NCERT Exemplar Problems Solutions Class 10 Maths PDF form free download. Now board for class 10 is restored. From 2017 – 18 onward the complete syllabus will be asked in final exam by CBSE Board. NCERT Exemplar books are also available to download. These exemplar problems solutions are updated for the CBSE examination 2017 – 2018. Also download sample papers, assignments, test papers, Board Papers, notes, practice material and NCERT solutions for all subjects.
Chapter 1: Real Numbers
- Euclid’s Division Lemma: Given two positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.
- Euclid’s Division Algorithm to obtain the HCF of two positive integers, say c and d, c > d.
- Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product of primes, and this expression (factorisation) is unique, apart from the order in which the prime factors occur.
- Let p be a prime number. If p divides square of a, then p divides a, where a is a positive integer.
- Square root of 2, 3, 5 are irrational numbers.
- The sum or difference of a rational and an irrational number is irrational.
- The product or quotient of a non-zero rational number and an irrational number is irrational.
- For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
Chapter 2: Polynomials
- Geometrical meaning of zeroes of a polynomial: The zeroes of a polynomial p(x) are precisely the x-coordinates of the points where the graph of y = p(x) intersects the x-axis.
- Relation between the zeroes and coefficients of a polynomial: If α and β are the zeroes of a quadratic polynomial ax2 + bx + c, then α + β = -b/a and αβ = c/a.
- The division algorithm states that given any polynomial p(x) and any non-zero polynomial g( x), there are polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).
Chapter 3: Pair of Linear Equations in Two Variables
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progressions
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 8: Introduction to Trigonometry and its Applications
Chapter 9: Circles
Chapter 10: Constructions
Chapter 11: Area Related to Circles
Chapter 12: Surface Areas and Volumes
Chapter 13: Statistics and Probability