Q2)Find all integer solutions to the equation **x³+(x+4)²=y²**.

Q3)Two right angled triangles are such that the incircle of one triangle is equal in size to the circumcircle of the other. If P is the area of the first triangle and Q is the area of the second triangle, then show that P/Q≥3+2√2.

Q4) (a)Find the maximum value k for which one can choose k integers from 1,2,.....,2n so that none of the chosen integers is divisible by any other chosen integer.

(b) F(x) is a polynomial of degree 2016 such that all the coefficients are non negative and non exceed F(0).Show that the coefficient of x^2017 in (F(x))² is at most F(1)²/2.

Q5) (a) n>=3 and a1, a2, a3,....., an are different positive integers. Given that, except the first and the last, each one is a harmonic mean of its immediate neighbors. Show that none of the given integers is less than n-1. (b)Show that the shortest side of a cyclic quadrilateral with circumradius 1 is at most √2.

Q6)C1,C2,C3 are circles with radii 1,2,3 respectively, touching each other as shown in Figure. Two circles can be drawn touching all these circles. Find the radii of these two circles.

## Comments

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TopNewestI have some questions about NMTC, please care to answer:

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– Ayush Rai · 6 months ago

Well NMTC screening test is objective and NMTC final test is subjective.It is Olympiad MathematicsLog in to reply

– Naitik Sanghavi · 6 months ago

Done!BTW I am getting only two solutions for (Q2)!Am I correct?Log in to reply

You have not mentioned question 5 b – Ayush Rai · 6 months ago

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I have posted Junior Level Paper here. – Svatejas Shivakumar · 6 months ago

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For question 6, use Descartes' Theorem. – Akshat Sharda · 6 months ago

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@Svatejas Shivakumar@Harsh Shrivastava@Abhay Kumar@Nihar Mahajan@Alan Joel@easha manideep d@Adarsh Kumar @Swapnil Das@Mehul Arora@Dev Sharma@Akshat Sharda – Naitik Sanghavi · 6 months ago

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– Swapnil Das · 6 months ago

Thanks for mentioning. Do you want me post the solutions, or you were just kind enough to help me have a glimpse of the paper?Log in to reply

– Naitik Sanghavi · 6 months ago

As you wish! 😊Log in to reply