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This post was updated on .
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


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


Question 2 Why is it sufficient?


can u plz tell how to do ques no.29


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


This post was updated on .


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


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.


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


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?


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.


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.


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


13.System is homogenous.So either trivial soln(0,0,0,)exists or infinite soln exists.
So for nonzero 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* (a1)/(n1)
P(not red,red)=(na)/n * a/(n1)
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


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^2x +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).


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


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


I have displayed the solution of 21 in above post.


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


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

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