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I.S.I. and C.M.I. Entrance

I.S.I. B.Stat and B.Math Entrance 2019 (UG) Solutions, Hints, and Answer Key

Indian Statistical Institute B.Stat, B.Math Entrance 2019 (UG Answer Key, Sequential Hints and more)

This is a work in progress. Please suggest improvements in the comment section.

Problems

Objective Section (Answer Key)

 

1. A2. A3. C4. A5. C6. B
7. C

8. C – Try

9. C10. B11. A12. D
13. C14. C15. D16. C17. B18. B
19. B20. B21. A22. A23. B24. B
25. C26. B27. B28. B29. B30. B

 

Subjective Section (Sequential Hints)

Faculty Team (for this section)

Ashani Dasgupta

Founder – Faculty at Cheenta.

Pursuing Ph.D. at University of Wisconsin, Milwaukee. USA

Research Interest: Geometric Group Theory

Srijit Mukherjee

Faculty – Admin at Cheenta

Pursuing B.Stat at Indian Statistical Institute, India

Writabrata Bhattacharya

Faculty at Cheenta

Pursuing B.Sc. Math at Chennai Mathematical Institute, India

Research Interest – Algebraic Geometry

Ishan Sengupta

Associate Faculty at Cheenta

Pursuing B.Stat from Indian Statistical Institute, India

By Dr. Ashani Dasgupta

Ph.D. in Mathematics, University of Wisconsin, Milwaukee, United States.

Research Interest: Geometric Group Theory, Relatively Hyperbolic Groups.

Founder, Cheenta

37 replies on “I.S.I. B.Stat and B.Math Entrance 2019 (UG) Solutions, Hints, and Answer Key”

In the third question the area of the resultant polygon is 2/3rd of the area of the triangle
Area = 2/3 x 9√3/2
= 3√3
The answer is option d

16th Question the right answer should be 33 , it’s not such an easy case of PHP as it seems like, for that we have to calculate
Number of Student who visited 5 days- 5C5=1
Number of Student who visited 4 days- 5C4=5
Number of Student who visited 3 days- 5C3=10
Number of Student who visited 2 days- 5C2=10
Number of Student who visited 1 day – 5C1=5
Number of Student who visited 0 day – 5C0=1
Total 32 cases, now applying Pigeon Hole Principle we need 33 students

For objective #16, if we represent the days visited as a YES/NO tuple of (a1,a2,…,a5), then for each student, 2^5=32 such tuples are possible. So, there are 32 boxes and so the minimum number of students needed to guarantee the condition (in question) has to be 33. So answer should be (C)33.

18’s correct option should be A.Let’s assume we sent two children together, one children alone and both adults separately then we found that the boat has to cross the river 9 times

In ques. 19, for adults it would be 4 times(2 for each) and for 2 children 2 times and as it is written no adult so ‘max’… So for last 1 children, 2 times so total 4+2+2=8.. Sir please tell options are true.

they have told m are integer’s’ and n is not equal to zero which includes all real numbers
they haven’t specifically said that values n are also are integers

I hope that works out. However, usually, when mathematicians say integers m and n not 0, they usually mean both m and n are integers and n is not 0. Anyway, maybe your answer is correct. We have posted unofficial options.

for the 11th march to 15th march question,why should we consider not swimming on any dates as a possibility ?The empty set should not be considered,since we are asked to figure out whether they ‘swim’ on the same dates.Not swimming at all shouldn’t be an option.

I gave ISI BMath 2019 and scored 93 in UGA, And in UGB I attempted total 6 questions,3 questions correctly with 2 being partially answered and one being fully wrong, I am OBC too, Will I be called for the interview?

but the one i did wrong was the first question…. is it something dangerous…. i mean about the impression to the checker?

HOW DID YOU GET THE SOLUTION FOR Q.26 ?

I COULD NOT FIND ANY SOLUTION SO I THINK ANSWER WILL BE 0 i.e (A).

IF YOU GET 1 SOLUTION STISFYING THE CONDITION THEN FOR WHAT VALUE OF n IS IT FOR?

sir #16 will be (b) 1
as the slope of e^x is always > any polynomial function.it only cut once in the 2nd quadrant.

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