#### Objective type questions

Mark the correct alternative in each of the following:

1.) Which of the following numbers is a perfect number?

(a) 4 (b) 12 (c) 8 (d) 6

Sol:

(d) 6

A number for which the sum of all its factors is equal to twice the number is called a perfect number. Factors of 6 are 1, 2, 3, and 6.

Sum of the factors of 6 = 1 + 2 + 3 + 6 = 12 = 2 x 6 Hence, 6 is a perfect number.

2.) Which of the following are not twin-primes?

(a) 3, 5 (b) 5, 7 (c) 11, 13 (d) 17, 23

Sol:

(d) 17, 23

Pairs of prime numbers that differ by 2 are called twin primes. The difference between 17 and 23 is 6. Hence, 17 and 23 are not twin primes.

3.) Which of the following are co-primes?

(a) 8, 10 (b) 9, 10 (c) 6, 8 (d) 15, 18

Sol:

(b) 9, 10

9 = 3 x 3 x1

10 = 2 x 5 x1

Though both 9 and 10 are composite numbers, the only factor common to them is 1.

Therefore, 9 and 10 are co-primes.

4.) Which of the following is a prime number?

a.) 263 (b) 361 (c) 323 (d) 324

Sol:

(a) 263

23 = 1 x 263

The number 262 has only two factors, 1 and 263.

Hence, it is a prime number.

5.) The number of primes between 90 and 100 is

a.) 0 (b) 1 (c) 2 (d) 3

Sol:

(b) 1

There is only one prime number between 90 and 100, i.e. 97.

6.) Which of the following numbers is a perfect number?

a.) 16 (b) 8 (c) 24 (d) 28

Sol:

(d) 28

A number for which the sum of all its factors is equal to twice the number is called a perfect number.

Factors of 28 are 1, 2, 4, 7, 14 and 28.

Sum of factors of 28 = 1 +2 +4 +7 +14 +28 = 56 = 2 x 28

Hence, 28 is a perfect number.

7.) Which of the following is a prime number?

a.) 203 (b) 139 (c) 115 (d) 161

Sol:

(b) 139

139 = 1 x 139

The number 139 has only two factors, 1 and 139

Hence, it is a prime number.

8.) The total number of even prime numbers is

a.) 0 (b) 1 (c) 2 (d) unlimited

Sol:

(b) 1

There is only one even number that is prime, i.e. 2.

9.) Which of the following is a prime number?

a) 161

b) 221

c) 373

d) 437

Sol:

(c) 373

373 = 1 x 373

The number 373 has only two factors 1 and 373.

Hence, it is a prime number.

10.) The least prime is

a) 1

b) 2

c) 3

d) 2

Sol:

(b) 2

2 is the least number. It is the only even prime number.

11.) Which one of the following numbers is divisible by 3?

a) 27326

b) 42356

c) 73545

d) 45326

Sol:

(c ) 73, 545

Sum of the digits in 73, 545 = 7+ 3 +5 +4+ 5 = 24

Since 24 is divisible by 3, 73545 is divisible by 3.

12.) Which one of the following numbers is divisible by 4?

a.) 8675231

b.) 9843212

c.)1234567

d.) 543123

Sol:

(b) 98, 43, 212

Here, the number formed by the last two digits is 12, which is divisible by 4.

Therefore, 98, 43, 212 is divisible by 4.

13.) Which one of the following numbers is divisible by 6?

a.) 7908432

b.) 68719402

c.) 45982014

d.)

Answer:

(a) 79, 08, 432 and (c) 4,59,82,014

A number divisible by 6 must also be divisible by 3 and 2 as 6 is a multiple of 3 and 2.

In 79, 08, 432, the sum of the digits = 7 + 9 + 0 + 8 + 4 + 3 + 2 = 33 Since 33 is a multiple of 3, this number is divisible by 3. Also, since the last digit is 2, it is also divisible by 2. Therefore, 79,08,432 is divisible by 6.

In number 4, 59, 82,014, the sum of the digits = 4 + 5 + 9 + 8 + 2 + 0 + 1 + 4 = 33. Since 33 is a multiple of 3, this number is divisible by 3. Also, since the last digit is 4, it is also divisible by 2. So, 4,59,82,014 is also divisible by 6.

14.) Which one of the following numbers is divisible by 8?

a.) 87653234

b.) 78956042

c.) 64298602

d.) 98741032

Sol:

(d) 98741032

In 98741032the number formed by the last three digits is 032, which is also divisible by 8.

Hence, 98741032 is divisible by 8.

15.) Which of the following numbers is divisible by 9?

a.) 9076185

b.) 92106345

c.) 10349576

d.) 95103476

Sol:

(a) 90, 76, 185

In 90, 76,185:

Sum of the digits = 9 + 0 + 7 + 6 + 1 + 8 + 5 = 36

Since 36 is divisible by 9, 90, 76, 185 is divisible by 9.

16.) Which of the following numbers is divisible by 11?

a.) 1111111

b.) 22222222

c.) 3333333

d.) 4444444

Answer: (b) 22222222

17.) If 1*548 is divisible by 3, then * can be replaced by

a.) 0

b) 2

c.) 7

d.) 8

Answer: (a) 0

18.) 5*2 is a three digit number with * as a missing digit. If the numbers is divisible by 6, the missing digit is

a.) 2

b.) 3

c.) 6

d.) 7

Answer: (a) 2

19.) What least value should be given to *so that the number 6342*1 is divisible by 3?

a.) 0

b.) 1

c.) 2

d.) 3

Answer: (a) 0

20.) What least value should be given to *so that the number 915*26 is divisible by 9?

a.) 1

b.) 4

c.) 2

d.) 6

Answer: (b) 4

21.) What least value should be given to *so that the number 653*47 is divisible by 11?

a.) 1

b.) 2

c.) 6

d.) 9

Answer: (a) 1

22.) What least value should be given to *so that the number 63576*2 is divisible by 8?

a.) 1

b.) 2

c.)3

d.)4

Answer: (c) 3

23.) Which one of the following numbers is exactly divisible by 11?

a.) 235641

b.) 245642

c.) 315624

d.) 415624

Answer: (d) 415624

24.) If 1*548 is divisible by 3, which of the following digit can replace *?

a.) 0

b.) 2

c.) 7

d.) 9

Answer: (a) 0

25.) The sum of the prime numbers between 60 and 75 is

a.) 199

b.) 201

c.) 211

d.) 272

Answer: (d) 272

26.) The HCF of two consecutive natural numbers is

a.) 0

b.) 1

c.) 2

d.) non-existent

Answer: (b) 1

27.) The HCF of two consecutive even numbers is

a.) 1

b.) 2

c.) 0

d.) non- existent

Answer: (b) 2

28.) The HCF of two consecutive odd numbers is

a.) 1

b.) 2

c.) 0

d.) Non-existent

Answer: (a) 1

29.) The HCF of even number and an odd number is

a.) 1

b.) 2

c.) 0

d.) non-existent

Answer: (a) 1

30.) The LCM of 24, 36 and 40 is

a.) 4

b.) 90

c.) 360

d.) 720

Answer: (c) 360

31.) If x and y are two co-primes, then their LCM is

a.) xy

b.) x + y

c.) \(\frac{x}{y}\)

d.) 1

Answer: (d) 1

32.) If the HCF of two numbers is 16 and their product is 3072, then their LCM is

a.) 182

b.) 192

c.) 12

d.) None of these

Answer: (b) 192

33.) The least number divisible by 15, 20, 24, and 32 and 36 is

a.) 1400

b.) 1660

c.) 1263

d.) None of these

Answer: (c) 1263

34.) The smallest number which when diminished by 3 is divisible by 11, 28, 36 and 45, is

a.) 1257

b.) 1260

c.) 1263

d.) None of these

Answer: (c) 1263

35.) Three numbers are in the ratio 1:2:3 and their HCF is 6, the numbers are

a.) 4, 8, 12

b.) 5, 10, 15

c.) 6, 2, 18

d.) 10, 20, 30

Answer: (c) 6, 2, 18

36.) The ratio of two numbers is 3:4 and their HCF is 4. Their LCM is

a.) 12

b.) 16

c.) 24

d.) 48

Answer: (d) 48