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.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

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

Log in to reply

Well NMTC screening test is objective and NMTC final test is subjective.It is Olympiad Mathematics

Log in to reply

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

Log in to reply

You have not mentioned question 5 b

Log in to reply

I have posted Junior Level Paper here.

Log in to reply

For question 6, use Descartes' Theorem.

Log in to reply

@Svatejas Shivakumar@Harsh Shrivastava@Abhay Kumar@Nihar Mahajan@Alan Joel@easha manideep d@Adarsh Kumar @Swapnil Das@Mehul Arora@Dev Sharma@Akshat Sharda

Log in to reply

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

As you wish! 😊

Log in to reply