Selina Class 10 Maths Solution – Complete Guide to Important Topics and Questions

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Selina Class 10 Maths solutions are an essential part of learning for students preparing for their class 10 exams. It provides detailed explanations for a wide variety of mathematical problems and concepts, making it easier for students to understand the topics. This comprehensive guide will cover key areas of the syllabus and help students grasp difficult concepts effectively. The book is widely used by students and recommended by educators to boost their understanding of the subject. Here, we present a set of important questions and answers that will help students in their preparation.

Selina Class 10 Maths Solution: Topics Covered

Topic	Key Areas Explored
Real Numbers	Euclid’s division algorithm, Fundamental Theorem of Arithmetic
Polynomials	Zeroes of a polynomial, Factorization of polynomials
Pair of Linear Equations	Solving systems of equations by substitution and elimination method
Quadratic Equations	Solving by factorization and completing the square
Arithmetic Progression	Finding the nth term, Sum of n terms
Triangles	Similarity, Pythagoras Theorem, Areas of triangles
Coordinate Geometry	Distance formula, Section formula, Area of a triangle
Areas and Volumes	Surface area and volumes of solids like cone, sphere, cylinder
Statistics	Measures of central tendency, Probability
Probability	Probability of an event, Theoretical probability

Question and Answer Section

Question
What is the Euclid’s division algorithm?
Answer
Euclid’s division algorithm states that for any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. This method helps to find the greatest common divisor (GCD) of two numbers.

Question
What is the Fundamental Theorem of Arithmetic?
Answer
The Fundamental Theorem of Arithmetic states that every integer greater than 1 is either a prime number or can be factored uniquely as a product of prime numbers.

Question
How do you find the zeroes of a polynomial?
Answer
To find the zeroes of a polynomial, set the polynomial equal to zero and solve for the variable. For example, for the polynomial p(x) = x² - 5x + 6, set it equal to zero: x² - 5x + 6 = 0. Factor the equation: (x - 2)(x - 3) = 0. Thus, the zeroes are x = 2 and x = 3.

Question
What is the quadratic formula?
Answer
The quadratic formula is used to find the roots of a quadratic equation ax² + bx + c = 0. It is given by:x = (-b ± √(b² - 4ac)) / 2a.

Question
How do you solve a pair of linear equations by substitution?
Answer
To solve a pair of linear equations by substitution, solve one equation for one variable and then substitute that expression into the second equation. For example, if you have the system:
x + y = 10
x - y = 4
Solve the first equation for x: x = 10 - y. Then substitute into the second equation:
(10 - y) - y = 4, solving gives y = 3, and substituting into x = 10 - y gives x = 7.

Question
What is the sum of the first n terms of an arithmetic progression?
Answer
The sum of the first n terms of an arithmetic progression is given by the formula:

Sₙ = n/2 [2a + (n - 1)d],
where a is the first term and d is the common difference.

Question
What is the distance formula?
Answer
The distance formula is used to find the distance between two points (x₁, y₁) and (x₂, y₂) in a plane. It is given by:d = √[(x₂ - x₁)² + (y₂ - y₁)²].

Question
How do you find the area of a triangle using coordinates?
Answer
The area of a triangle with vertices at (x₁, y₁), (x₂, y₂), and (x₃, y₃) can be found using the formula:
Area = ½ | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |.

Question
What is the Pythagoras Theorem?
Answer
The Pythagoras Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, a² + b² = c², where c is the hypotenuse.

Question
What is the surface area of a cone?
Answer
The surface area of a cone is given by the formula:
Surface Area = πr(r + l),
where r is the radius of the base and l is the slant height.

Question
How do you find the volume of a cylinder?
Answer
The volume of a cylinder is given by the formula:
Volume = πr²h,
where r is the radius of the base and h is the height of the cylinder.

Question
What is a probability of an event?
Answer
The probability of an event is a measure of the likelihood of that event occurring. It is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.

Question
How do you calculate the mean of a data set?
Answer
The mean of a data set is calculated by adding all the values together and then dividing by the number of values. For example, for the data set 3, 5, 7, 9, the mean is (3 + 5 + 7 + 9) / 4 = 6.

Question
What is a frequency distribution table?
Answer
A frequency distribution table is a table that shows how often each different value in a set of data occurs. It lists the values and their corresponding frequencies.

Question
What is the difference between permutation and combination?
Answer
Permutation refers to the arrangement of objects in a specific order, while combination refers to the selection of objects without considering the order. The number of permutations is greater than the number of combinations for the same set of objects.

Question
What is the formula for the sum of the first n natural numbers?
Answer
The formula for the sum of the first n natural numbers is

 

Sum = n(n + 1) / 2.

Question
How do you calculate the area of a circle?
Answer
The area of a circle is calculated by the formula:
Area = πr²,
where r is the radius of the circle.

Question
What is the difference between mean and median?
Answer
The mean is the average of all data points, while the median is the middle value when the data is arranged in ascending or descending order. If the data has an even number of values, the median is the average of the two middle numbers.

Question
What is the volume of a sphere?
Answer
The volume of a sphere is given by the formula:
Volume = (4/3)πr³,
where r is the radius of the sphere.

Question
What is the formula for finding the total surface area of a sphere?
Answer
The total surface area of a sphere is given by:
Surface Area = 4πr²,
where r is the radius of the sphere.

Question
How do you solve a quadratic equation by factorization?
Answer
To solve a quadratic equation by factorization, express the quadratic equation in the form of (ax + b)(cx + d) = 0, and solve for x by setting each factor equal to zero. For example, for the equation x² - 5x + 6 = 0, factor it as (x - 2)(x - 3) = 0, so the roots are x = 2 and x = 3.

 

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