Organisation : Bhaskaracharya Pratishthana & Homi Bhabha Centre for Science Education
Exam Name : Madhava Mathematics Competition (MMC)
Applicable For : Undergraduate Students
Download : Specimen Question Paper
Year : 2024
Website : https://madhavacompetition.in/OldQuestionPapers.aspx
What is Madhava Mathematics Competition?
Madhava Mathematics Competition is a Mathematics Competition for Undergraduate Students, Organized by Bhaskaracharya Pratishthana, Pune Funded by National Board for Higher Mathematics. The competition is basically meant for the S. Y. B. Sc. / S. Y. B. Sc. (Computer Science) students with Mathematics as one of the subjects and thus the question paper will be set with the background of these students in mind.The selection of the students for participation in the International Mathematics Competition (IMC), 2025 will be made on the basis of the performance of the students in the Madhava Mathematics Competition.
How To Download Madhava Mathematics Competition Question Paper?
Last 5 years speciman papers and solutions are available in the link given above. Click on the link to download the Previous Question Papers (Old Question Paper) of Madhava Mathematics Competition
Sample Questions 2024:
Part I:
1. Let S be the set of all last two digits of the powers of 3. (For example, 03, 09, 27, 81, 43 S) Then, the number of distinct elements of S is
(A) 20
(B) 25
(C) 30
(D) 40.
2. Find the value of a real number b for which the sum of the squares of the zeros of x2 − (b − 2)x − b − 1 is minimal.
(A) 2
(B) 3
(C) −5
(D) 1.
3.The sum of the roots of x2 − 31x + 220 = 2x(31 − 2x − 2x) is
(A) 10
(B) 7
(C) 3
(D) 4.
4.Let A(0, 0), B(0, 23), C(23, 0) be the points in the plane. The number of points with integral coordinates that lie inside the triangle ABC (not on the boundary) is
(A) 253
(B) 242
(C) 231
(D) 219
Part II:
Consider a right angled triangle P RQ with coordinates of the vertices integers. If slope and length of the hypotenuse P Q are integers, then show that P Q is parallel to the X-axis.
Part III:
1. Let Z10 denote the set of integers modulo 10.
(a) i. Find a nonzero solution to the following system of equations in Z10 : [2]
4x + 6y = 0
2x + 4y = 0
ii. Find a nonzero solution to the following system of equations in Z10 : [2]
4x + 3y = 0
x + 2y = 0
(b) Prove that the system of equations
ax + by = 0
cx + dy = 0
has a unique solution x = 0, y = 0 in Z10 if and only if the number
(ad − bc) (mod 10) ∈ {1, 3, 7, 9}.
2. Let f (x) = a0 + a1x + a2x2 + a10x10 + a11x11 + a12x12 + a13x13 and g(x) = b0 + b1x + b2x2 + b3x3 + b11x11 + b12x12 + b13x13 be polynomials with real coefficients such that a13̸ = 0, b3̸ = 0. Prove that the degree of gcd(f, g) ≤ 6. [12
3.Let n be a positive integer greater than 1. Let ρ(n) be the smallest possible rank of an n × n matrix that has zeros along the main diagonal and strictly positive real numbers off the main diagonal.
(a) Find ρ(2) and ρ(3). [4]
(b) Find ρ(4). [3]
(c) Find ρ(n) for each n. [6]
Download Madhava Mathematics Competition
Download Specimen Question Paper of Madhava Mathematics Competition 2024 here
Download Here : https://www.pdfquestion.in/uploads/pdf2024/43060-Paper.pdf