Gokhale Sample Paper Doubts

[Ayushya Kaul]

Hey,
Here's the link:
http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/gipe_modelquestions_ma.pdf

My doubts:
SECTION-C

6. What is the fourth term of (2a - 6b)^8?
a) 28*16*1296
b) 28*32*216
c) 70*32*216
d) 56*32*216

9. On which of the following interval(s) must the function f (x) = 2+x^2−x^3
have a root?
a) [−1, 0]
b) [0, 1]
c) [1, 2]
d) [2, 3]

4. If random variable X has probability density function given by
f(x)= e^-x     x
      = 0 Otherwise
Find P [2x + 3 = 5]
a) 1/2
b) 1/4
c) 0
d) 1

SECTION-B

5. You are an analyst for a metropolitan transportation authority. You are asked if it would
improve efficiency to buy more buses, and if so, how many more should be bought. The
operating cost of a bus is 30 during the day and 60 during the night, when higher wages
must be paid to drivers and other workers. The daily capital cost of a bus, whether or not
it is used, is 10. The demand for buses aggregated over persons and stops during the 12
hours of day and night, respectively D and N, are
QD = 160− PD
QN = 80− PN


What prices should be charged to induce efficient ridership?
a) PD= 45, PN= 55  
b) PD= 40, PN= 60  
c) PD= 70, PN= 80  
d) PD= 60, PN= 40

SECTION-A

5. What is the next number in the sequence 8 13 5 15 20 12 ?
a) 17
b) 15
c) 36
d) None of the above


Thanks in advance. And any hint/help/clue would be greatly appreciated :)
Cheers!

[Ayushya Kaul]

And does anyone have any clue whether the sample paper on  link is the actual paper patter for Gokhale?
Thanks in advance!

[Ayushya Kaul]

Bump.

[Mauli]

hi ayushya :)
visit gip's site.
thy have uploaded 3 model papers too.
and i think the paper format will be somewhat on the same lines.


here are the links for the papers:-


http://www.gipe.ac.in/pdfs/Model%20question%20paper%201.pdf

http://www.gipe.ac.in/pdfs/Model%20question%20paper%202.pdf

http://www.gipe.ac.in/pdfs/Model%20question%20paper%203.pdf

[Ayushya Kaul]

Any idea how to prepare for Section-A?

[Mauli]

the essays?

[Ayushya Kaul]

Yes!

[Mauli]

i am just doing the topics given by them.
google!

[Target MA]

there is no essay this year..

[Ayushya Kaul]

How sure you about this mate?

[Ayushya Kaul]

Btw, any takers on the doubts?

[Nag27]

Q No. 6: Answer is option (D).

1) From (2a-6b)^8, first take out 2^8 so you get (a-3b)^8.
2) By the Pascal Triangle you get the 4th term's coefficient as 56.
3) b's exponent in the term will be 3, so 3^3 is also multiplied to the coefficient.

As a result, you will see that the coefficient is (2^8)*(3^3)*(56) which (with some arithmetic manipulation) is nothing but option (D)

[Nag27]

Q. No. 9: I am not sure about the following answer, if anyone is getting another answer then please share!

Equation in the question can be boiled down to this:
x^3 - x^2 - 2 = 0 (since we want to find out the root)
this is the same as x^2(x-1)=2
which means that x cannot be zero or one since that would violate the equation by making it 0=2

All the given options are closed intervals and the first three options include either zero or one. Hence the answer by elimination is Option (D).

[pbansal]

target ma-is there is no essay this year

[Ayushya Kaul]

Seems quite logical Nag.
(refering to Q9!)

[Sinistral]

f(x) = 2 + x^2  - x^3
f(x) is a continuous function
f(1) = 2 + 1 -1  = 2 > 0
f(2) = 2 + 4 -8 = -2 < 0

so f(x) will cross x axis at least once in between [1,2]
so at least one root in between [1,2]
option c

[Ayushya Kaul]

Thanks for clearing that up Sinistral!
Any idea on the rest?

[duck]

Hi Ayushya.. :)

Q4) X is a continuous random variable. And you're asked to find a probabilty of X at a point. Hence, it will be zero.

SectionB:
Q5) Maximise the total surplus minus cost.

Section A:
Q5) I think None of the above.
8 , 13, 5, 15, 20, 12:
Difference of 5,8,10,5,8 between the terms. So, next difference must be of 10. Hence, next term should be 32.

[rb.]

can some one please tell me what the expected cut off is? :(
its a request!please.