Subjective tests are a type of assessment that requires students to provide detailed and descriptive answers to questions. These tests aim to evaluate the student's understanding, critical thinking skills, and ability to communicate effectively. Here is a chapter-wise breakdown of subjective tests for Mathematics (Maths) Class 10:

Chapter 1: Real Numbers
1. Discuss the properties and applications of irrational numbers.
2. Prove that √2 is an irrational number.
3. Explain the Euclidean division algorithm and its significance.
4. Solve the following problems using the Euclidean division algorithm:
a) Find the HCF of 56 and 72.
b) Determine the LCM of 15 and 20.

Chapter 2: Polynomials
1. Define a polynomial and its various terms.
2. Explain the division algorithm for polynomials.
3. Solve the following problems:
a) Divide x^3 + 3x^2 - 5x - 7 by x + 2.
b) Find the remainder when x^4 + x^3 - 3x^2 + 2x + 1 is divided by x + 1.

Chapter 3: Pair of Linear Equations in Two Variables
1. Solve the following system of equations:
a) 2x + 3y = 7
4x - 2y = 10
b) 3(x - 1) + 2(y + 3) = 5
2(x + 1) - 5(y - 2) = -11
2. Discuss the graphical representation and interpretation of simultaneous linear equations.

Chapter 4: Quadratic Equations
1. Solve the quadratic equations using the quadratic formula:
a) x^2 - 3x + 2 = 0
b) 4x^2 + 4x + 1 = 0
2. Discuss the nature of the roots of a quadratic equation based on the discriminant.

Chapter 5: Arithmetic Progressions
1. Define an arithmetic progression (AP) and its common difference.
2. Find the sum of the first 30 terms of an AP if the first term is 2 and the common difference is 3.
3. Prove that the sum of n terms of an AP is given by Sn = (n/2)(2a + (n-1)d), where a is the first term and d is the common difference.

Chapter 6: Triangles
1. Prove the Pythagorean theorem.
2. Discuss the properties of similar triangles and their applications.
3. Solve the following problems:
a) In ΔABC, ∠A = 40°, ∠B = 60°. If AB = 5 cm, find BC and AC.
b) In ΔPQR, ∠P = 90°, PR = 12 cm, and QR = 5 cm. Find PQ.

Chapter 7: Coordinate Geometry
1. Find the distance between two points in a coordinate plane.
2. Prove that the points A(2, 3), B(6, 7), C(10, 11), and D(14, 15) form a parallelogram.
3. Determine the coordinates of the point which divides the line segment joining two given points in a given ratio.

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