DSE 2015 answer

[Mike]

Sir, can you help us in 57 and 58?

[maecon]

we will discuss mike this evening

[Ansh malhotra]

[Mike]

MC1 = q
MC2= 2q
Now if you take the horizontal summation of the quantities, q = MC .....(1)
                   q= MC/2 ......(2)
Adding 1 and 2 we get q= 3MC/2
So MC = 2q/3
Comparing the three MC's, we see that the MC is lowest in the third case. So answer is (b)

[Ansh malhotra]

 please help

[Ansh malhotra]

[maecon]

ansh the mean of this uniform distribution is not dependent on the length of interval , one intutive reason is that mean is like the point of center of mass  so if there is uniform distribution then center of mass just lies at the mid point

and variance is just how much is the spread around the mean so if you increase the interval that does mean that points will be more distant from mean so we have a larger variance and standard deviation.

[maecon]

sorry mike my sem exams are still going, please let us start with 54 and will go to 59 .


also mike for 57 i am getting b as an option but the answer is a .:(

so according to question the income Y(t) is distributed equally among labor and capital

by solow model at steady state the k(t){ K(t)/L(t) } will not change , thus writing the equation :


                              k(t)*n = s(w)*y(t)/2 + s(r)*y(t)/2


                               
                               

                                       

[Mike]

And, for question 8, dimension of solution space  is same as dimension of null space or nullity. Don't confuse it with the rank.

[Ansh malhotra]

[maecon]

ansh if you look carefully then you see that when f'x = 0 then f''x is positive = 1 , now we know that if f''x is positive then fx is convex ,,, you can guess now .

[Ansh malhotra]

Thank you so much maecon

[Ansh malhotra]

[Mike]

For that vector question ansh,
* Linear independence implies affine independence and not the other way round.
* If vectors v1, v2, v3,........, vn are affinely independence, than the set of vectors
  (v2-v1), (v3-v1),............,(vn-v1) are linearly independent.
 So option (a) is ruled out. Option (b) is correct.
 About that third option n<=m. Take the simple case of a vector in 2D. A vector "v not equal to zero" in 2D
is linearly independent. But if we take three vectors in 2D than they are linearly dependent. That's why n<=m for linear independence.

[Ansh malhotra]

Thank you mike. I have answer which I downloaded from answer from dse site their the answer is d to question 9 but I also think it is b.

[Ansh malhotra]

You answered my question 8 query can you please explain null space or nullity

[Ansh malhotra]

[Ansh malhotra]

[Mike]

ansh, for question 9, answer is (d)
read carefully what i have written. I said that linear independence implies affine independence and not the other way round. Also n<=m

[Mike]

I request you ansh to kindly write the question number only . It takes time to upload the image.