CSIR-NET Mathematical Science and Life Science (Part A Solved):2015 June ~ APRAJITA'S BLOG

1. A pyramid shaped toy is made by tightly placing cubic blocks of $1\times 1 \times 1$ $cm^3$ . The base of the toy is a square $4\times 4$ $Cm^2$ . The width of each step is 0.5 Cm . how many blocks are required to make the toy?

Solution:

Number of Cubic block required for

$4\times 4$ =

$16.$

Similarly Number of Cubic block required for

$3\times 3$ =

$9$ and

$4$ and

$1$ respectively .

Total=

$16+9+4+1=30$

2. Of three persons A, Band C, one always lies while the others always speak the truth. C asked A, "Do you
always speak the truth, yes or no?" He said something that C could not hear. So, C asked B, "what did A say?"
B replied, "A said No. So, who is the liar?

A
B
C
cannot be determined

Solution: Here

$C$ lie or not , doesn't matter. So Of the persons

$A$ and

$B$ at least one always speak truth.

now

$A$ and

$B$ both can't speak truth. Since in this condition

$A$ can't reply NO! So this case is not possible.

Now let

$A$ is a lair then

$A$ can't reply NO!! So,

$B$ is Liar!

3. Two plane mirrors facing each other are kept at 60° to each other. A point is located on the angle bisector. The number of images of the point is

6
3
5
Infinite

Solution: Formula for this type of problem:

Number of Images=

$\frac{360}{\theta}-1$ So Here it will be

$360/60-1$ =

$5$

4.What is angle x in the schematic diagram given below?

Solution:

From the above picture it is clear that

$x=180-(100+50)=30$

5. A 3 m long car goes past a 4 m long truck at rest on the road. The speed of the car is 7 m/s. The time taken to go past is

4/7
1 s
7/4 s
10/7 s

Solution: Total distance covered is

$3+4$ m So Time=

$1$ Sec.

6.Consider 3 parallel strips of 10m width running around the Earth, parallel to the equator; A1 at the
Equator, A2 at the Tropic of Cancer and A3 at the Arctic Circle. The order of the areas of the strips is

A1<A2< A3
A1=A2> A3
A1>A2= A3
A1>A2> A3

Solution:

Tropic of cancer is between Equator and Arctic circle. So 4th option is correct.

7.Let m and n be two positive integers such that $m+n+mn=118$ Then the value of $m + n$ is

not uniquely determined
18
20
22

Solution :

$m+mn+n+1=119$

$\Rightarrow m(n+1)+(n+1)=(m+1)(n+1)=119$ Now find all factors of

$119$

$119=17\times 7$ . So

$m=16$ and

$n=6$ So

$m+n=22$

8.I bought a shirt at 10% discount and sold it to a friend at a loss of 10%. If the friend paid me Rs. 729.00 for the shirt, hat was the undiscounted price of the shirt?

Rs. 900
Rs. 800
Rs. 1000
Rs.911.25

Solution: Let Undiscounted Price=

$100\times x$ . So C.P.(Discounted price)=

$90x$ Selling price=

$90x-9x$ =

$81x$ Now it is given that

$81x=729$ So Undiscounted price=

$900$

9. Suppose

(1) x = 4

(2) Then x - 4 = x2 - 42(as both sides are zero)

(3) Therefore (x - 4) = (x - 4)(x + 4)

Cancelling (x - 4) from both sides

(4) 1 = (x + 4)

(5) Then x = -3

Which is the wrong step?

1 to 2
2 to 3
3 to 4
4 to 5

Solution: Recall Cancellation Law:

$ax=ab \Rightarrow x=b$ only if

$a\neq 0$ . Here

$x-4=0$ So we can’t cancel it out. So 4^th Step is wrong. Hence 3^rd option is correct.

10. From a group of 40 players, a cricket team of 11 players is chosen. Then, one of the eleven is chosen as the captain of the team. The total number of ways this can be done is

$\binom{40}{11}$
$11 \binom{40}{11}$
$29 \binom{40}{11}$
$\binom{39}{10}$

Solution: The total number of way we can select 11 out of 40 objects is

$\binom{40}{11}$ So, 2^nd option is correct.

Solution: The total number of way we can select 11 out of 40 objects is $\binom{40}{11}$ So, 2^nd option is correct.

11. Information in DNA is in the form of sequence of 4bases namely A, T, G and C. The proportion of G is the same as that of C, and that of A is the same as that of T. Which of the following strands of DNA will potentially have maximum diversity (i.e., maximum information content per-base)?

length 1000 bases with 10% G
length 2000 bases with 10% A
length 2000 bases with 40% T
length 1000 bases with 25% C

Solution:Well, I Could not solve this problem.

12. if aN=>S
eF=>I
gH=>M
then nS=?

Solution:

$aN\rightarrow Na$ means Sodium So

$\rightarrow S$

$eF\rightarrow Fe$ means Iron So

$\rightarrow I$

Therefore

$nS\rightarrow Sn$ So Tin

$\rightarrow T$

13.In each of the following groups of words is a hidden number, based on which you should arrange them in ascending order. Pick the right answer:
A. Tinsel event B. Man in England
C. Good height D. Last encounter

A, B, C, D
C, B, D, A
A, C, D, B
C, D, B, A

Solution:

A. Tinsel event B. Man in England
C. Good height D. Last encounter

So C,B,DA is the right order.

2nd option is correct.

14 A single celled spherical organism contains 70% water by volume. If it loses 10% of its water content,
how much would its surface area change by approximately?

Solution:

Let

$r$ be the original radius the original volume of water is

$V_1=\frac{70}{100}\times \frac{4}{3}\pi r^3=\frac{14}{15}\pi r^3$ & volume of organic material

$V_2=\frac{30}{100}\times \frac{4}{3}\pi r^3=\frac{2}{5}\pi r^3$
& surface area

$S_0=4\pi r^2$

when it loses

$10$ % of water then remaining volume of water

$V_1'=\frac{90}{100}\times V_1= \frac{90}{100}\times\frac{70}{100} \times \frac{4}{3}\pi r^3=\frac{21}{25}\pi r^3$
If

$r'$ is the radius of remaining cell then new volume of cell

$V_1'+V_2=\frac{21}{25}\pi r^3+\frac{2}{5}\pi r^3$

$r'=\left(0.93 \right)^{1/3}r$
hence the new surface area of cell

$S'=4\pi r'^2=4\pi \left(\left(0.93\right)^{1/3}r\right)^2=4\pi \left(0.93 \right)^{2/3}r^2$

hence % change in surface area of the cell

$\frac{S'-S_0}{S_0}\times 100$

$=\frac{4\pi \left(0.93 \right)^{2/3}r^2-4\pi r^2}{4\pi r^2}\times 100=4.722877503\approx 5\ \text{%}$

15. Jar W contains 40 white - marbles and Jar B contains 40 black marbles. Ten black from B are transferred to W
and mixed thoroughly. Now, ten randomly selected marbles from W are put back in Jar B to make 40 marbles in each jar. The number of black marbles in W

would be equal to the number of white marbles in B.
would be more than the number of white marbles in B.
would be less than the number of white marbles in B
cannot be determined from the information given

Solution:

1st option is correct.

16. How many non-negative integers less than 10,000 are there such that the sum of the digits of the number is divisible by three?

1112
2213
2223
3334

Solution: the sum of digits are divisible by 3 that means the number is divisible by 3. So the numbers are:

0, 3,6,9… 9999 So total 3334 . Hence 4 is the right Option.

17. Two ants, initially at diametrically opposite points A and B on a circular ring of radius R, start crawling towards each other. The speed of the one at A is half of that of the one at B. The point at which they meet is at a straight line distance of

R from A
3R/2 from A
R from B
R/2 from B

Solution: Since the speed of B is double than A. So it will cover double distance than A.

So Angle Subtend by the arc followed by B is double than A.

See the picture below. Since triangle formed is an equilateral triangle so all sides are equal and hence distance=

$R$ . Option 1 Is correct.

18. Starting from a point A you fly one mile south, then one mile east, then one mile north which brings you back to point . Point A is NOT the north pole. Which of the following MUST be true?

You are in the Northern Hemisphere
You are in the Eastern Hemisphere
You are in the Western Hemisphere
You are in the Southern Hemisphere

Solution: This is a famous Puzzle Globe Walker.

The trivial answer to this question is one point, namely, the North Pole. But if you think that answer should suffice, you might want to think again!

Let's think this through methodically. If we consider the southern hemisphere, there is a ring near the South Pole that has a circumference of one mile. So what if we were standing at any point one mile north of this ring? If we walked one mile south, we would be on the ring. Then one mile east would bring us back to same point on the ring (since it‟s circumference is one mile). One mile north from that point would bring us back to the point were we started from.

So 4th option is correct.

19. AB is the diameter of a circle. The chord CD is perpendicular to AB intersecting it at P. If CP = 2 and PB =1, the radius of the circle is

1
2.5
2
5

Solution: From the picture it’s clear that

$r^2 =2^2+{(r-1)}^2$ So,

$r$ is equal to

$2.5$ .

20. Based on the graph, which of the following which of the following statements is not true?

Number of gold medals increased whenever total number of the medals increased.
Percentage increase in gold medals in 2010 over 2006 is more than the corresponding increasing in total medals.
Every time non-gold medals together account for more than 50% of the total medals.
Percentage increase in gold medals in 2010 over 2006 is more than the corresponding increase in 2002 over 1998