### This are NCERT Chapter Wise Previous  Years Questions Asked in Board Exam

1.Show that any positive odd integer is of the form 6q+ 1 or 6q + 3 or 6q + 5, where q in integer.

#### [ CBSE 2012,11,10]

2.An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

#### [ CBSE 2012,11,10]

3.Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1, for some integer m.

#### [CBSE 2012,11,10]

4.Use Euclid's division lemma to show that the cube of any positive integer is either of the form 9m or 9m + 1or 9m + 8.

#### [CBSE 2015,12,11,10]

5.Check whether     $6^{n}$    can end with the digit 0 for any natural number n.

#### [CBSE 2012,11,10]

6.Explain, why (7 x 11x 13) + 13 and (7x6x 5 x 4 x 3x 2x 1) + 5 are composite numbers?

#### [CBSE 2012,14,15]

7.Prove that    $\sqrt{5}$ is an irrational number.

Extra

### This are Extra Questions Which  are Asked Board Exam

8.There are 156, 208 and 260 students in groups A, B And C, respectively. Buses are to be hired to take them for a field trip. Find the minimum number of buses to be hired, if the same number of students should be accommodated in each bus.                                                                  [CBSE 2012]

9.Find the HCF of 180, 252 and 324 by using Euclid's division lemma.                  [CBSE 2016,12,10]

10.Write the HCF of the smallest composite number and the smallest prime number.
[CBSE 2008]

11.If HCF (253, 440) = 11 and LCM (253, 440) = 253 x R.Find the value of R .        [CBSE 2012, 11]

12.$\sqrt{2}$ is irrational.                                                                                                    [CBSE 2010,09,08]

13.Find the greatest number which on dividing 1657 and 2037 leaves remainders  6 and 5, respectively.                                                                                                                    [CBSE 2010,08]