceles but not right-angled
3. right-angled but not isosceles
4. neither isosceles nor right-angled

Solution Slope of $y=x$ is $45$ degree. Slope of $y=1-x$ is $180-45$ degree. So In the triangle, two angles are $45$ and $45$. So $1$st option is correct.

4. Statement A. The following statement is true
Statement B. The preceding statement is false.
Choose the correct inference from the following:

1. Statements A and B are always true
2. Statements A and B can be true if there is at least one statement between A and B
3. Statements A and B can be true if there are at least two statements between
A and B
4. Statements A and B can never be true, independently.

Solution: option $3$ is correct.

The number of squares in the above figure is
1. $30$

2. $29$

3.$25$

4.$20$

Solution:

 $29$

6. A person walks downhill at $10$ km/h, uphill at $6$ km/h and on the plane at $7.5$ km/h. If the person takes $3$ hours to go from a place A to another place B, and $1$ hour on the way back, the distance between A and B is
1. $15$ km.
2. $23.5$ km.
3. $16$ km.
4. Given data is insufficient to calculate the distance.

Solution: Data is not sufficient to solve it.

7. A bird leaves its nest and flies away. Its distance x from the nest is plotted as a function of time t. Which of the following plots cannot be right?

Sotution: $3$. is not possible . Since at one time two value of $x$ is not possible.

8. A car is moving at 60 km/h. The instantaneous velocity of the upper most points of its wheels is
1. 60 km/h forward
2. 120 km/h forward
3. 60 km/h backward
4. 120 km/h backward

Solution:
option  $2$ is correct. $120$ km/h Forward.

9. A living cell has a protoplasm which is water based and demarcated by a lipid bilayer membrane. If a cell is pierced up to $1/5$ th of its diameter with a very sharp needle, after taking the needle out
1. no effect will be observed.
2. protoplasm will leak out from the hole made by the needle for a few minutes until the cell heals the wound.
3. protoplasm will keep on leaking out till the cell is dead.
4. the cell will burst like a balloon.

Solution: No effect will be observed. ( Don't know how)

10.   If    D + I + M = 1501
C+ I + V + I + L = 157
L + I + V + I + D = 557
C +I + V+ I + C = 207
What is V + I + M = ?
1. Cannot be found
2. 1009
3. 1006
4. 509

Solution: Letters are written in Roman Numerals. So, Answer is \(5+1+1000=1006\). So, third option is correct.

11. Density of a rice grain is 1.5 g/cc and bulk density of rice heap is 0.80 g/cc. If a 1 litre container is completely filled with rice, what will be the approximate volume of pore space in the container?
1. 350 cc 2. 465 cc
3. 550 cc 4. 665 cc

Solution: Using allegation Formula:

Quantity of Cheaper/ Quantity of dearer= (high value-mean value)/(mean value-low value)

volume of pour Space/Volume of rice=$\frac{1.5-0.8}{0.8-0}$=$\frac{7}{8}$

So volume of pour space=$1000/15\times 7$=$466.66$ approximately $465$.

12. Four circles of unit radius each are drawn such that each one touches two others and their centres lie on the vertices of a square. The area of the region enclosed between the circles is
1. $\pi-1$                         2. $\pi-2$
3. $3-\pi$                        4. $4-\pi$

Solution:

 $4-\pi$ as the required area=Area of square - area of circle

13. A turtle starts swimming from a point A located on the circumference of a circular pond. After swimming for 4 meters in a straight line it hits point B on the circumference of the pond. From there it changes direction and swims for 3 meters in a straight line and arrives at point D diametrically opposite to point A. How far is point D from A?
1.   3 m                                                                        2.   4 m
3.   7 m                                                                        4.   5 m

Solution:  Thales theorem states that any diameter of a circle  Subtends a right angle to any point on the circle.

So by applying Pythagoras's theorem  , We get the required distance=$5$

14. A film projector and microscope give equal magnification. But a film projector is not used to see living cells because
1. a living cell cannot be placed in a film projector.
2. the viewer’s eye is close to a microscope whereas it is far away from the projector’s screen.
3. a microscope produces a virtual image whereas a projector produces a real image.
4. a microscope has greater resolving power than a projector.

Solution: Resolving power is the ability of  of an optical instrument or type of film to separate or distinguish small or closely adjacent images. SO $4$ option is correct.

15. In each of the following groups of words is a hidden number, based on which you should arrange them in descending order. Pick the correct answer:
E. Papers I Xeroxed
F. Wi-Fi veteran
G. Yourself ourselves
H. Breaks even
1. H, F, G, H 2. E, G, F, H
3. H, F, G, E 4. H, E, F, G

Solution: 

E. Papers I Xeroxed
F. Wi-Fi veteran
G. Yourself ourselves
H. Breaks even
So, correct order is  H, E, F, G

16. Five congruent rectangles are drawn inside a big rectangle of perimeter 165 as shown. What is the perimeter of one of the five rectangles?

1. 37                                  2. 75
3. 15                                 4. 165

Solution: 
let length and breadth of one rectangle is $l$ and $b$ respectively. Then from this picture it's clear that

$3\times b=2\times l$ (see pic)

Also perimeter of big rectangle is $2\times l+2\times(l+b)+3\times b=165$ Solving these two equation we get $l=3/2\times 15$ and $b-15$ So, perimeter =$2\times (l+b)=75$

17. At one instant, the hour hand and the minute hand of a clock are one over the other in between the markings for 5 and 6 on the dial. At this instant, the tip of the minute hand
1. is closer to the marking for 6
2. is equidistant from the markings for 5 and 6
3. is closer to marking for 5
4. is equidistant from the markings for 11 and 12

Solution: $\theta=|30h-11/2m|$ So here hour hand is between $5$ and $6$ So $h=5$ and $\theta=0$ So we have $0=150-11/2 \times m$ That is, $m=25.4$ that means close to $5$. so correct option  is $3$.

18. A cubical cardboard box made of 1 cm thick card board has outer side of 29 cm. A tight-fitting cubical box of the same thickness is placed inside it, then another one inside it and so on. How many cubical boxes will be there in the entire set?
1. 29                                     2. 28                                     3. 15                              4. 14

Solution:  Side of $1$st Cube is 29 . Inside it Cube will have a side =$27$. So sequence will be

$29,27,...,2$ So, Let  number of terms in this sequence is $n$.  then $2=29+(n-1)\times (-2)$ and $n$ is  a bit greater than $14$ But here cube can be fractional So answer is $14$.

19. There are two buckets A and B. Initially A has 2 litres of water and B is empty. At every hour 1 litre of water is transferred from A to B followed by returning litre back to A from B half an hour later. The earliest A will get empty is in:
1. 5 h                    2. 4 h
3. 3 h                   4. 2 h

Solution: 

So Answer will be $3$ Hours.

20. Secondary colours are made by a mixture of three primary colours, Red, Green and Blue, in different proportions; each of the primary colours comes in 8 possible levels. Grey corresponds to equal proportions of Red, Green and Blue. How many shades of grey exist in this scheme?
1. $8^3$                  2. 8                         3. $3^8$                            4. $8\times 3$

Solution:  every Shades have $8$ options to get selected to produce required color. So Answer will be $8$