If the sum of first m terms of an A.P. is some as
Question 5: If the sum of first m terms of an A.P. is some as the sum of its first n terms, show that the sum of its first (m + n) terms is zero. … Read more
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The digits of a positive number of three digits are in A.P.
Question 4: The digits of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. Solution: Let the required three digits in A.P. of three digit number = (a – d), a, (a + … Read more
If the sum of the first 6 terms of an A.P. is 36
Question 3: If the sum of the first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of the first 10 terms. [CBSE 2016, 13, 12] Solution: Let the first term of A.P. = and Common difference = d Given, ——(i) Again, ——(ii) … Read more
The first term of an A.P. is -5 and the last term is 45
Question 2: The first term of an A.P. is -5 and the last term is 45. If the sum of the terms of the A.P. is 120, then find the number of terms and the common difference. [CBSE 2019, 17, … Read more
Vector Space and properties of Vector space
Vector Space Defnition: Let (F, +, .) be a field. The element of F will be called scalars. Let V be a non-empty set whose elements will be called Vectors. Then V is vector space over the field. If 1. There is defined an internal composition in V called addition of vectors and denoted by … Read more
Ramkali would require Rs 5000 for getting her daughter
Question 1: Ramkali would require Rs 5000 for getting her daughter admitted in a school after a year. She saved Rs 150 in the first month and increased her monthly by Rs 50 every month. Find, if she will be able to arrange the required money after 12 months. Which value is reflected in her … Read more
Class 10 case study Chapter 11 Area related to circle 2
Class 10 Chapter 11(Area related to circle) The south central zone of Indian Railways has commissioned the longest electrified railway tunnel in the country. According to local media reports, the construction of the 6.6 km long tunnel took 43 months to complete. The electrified railway tunnel is situated between Chelopalli and Rapuru station as a … Read more
Class 10 case study chapter 11 Area related to circle
Chapter 11: Area Related to Circle We all love to eat pizzas, especially kids. And a variety of pizzas are available in India which have been modified according to Indian taste and menu. From the Greeks to the Egyptians, from the persians to the Indians, there have been incarnations of pizza served throughout history. Flatebreads, … Read more
In a flight of 600 km an aircraft was slowed due to
Question 5: In a flight of 600 km an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200km/hr and time of flight increased by 30 minutes. Find the original duration of flight. [CBSE 2020] Solution : Let the actual speed of flight = ‘x’ km/h … Read more
A train travels 360 km at a uniform speed If the speed
Question 6: A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hours less for the same journey. Find the speed of the train. … Read more