Organisation : Homi Bhabha Centre for Science Education
Exam : Madhava Mathematics Competition (MMC)
Document Type : Previous Question Paper
Year : 2022
Website : https://madhavacompetition.in/OldQuestionPapers.aspx
Madhava Mathematics Competition MMC Question Paper
The competition is named after Madhava, who introduced in the fourteenth century, profound mathematical ideas that are now part of Calculus.The “Madhava School”, consisting of a long chain of teachers-students continuity, flourished for well over two centuries, making significant contributions to mathematics and astronomy. The Madhava Mathematics Competition MMC Question Paper for the year 2022.
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Madhava Mathematics Competition MMC Question Paper
1. Let the sequence {xn} be defined as follows: x1 = 1 and xn is the smallest prime factor of n. Then the sequence {xn}
(a) is monotonic
(b) diverges to infinity
(c) has a convergent subsequence
(d) is not bounded below
Ans:(c)
2. The equation x6 − x − 1 = 0 has
(a) no positive real root
(b) exactly one positive real root
(c) exactly two positive real roots
(d) all roots are real and positive
Ans:(b)
3. The value of θ (0 ≤ θ ≤ π/2) for which the number 2 + 3i sin θ 1 − 2i sin θ is purely imaginary is
(a) π/6
(b) π/3
(c) sin−1(√3/4)
(d) sin−1(1/√3)
Ans:(d)
4. Consider the curve y = 2×4 + 7×3 + 3x − 5. Let Pi = (xi, yi) be four distinct points of intersection of a line with the given curve. Then the value of x1 + x2 + x3 + x44 is
(a) −7/8
(b) −7/2
(c) 7/8
(d) 7/2
Ans:(a)
5. If one root of the equation x2 + px + 12 = 0 is 4 while the equation x2 + px + q = 0 has equal roots, the value of q is
(a) 4/49
(b) 49/4
(c) −49/4
(d) −4/49
Ans:(b)
6. Which of the following equations has greatest number of real solutions?
(a) x3 = 10 − x
(b) x2 + 5x − 7 = x + 8
(c) 7x + 5 = 1 − 3x
(d) ex = x
Ans:(b)
7. Let gcd(a, b) = 1, then gcd(a + b, a2 − ab + b2) =
(a) 2
(b) 1 or 2
(c) 1 or 3
(d) 2 or 3
Ans:(c)
8. Suppose f is continuous in [0, 2] and differentiable in (0, 2). If f (0) = 0 and |f ′(x)| ≤ 1/2 for all x ∈ [0, 2], then
(a) |f (x)| ≤ 1
(b) |f (x)| ≤ 1/2
(c) f (x) = 2x
(d) f (x) = 3 for at least one x [0, 2].
Ans:(a)
9. Let A = {a, b, c, d} and B = {1, 2, 3}. The number of functions from A to B such that exactly one element in B has two pre-images is
(a) 12
(b) 18
(c) 24
(d) 36
Ans:(d)
10. Consider a square matrix A = [aij ] of order 3, all whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. Also aij = aji for all 1 ≤ i, j ≤ 3. Then the number of such matrices is
(a) 12
(b) 9
(c) 3
(d) 1
Ans:(a)
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