ISI Sample Paper PEA 2016 Discussion

[Dr. Strange]

   I found these choices to be true. Please let me know if mistakes are present.

Updated with Sir's answer key.
1. c
2. b
3. d
4. a
5. c
6. d
7. d
8. b
9. a
10. a
11. d
12. b
13. a
14. Question not correct
15. c
16. d
17. c
18. b
19. c
20. c
21. d
22. a
23. b
24. a
25. c
26. d
27. a
28. a
29. a
30. c

[sasdthds]

how di u got q. 16 answer as d)
plzz explain

[samuraijack]

Question 2 Why is it sufficient?

[varnika1880]

can u plz tell how to do ques no.29

[samuraijack]

@varnika

take f(x,y) = x^2-y^2 and solve

[Dreyfus]

[varnika1880]

thnx but my query is in the second eq of the question x,y{r2) . but the fn goes from r2to r1..won't this fact be considered while solving

[Dr. Strange]

Are you implying this because of the equality sign present?
Since it is mentioned that function is twice differentiable I have doubt whether this means higher derivatives don't exist or are equal to 0. In second case second derivative must be nonzero where first derivative is 0 and it will be necessary and sufficient condition.However if third or higher derivatives exist then it will only be a necessary condition as the point can be inflection point. My doubt lies on meaning of twice differentiable.

[samuraijack]

Yes, I think twice differentiable can be there to distinguish it from a straight line y=c; so we should consider inflection points too.

[Dr. Strange]

So what is your opinion: can we call y=x^3 a twice as well as a thrice differentiable function or shall we call it only a thrice differentiable function?

[samuraijack]

x^3 is both twice and thrice differentiable, we're only given it's a twice differentiable fuction nothing about possibilities of higher order derivatives, it may or may not exist. But again I am not sure.

[Dr. Strange]

However I think you are right. Since it is not mentioned about higher derivatives I can't take it for granted. Changing my option  and making it only a necessary condition.

[Tania123]

@Dr Strange
Can you explain Q13,14,21,26.

[Dr. Strange]

13.System is homogenous.So either trivial soln(0,0,0,)exists or infinite soln exists.
So for non-zero soln to exist determinant should be 0.
Making determinant zero we get the soln.

21.four cases are possible: (red,not red),(red,red),(not red,red),(not red,not red)
P(red,red)=a/n* (a-1)/(n-1)
P(not red,red)=(n-a)/n * a/(n-1)
p(second ball is red)=P(red,red)+P(not red,red)= a/n

26.given constraint x=y
put x=y in target equation and optimise

[Dr. Strange]

14.Since cumulative distribution function attains value 1 at x=infinity so it is only possible if a=0 and b=1
    F(x)= 1 for x>=0
          =x^2-x +1 for x<0
  Since x is defined for [0,1] so second part becomes redundant.
so the distribution is discrete having p(x)=1 at x=0 and p(x)=0 elsewhere
problem is  question mentions that 'a' belongs to (0,1) so a=0 is not a viable solution.I am stuck in here.
If ' a ' is considered to be 0 then F becomes continuous in (0,1).

[varnika1880]

I read it in a book which says it's both a sufficient and necessary condition

[varnika1880]

Can u please tell how u r getting d as an ans for 21

[Dr. Strange]

I have displayed the solution of 21 in above post.

[varnika1880]

If we sum up the two value over two intervals and equate it to one ...and then in that eq replacing X by a ...we will get a=1 but 1 Doesn't belong to the given interval...so it might be the case that it's not continuous at a

[Dr. Strange]

a can't be 1 because in that case in interval [0,1/2] F(x) is decreasing which is not possible.