real numbers

Class 9 | Full Chapter | NCERT

Class 9 Chapter 1 | All Solutions | Number System

All Mathemafia YouTube videos of Class 9 chapter 1 (Number System) are embedded on this webpage. You can watch all these videos right here in the same order as they appear in the NCERT textbook. Number system is the base…

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Class 10 | Chapter 2 | Polynomials | Exercise 2.1

Question 1: The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case. Class 10 | Examples Class 10 | Exercise 2.2

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Class 10 | Chapter 2 | Polynomials | Exercise 2.3

Question 1: Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : (i) p(x) = x3 – 3×2 + 5x – 3, g(x) = x2 – 2 (ii) p(x) =…

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Class 10 | Chapter 2 | Polynomials | Exercise 2.2

Question 1: Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) x2 –2x–8 (ii) 4s2 –4s+1 (iii) 6×2 –3–7x (iv) 4u2 +8u (v) t2 –15 (vi) 3×2 –x–4 Question 2:…

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Class 10 | Chapter 2 | Polynomials | Examples

Example 1: Look at the graphs in Fig. 2.9 given below. Each is the graph of y = p(x), where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x). Example 2: Find the…

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Class 10 | Chapter 1 | Real Numbers | Exercise 1.4

Question 1: Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: Question 2: Write down the decimal expansions of those rational numbers in Question 1…

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Class 10 | Chapter 1 | Real Numbers | Exercise 1.2

Question 1: Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429 Question 2: Find the LCM and HCF of the following pairs of integers and verify that LCM ×…

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Class 10 | Chapter 1 | Real Numbers | Exercise 1.1

Question 1: Use Euclid’s division algorithm to find the HCF of :(i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Question 2: Show that any positive odd integer is of the form 6q+1, or 6q+3, or 6q+5,…

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