10th Maths Chapter 1

Chapter 1

Real Numbers

Q1. Choose the correct option:

1. HCF of (96, 404) is :

a)  4    b) 120    c) 11    d) 5

2. HCF of (6, 20) is :

a) 20    b) 6    c) 120    d) 2

3. HCF of  (91, 21)  is :

a) 91    b) 21    c) 7     d) 12

4. If the product of two numbers is 32 and LCM is 8 then its HCF is :

a) 4    b) 2    c) 1    d) 00

5. If two positive integers p and q are expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM. (p,q) is :

a) ab    b) a²b²    c) a³b²    d) a³b³

Answer: 1. b, 2. c, 3. c, 4. a, 5. c

Q2. Fill in the blanks:

1. HCF. (a, b)×LCM. (a, b) = ..................  .

2. If `a = x^3y^2` and `y = xy^3`, where `x, y` are prime numbers, then HCF. (a, b) will be ............  .

3. `sqrt3` is a ............. number.

4. Rational and irrational numbers both are .......... numbers.

5. `sqrt3` is a ............ number.

Answer: 1. a×b, 2. `xy^2`, 3. irrational, 4. real, 5. irrational. 

Q3. Match the column :

                  A                                                                    B

1. Rational and irrational 

numbers                       a) Always rational number

2. 2k+1, where k is a positive 

integer                                            b) Even numbers

3. 2k, where k is a positive 

integer                                              c) Odd numbers

4. Product of non-zero rational 

number and irrational number  d) Real numbers 

Answer: 1. d, 2. c, 3. b, 4. a

Q4. True/False:

1. `sqrt5` is an irrational number.

2. Every natural number is a whole number.

3. Every whole number is a natural number. 

4. Every composite number can be expressed as a product of prime numbers.

5. `sqrt7` is a rational number.

Answer: 1. T, 2. T, 3. F, 4.T, 5. F

Q5. Write the answer in one word/sentence:

1. if `sqrtp` is an irrational number, then p is which type of number?

2. What is the fundamental Theorem of Arithmetic?

3. If a and b are two natural numbers, then what is the relation between HCF. and LCM.?

4. p is a prime number and a be a positive integer, if p divides a², then which can say the statement?

5. If a=bq then what is the relation between a and b?

Answer: 1. p will be prime number. 

2. Every composite number can be factorzed as a product of primes and this factorization is unique, apart from the order in which the prime  factors occur.

3. HCF (a, b)×LCM(a, b) = a×b.

4. Definitely say's that p divides a. 

5. b is a factor of a.