CBSE Guess > Papers > Important Questions > Class X > 2008 > Maths > Mathematics By :- Mr. P. A. Bony Mathematics Q. 1. Let us think about the sequence of natural numbers. It starts from 1 and continue as 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 …. First we make these numbers as the groups of 2 as (1,2) (3,4) (5,6) (7,8) ( 9,10) (11,12)….The group sum is 3,7,11,15,19,23…. The group sum form an A P clearly. Its common difference is 22 .If we make the group by three we get common difference 32 .Continue this process by 4,5,6… . We get c d 42 , 52…. (tenth standard students of H I B H S Varapuzha completes this as their mathematics project 2008) Q. 2. The interior angles of a polygon form an A P. The smallest angle is 120 degree. Common difference 5.
Q. 3. The sum of the first n terms of an A P and the sum of the next n terms of the same A P is differ by n2d PROVE! Q. 4. Prove that the sum of ( m + n) th term and (m─ n) th term is twice m th term Q. 5. Can the base altitude and hypotenuse of a right triangle form an A P ? If possible find an example Q. 6. Appu put 1 rupee in the first day , 2 rupee in the second day 3 rupee in the third day, 4 rupee in the fourth day and so on in his money box.. After some days he decided to save 1 rupee less in the subsequent days. In the last day he put 1 rupee. The total amount in the box is in between 900 and 1000. Calculate total amount and days he continue this process. Q. 7. Look at the pattern given below
Q. 8. Look at the pattern
Q. 9. Appu put 1 rupee in the first day,2 rupee in the second day, 3 rupee in the third day and so on . After some days he decided to put one rupee less in the subsequent days. At last he put 1 rupee . He opened the box and found the amount which was in between 900 and 1000.
Q. 10. Prove that the sum of the first n terms and the sum of the next n terms of an A P is differ by n2 d where d is the common difference Q. 11. x,y,z are in A P. Also x ─ y = k( z ─ x) find the value of k
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