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CBSE Class 10 Mathematics Worksheet

UNIT I: Number systems - Real numbers

1.

The smallest number by which √27 should be multiplied so as to get a rational number is

A)

3

B)

√27

C)

√3

D)

3√3

2.

Prove that 7/20 is terminating decimal.

3.
Fill in the blanks: The product of conjugate binomial surds is always a ________ number.
4.

For some integer m, every odd integer is of the form

A)

m

B)

m+1

C)

2m

D)

2m+1

5.
Write 2/13 rational number in decimal form.
6.

The sum or difference of a rational and an irrational number is

A)

always irrational

B)

always rational

C)

rational or irrational

D)

none of these

7.

 is an irrational number

A) True B) False
8.

If n is any natural number, then  always ends with

A)

1

B)

3

C)

5

D)

7

9.

The decimal expansion of the rational number  will terminate after

A)

one decimal place

B)

two decimal places

C)

three decimal places

D)

more than three decimal places

10.

If 'm' is a positive prime number then √m

A)

Rational number

B)

Irrational number

C)

Integer

D)

None of these

11.
Use Euclid’s division algorithm to find the HCF of 200 and 40000
12.

 The sum of a rational and irrational number is

A)

rational

B)

irrational

C)

both of above

D)

none of above

13.

If x and y are prime numbers, then HCF of  and  is

A)

B)

C)

D)

xy

14.

Prove that is an irrational number.

15.

 If two positive integers a and b are written as a = p3q2 and b = pq3; p, q are prime numbers, then HCF (a, b) is:

A)

pq

B)

pq2

C)

p3q3

D)

p2q2

16.
Fill in the blanks: All terminating decimal fractions represent _______ numbers.
17.
What number should be added to 3/8 to get -1/24?
18.

π is

A)

An integer

B)

A rational number

C)

An irrational number

D)

None of these

19.

The exponent of 2 in the prime factorisation of 144, is?

A)

4

B)

5

C)

6

D)

3

20.

For all a,b belong R, this imply

A) a < b B) a > b C) a = b D) 1â??a < 1â??b

CBSE Class 10 Mathematics Worksheet

UNIT I: Number systems - Real numbers

Answers

1.
Option C

2.

20 = 4 X 5 = 22 X 5, the prime factor of 20 are both 2s & 5s. Hence 7/20 is terminating decimal

3.
Rational
4.
Option D

5.
0.15384600000000001
6.
Option A
7.
Option B
8.
Option A
9.
Option B
10.
Option B

11.
200

Solution: In the given pair, 40000 > 200 thus let 40000 = a and 200 = b

Now by applying the Euclid’s division algorithm, we get
40000=200*199+0 (where q= 199,r=0)

Since, in the above equation we get, r = 0, therefore, 200 is the HCF of the given pair 200 and 40000.

12.
Option B
13.
Option C

14.

Let's assume that is a rational number Therefore, we can f ind two integers and b, such that = a/b where,b is not equal to zero.Now, . Now,.Since a and b are integers, (6b + a) and (10b) are also integers. Thus 6b+a/10b is rational hence, should also be rational. This contradicts the f act that is irrational.Theref ore, our assumption is f alse and hence, is irrational.

15.
Option B

16.
Rational
17.
-0.41666666670000002
18.
Option C
19.
Option A
20.
Option A

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