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Class 10 Video Tutorials
Arithmetic Progression : Exercise 5.1
Write first four terms of the AP, when the first term 'a' and the common difference 'd' are given as follows:
(i) a = 10, d = 10
Write first four terms of the AP, when the first term 'a' and the common difference 'd' are given as follows:
(ii) a = -2, d = 0
Write first four terms of the AP, when the first term 'a' and the common difference 'd' are given as follows:
(iv) a = -1, d = 1/2
Real Numbers : Exercise 1.1
Use Euclid's division algorithm to find the HCF of 135 and 225.
Use Euclid's division algorithm to find the HCF of 196 and 38220
Use Euclid's division algorithm to find the HCF of 867 and 255.
Show that any positive odd integer is of the form 6q+1, or 6q+3, or 6q+5, where q is some integer.
An army contingent of 616 members is to march behind an army of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum numbers of columns in which they can march
Use Euclid's division lemma to show that square of any positive integer is either of the form 3m or 3m + 1 for some integer m
Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m, 9m+1 or 9m+8
Real Numbers : Exercise 1.2
Express each number as a product of its prime factors:
(i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
Find the LCM and HCF of the following pairs of integers and verify the LCM X HCF = Product of two numbers:
(i) 26 and 91
Find the LCM and HCF of the following pairs of integers and verify the LCM X HCF = Product of two numbers:
(ii) 510 and 92
Find the LCM and HCF of the following pairs of integers and verify the LCM X HCF = Product of two numbers:
(iii) 336 and 54
Find the LCM and HCF of 12, 15 and 21 by applying prime factorization method
Find the LCM and HCF of 17, 23 and 29 by applying prime factorization method
Find the LCM and HCF of 8, 9, 25 by prime factorization method
Given that the HCF (306, 657) = 9, find LCM (306, 657)
Check Whether 6^n can end with the digit 0 for any natural number n
Explain why 7 X 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite number
There is a circular path around sports field. Sonia takes 18 minutes to drive one round of the field while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in same direction. After how many minutes
Real Numbers : Exercise 1.3
Prove that under root 5 is irrational
Prove that 3 + 2 under root 5 is irrational
Prove that 1 / under root 2 is irrational
Prove that 7 under root 5 is irrational
Prove that 6 + under root 2 is irrational
Prove that 6 + under root 2 is irrational
Real Numbers : Exercise 1.4
Without actually performing the long division, state whether 13 / 3125 will have terminating decimal or non terminating decimal expansion.
Without actually performing the long division, state whether 17 / 8 will have terminating decimal or non terminating decimal expansion.
Without actually performing the long division, state whether 64 / 455 will have terminating decimal or non terminating decimal expansion.
Without actually performing the long division, state whether 15 / 1600 will have terminating decimal or non terminating decimal expansion.
Without actually performing the long division, state whether 23 / 2^3 5^2 will have terminating decimal or non terminating decimal expansion.
Without actually performing the long division, state whether 29 / 343 will have terminating decimal or non terminating decimal expansion.
Without actually performing the long division, state whether 129 / 2^2 5^7 7^5 will have terminating decimal or non terminating decimal expansion.
Without actually performing the long division, state whether 6 / 15 will have terminating decimal or non terminating decimal expansion.
Without actually performing the long division, state whether 35 / 50 will have terminating decimal or non terminating decimal expansion.
Without actually performing the long division, state whether 77 / 210 will have terminating decimal or non terminating decimal expansion.
The following real numbers have decimal expansions as given below. In each case decide whether they are rational or not. If they are rational and of the form p/q, what can you say about the prime factors of q?
(i) 43.123456789 (ii) 0.1201200
The following real numbers have decimal expansions as given below. In each case decide whether they are rational or not. If they are rational and of the form p/q, what can you say about the prime factors of q?
(i) 43.123456789
(ii) 0.120120012000120000
(iii) 43.123456789
Polynomials : Exercise 2.2
Find the zeroes of the quadratic polynomials ( x^2 - 2x - 8) and verify the relationship between the zeroes and the coefficients
Find the zeroes of the quadratic polynomials (4s^2 - 4s + 1) and verify the relationship between the zeroes and the coefficients
Find the zeroes of the quadratic polynomials (6x^2 - 3 - 7x) and verify the relationship between the zeroes and the coefficients
Find the zeroes of the quadratic polynomials (4u^2 + 8u) and verify the relationship between the zeroes and the coefficients
Find the zeroes of the quadratic polynomials (t^2 - 15) and verify the relationship between the zeroes and the coefficients
Find the zeroes of the quadratic polynomials (3x^2 - x - 4) and verify the relationship between the zeroes and the coefficients
Find a quadratic polynomial each with the given numbers (1/4, -1) as the sum and product of zeroes respectively.
Find a quadratic polynomial each with the given numbers (square root 2, 1/3) as the sum and product of zeroes respectively.
Find a quadratic polynomial each with the given numbers (0, square root 5) as the sum and product of zeroes respectively.
Find a quadratic polynomial each with the given numbers (1, 1) as the sum and product of zeroes respectively.
Find a quadratic polynomial each with the given numbers (-1/4, 1/4) as the sum and product of zeroes respectively.
Find a quadratic polynomial each with the given numbers (4, 1) as the sum and product of zeroes respectively.
Polynomials : Exercise 2.3
Q 1: (i) Divide the polynomial (x^3 - 3x^2 + 5x - 3) by the polynomial (x^2 - 2) and find the quotient and remainder
Q 1: (ii) Divide the polynomial (x^4 - 3x^2 + 4x + 5) by the polynomial (x^2 + 1 - x) and find the quotient and remainder
Q 1: (iii) Divide the polynomial (x^4 - 5x + 6) by the polynomial (2 - x^2) and find the quotient and remainder
Q 2: (i) Check whether the first polynomial (t^2 - 3) is a factor of second polynomial (2t^4 + 3t^3 - 2t^2 - 9t - 12) by dividing second polynomial by the first polynomial.
Q 2: (ii) Check whether the first polynomial (x^2 + 3x + 1) is a factor of second polynomial (3x^4 + 5x^3 - 7x^2 + 2x +2) by dividing second polynomial by the first polynomial.
Q 2: (iii) Check whether the first polynomial (x^3 - 3x + 1) is a factor of second polynomial (x^5 - 4x^3 + x^2 + 3x +1) by dividing second polynomial by the first polynomial.
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