Explore chapter-wise NCERT solutions for Class 9 Maths in PDF format. Below, you'll find detailed answers to common questions, making learning easier and more effective. These solutions are structured to provide step-by-step explanations, ensuring a better understanding of mathematical concepts.
Chapter-Wise Sample Questions and Answers
Chapter 1: Number Systems
Q: What is an irrational number?
A: An irrational number is a number that cannot be expressed as a simple fraction. It has non-repeating, non-terminating decimal expansions, such as √2 or π.
Q: How do you represent √3 on a number line?
A: To represent √3 on a number line, construct a right-angled triangle with legs of 1 and 2 units. The hypotenuse will be √3. Using a compass, mark this length on the number line.
Chapter 2: Polynomials
Q: What is the degree of the polynomial 3x⁵ + 4x³ + 2x + 7?
A: The degree of a polynomial is the highest power of the variable. Here, the highest exponent is 5, so the degree is 5.
Q: What is the remainder when x³ + 3x² - x + 5 is divided by x - 1?
A: Using the remainder theorem, substitute x = 1 in the polynomial:1³ + 3(1²) - 1 + 5 = 1 + 3 - 1 + 5 = 8.
So, the remainder is 8.
Chapter 3: Coordinate Geometry
Q: What is the distance between the points (3,4) and (6,8)?
A: The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
√[(x₂ - x₁)² + (y₂ - y₁)²].
Here, the distance is √[(6 - 3)² + (8 - 4)²] = √[9 + 16] = √25 = 5 units.
Q: What is the x-coordinate of a point on the y-axis?
A: The x-coordinate of any point on the y-axis is always 0.
Chapter 4: Linear Equations in Two Variables
Q: How many solutions does a linear equation in two variables have?
A: A linear equation in two variables has infinitely many solutions since it represents a straight line on a graph.
Q: Find the value of k if the equation 2x + ky = 8 passes through the point (1,2).
A: Substituting x = 1 and y = 2 in the equation:
2(1) + k(2) = 8
2 + 2k = 8
2k = 6
k = 3
Chapter 5: Introduction to Euclid’s Geometry
Q: State Euclid’s first postulate.
A: Euclid’s first postulate states that a straight line may be drawn from any one point to any other point.
Q: What is a theorem?
A: A theorem is a mathematical statement that can be proven based on previously established statements, such as axioms and postulates.
Chapter 6: Lines and Angles
Q: What is the sum of the angles in a linear pair?
A: The sum of the angles in a linear pair is always 180°.
Q: If two parallel lines are cut by a transversal, what can you say about the alternate interior angles?
A: Alternate interior angles are equal when two parallel lines are cut by a transversal.
Chapter 7: Triangles
Q: State the Pythagoras theorem.
A: The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Q: What is the condition for two triangles to be congruent by the SAS criterion?
A: Two triangles are congruent by the SAS criterion if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
Chapter 8: Quadrilaterals
Q: What is the sum of the interior angles of a quadrilateral?
A: The sum of the interior angles of a quadrilateral is always 360°.
Q: Define a parallelogram.
A: A parallelogram is a quadrilateral in which opposite sides are equal and parallel.
Chapter 9: Circles
Q: What is the radius of a circle?
A: The radius of a circle is the distance from the center of the circle to any point on its circumference.
Q: What is the relationship between the diameter and the radius of a circle?
A: The diameter of a circle is twice its radius.
Chapter 10: Heron’s Formula
Q: What is Heron’s formula for the area of a triangle?
A: Heron’s formula states that the area of a triangle with sides a, b, and c is given by:
Area = √[s(s-a)(s-b)(s-c)], where s = (a + b + c)/2.
Q: Can Heron’s formula be used for right-angled triangles?
A: Yes, Heron’s formula can be applied to right-angled triangles, but using ½ × base × height is usually simpler.
Chapter 11: Surface Areas and Volumes
Q: What is the formula for the volume of a cylinder?
A: The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height.
Q: What is the total surface area of a sphere with radius r?
A: The total surface area of a sphere is 4πr².
Chapter 12: Statistics
Q: What is the mean of the numbers 2, 4, 6, 8, and 10?
A: The mean is the sum of all values divided by the number of values:
(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.
Q: What is the mode of the data set 3, 5, 3, 7, 3, 8, 5?
A: The mode is the number that appears most frequently, which is 3.
Chapter 13: Probability
Q: What is the probability of getting a head when tossing a fair coin?
A: The probability of getting a head is 1/2, as there are two equally likely outcomes: head or tail.
Q: If a bag contains 5 red balls and 3 blue balls, what is the probability of drawing a red ball?
A: The probability is the number of red balls divided by the total number of balls:
5/(5+3) = 5/8.
These NCERT solutions for Class 9 Maths are designed to help students understand concepts clearly and solve problems effectively. Download the PDF now for complete chapter-wise solutions.
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