## Problems on Divisibility

1. Determine the following numbers which are divisible by 2, using the test of divisibility by 2:

(i) 176, (ii) 221, (iii) 327, (iv) 90, (v) 192

2. Let us consider the following numbers to find whether the numbers are divisible or not divisible by 3:

(i) 176, (ii) 221, (iii) 327, (iv) 90, (v) 192

3. Is 7248 is divisible (i) by 4, (ii) by 2 and (iii) by 8?

4. Without actual division, find if 235932 is divisible (i) by 4 and (ii) 8.

5. Determine which of the following numbers which are divisible by 6, using the test of divisibility by 6: 42, 144, 180, 258, 156

6. Determine which of the following numbers which are divisible by 9, using the test of divisibility by 9:

99, 198, 171, 9990, 3411.

## Mental Ability – Competitive Exam Preparation – Number Series by adding fixed number – NTSE, NCO, NSO, IMO and other Competitive Exams

The sequence or series of numbers created by adding fixed number :

1. 5 , 7 , 9 , 11 , 13 etc – Number sequence obtained by adding fixed number 2
2. 6, 11, 16, 21, 26 etc – Number sequence obtained by adding fixed number 5

Similarly number sequence can be obtained by adding two fixed numbers alternatively or by adding two fixed numbers after repeated series. Example below:

5, 7, 10,12, 15, 17, 20 etc – This number sequence is formed by adding 2 and 3 alternatively

5, 6, 7, 9, 11, 13, 16, 19, 22 etc – This number sequence is formed by adding fixed number 1 , 2 and 3 after regular interval i.e after 3 numbers

We will revert back with right answers at the earliest

Complete the sequence by adding fixed numbers

1. 1234, 1236, 1238, _____, 1242, 1244, _____
2. 1400, 1500, ______ , 1700, 1800, 1900, ______
3. 3, 9, 15, _____, 27, 33, 39, ______, 51
4. 8, 17, _____, 35, 44, _____, 62
5. 10, 15, 25, 35, 40, 45, 55, 65, _____ , 75, 85, ______
6. 6, 9, 15, 21, 24, 27, 33, ______ , 42, ______
7. 3, 5, 7, 10, 13, 16, 18, 20, _____, 25, ______, 31
8. 10, 20, 50, _____, 90, 100, 130, 160, _____, 180, 210, 240
9. 1000, 1200, 1600,________, 2200, 2400, 2800, 3200
10. 86, 96, 116, 136, 166, ______, 236, 276, 326, 376

#### Real Numbers Types – Rational and Irrational – Math Cheatsheet – Class 9 and 10

Chart – Number Systems

Real Numbers

1. Rational Numbers ( Example : -9, 0 , 5/7, 2/5 etc )
• Integers ( Example : -2 , -1 , 0 , 1 , 2 , etc )
• Negative Integers ( Example : -2 , -1 , -3 etc )
• Whole Numbers ( Example : 0, 1, 2, 3, 4, 5 etc )
• Zero ( 0 )
• Positive Integers ( Example : 2 , 3 , 4 etc )
• Non Integral Rationals ( Example : -5/8 , 8/15 , 2 3/7 etc. )
2. Irrational Numbers ( Example : 5 , 8 , 3 2 , 3 – 7 etc