NCERT Exemplar Problems Class 10 Maths

NCERT Exemplar Problems Class 10 Maths is given below to download in PDF form free. All the solutions are being updated for new academic session 2024-25. NCERT Exemplar Problems solutions for class 10 Maths will be available till May, 2020. Exemplar Books are given below to free download.

Euclid’s Division Lemma: Given two positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 is less than or equal to r is less than 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.

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) is less than degree g(x).

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