Number Systems Class 9 MCQs Questions with Answers ( Handwritten )

NEW LEARNET EDUCATION

Chapter 1 

Number Systems ( Handwritten )

 MCQ PART-1

1.) Can we write 0 in the form of p/q?

a. Yes

b. No

c. Cannot be explained

d. None of the above

Answer: a

Explanation: 0 is a rational number and hence it can be written in the form of p/q.

Example: 0/4 = 0

2.) The three rational numbers between 3 and 4 are:

a. 5/2, 6/2, 7/2

b. 13/4, 14/4, 15/4

c. 12/7, 13/7, 14/7

d.11/4, 12/4, 13/4

Answer: b

Explanation: There are many rational numbers between 3 and 4

To find 3 rational numbers, we need to multiply and divide both the numbers by 3+1 = 4

Hence, 3 x (4/4) = 12/4 and 4 x (4/4) = 16/4

Thus, three rational numbers between 12/4 and 16/4 are 13/4, 14/4 and 15/4.

3.) In between any two numbers, there are:

a. Only one rational number

b. Two rational numbers

c. Infinite rational numbers

d. No rational number

Answer: c

Explanation: Take the reference from question number 2 explained above.

4.) Every rational number is:

a. Whole number

b. Natural number

c. Integer

d. Real number

Answer: d

5.) √9 is  __________ number.

a. A rational

b. An irrational

c. Neither rational nor irrational

d. None of the above

Answer: a

Explanation: √9 = 3

Hence, √9 is a rational number.

6.) Which of the following is an irrational number?

a. √16

b. √(12/3)

c. √12

d. √100

Answer: c

Explanation: √12 cannot be simplified to a rational number.

7.) 3√6 + 4√6 is equal to:

a. 6√6

b. 7√6

c. 4√12

d. 7√12

Answer: b

Explanation: 3√6 + 4√6 = (3 + 4)√6 = 7√6

8.) √6 x √27 is equal to:

a. 9√2

b. 3√3

c. 2√2

d. 9√3

Answer: a

Explanation: √6 x √27 = √(6  x 27) = √(2 x 3 x 3 x 3 x 3) = (3 x 3)√2 = 9√2

9.) Which of the following is equal to x3?

a. x6 – x3

b. x6.x3

c. x6/x3

d. (x6)3

Answer: c

Explanation: x6/x3 = x6 – 3 = x3

10.) Which of the following is an irrational number?

a. √23

b. √225

c. 0.3796

d. 7.478478

Answer: a

Explanation: √23 = 4.79583152331…

Since the decimal expansion of the number is non-terminating non-recurring. Hence, it is an irrational number.

MCQ PART-2

Question 1.
The value of 22−−√3−−−−√4 is equal to
(a) 2–16
(b) 2-6
(c) 216
(d) 26

Answer

Answer: (c) 216

---

Question 2.
Find the value of 54250−−−√3
(a) 925
(b) 35
(c) 27125
(d) 2√35

Answer

Answer: (b) 35

---

Question 3.
Simplified value of (16)–14 × 16−−√4 is
(a) 16
(b) 4
(c) 1
(d) 0

Answer

Answer: (c) 1

---

Question 4.
Find the value of 64−2−−−−√4.
(a) 18
(b) 12
(c) 8
(d) 164

Answer

Answer: (a) 18

---

Question 5.
Find the value of 216−−−√3 – 125−−−√3
(a) 1
(b) -1
(c) 91−−√3
(d) 65

Answer

Answer: (a) 1

---

Question 6.
When 1515−−√ is divided by 3√3 find the quotient.
(a) 5√3
(b) 3√5
(c) 5√5
(d) 3√3

Answer

Answer: (c) 5√5

---

Question 7.
If √3 = 1.732 and √2 = 1.414, find the value of 1√3−√2
(a) 0.318
(b) 3.146
(c) 13.146
(d) 1.732−−−−√ – 1.414−−−−√

Answer

Answer: (b) 3.146

---

Question 8.
Which of the following numbers is an irrational number?
(a) 16−−√ – 4
(b) (3 – √3) (3 + √3)
(c) √5 + 3
(d) –25−−√

Answer

Answer: (c) √5 + 3

---

Question 9.
The decimal expansion of √2 is
(а) finite decimal
(b) 1.4121
(c) non-terminating recurring
(d) non-terminating non-recurring

Answer

Answer: (d) non-terminating non-recurring

---

Question 10.
If x = √75 and 5x = p√7, then the value of p is
(а) 5√7
(b) 257
(c) 725
(d) √75

Answer

Answer: (b) 257

---

Question 11.
The sum of 0.3¯ and 0.2¯ is
(а) 599
(b) 59
(c) 510
(d) 5100

Answer

Answer: (b) 59

---

Question 12.
(√a + √b) (√a – √b) is
(a) a + b
(b) a – b
(c) 2√a
(d) 2√b

Answer

Answer: (b) a – b

---

Question 13.
12−−√ × √8 is equal to
(a) 2√6
(b) 3√6
(c) 4√6
(d) 6√6

Answer

Answer: (c) 4√6

---

Question 14.
Find the value of 20+7050
(a) 2
(b) 0
(c) 95
(d) 15

Answer

Answer: (a) 2

---

Question 15.
A rational number lying between √2 and √3 is
(a) √2+√32
(b) √6
(c) 1.6
(d) 1.9

Answer

Answer: (c) 1.6

---

Question 16.
The rational number between –15 and –25 is
(a) 4
(b) –14
(c) –310
(d) –725

Answer

Answer: (c) –310

---

Question 17.
If 8x = 642x then find the value of x.
(a) 4
(b) 2
(c) 12
(d) 32

Answer

Answer: (d) 32

---

Question 18.
The simplified value of (81)–14 × 81−−√4 × (81)0.2 is
(a) 9
(b) 3
(c) 1
(d) 0

Answer

Answer: (a) 9

---

Question 19.
Value of [(81-1/2)-1/4]² is
(a) 3
(b) 13
(c) 9
(d) 19

Answer

Answer: (a) 3

Question 20.
If x1/12 = 491/24 then find the value of x.
(a) 49
(b) 2
(c) 12
(d) 7

Answer

Answer: (d) 7

MCQ PART- 3

1.  From the choices given below mark the co-prime numbers

      (a)   2, 3

(b)   2, 4

(c)   2, 6

(d)   2, 110

2.  A rational number equivalent to  is

      (a)   

(b)   

(c)   

(d)   

3.  An example of a whole number is

      (a)   0

(b)   

(c)   

(d)   –7

4.  Given a rational number  This rational number can also be known as

      (a)   a natural number

(b)   a whole number

(c)   a fraction

(d)   a real number

5.  The rational number  can also be written as

      (a)   0.3

(b)   

(c)   0.33

(d)   

6.  If the decimal representation of a number is non-terminating, non-repeating then the number is

      (a)   a natural number

(b)   a rational number

(c)   a whole number

(d)   an irrational number

7.  The square root of which number is rational

      (a)   7

(b)   1.96

(c)   0.04

(d)   13

8.  A rational number between  is

      (a)   

(b)   

(c)   

(d)   

9.  The number 1.101001000100001... is

      (a)   a natural number

(b)   a whole number

(c)   a rational number

(d)   an irrational number

10.  On adding  we get

      (a)   

(b)   

(c)   

(d)   none of these

11.  On dividing  we get

      (a)   

(b)   6

(c)   9

(d)   none of these

12.   is

      (a)   an irrational number

(b)   a positive rational number

      (c)   a negative rational number

(d)   an integer

13.   is

      (a)   a positive rational number

(b)   equal to zero

      (c)   an irrational number

(d)   a negative integer

14.   is

      (a)   a positive rational number

(b)   an irrational number

      (c)   a negative rational number

(d)   equal to zero

15.  The number  is

      (a)   an irrational number

(b)   a rational number

      (c)   not a natural number

(d)   none of these

16.  On simplifying  we get

      (a)   12

(b)   

(c)   

(d)   

17.  On simplifying 83 × 24, we get

      (a)   167

(b)   213

(c)   210

(d)   84

18.  For rationalising the denominator of the expression  we multiply and divide by

      (a)   

(b)   12

(c)   

(d)   

19.  The value of  when  is

      (a)   .3162

(b)   31.62

(c)   .03162

(d)   316.2

20.  (16)3/4 is equal to

      (a)   2

(b)   4

(c)   8

(d)   16

Answers

1. (a)	2. (c)	3. (a)	4. (d)	5. (d)
6. (d)	7. (b),(c)	8. (d)	9. (d)	10. (c)
11. (c)	12. (a)	13. (c)	14. (b)	15. (b)
16. (d)	17. (b)	18. (d)	19. (a)	20. (c)

MCQ PART- 4

1. The value obtained on simplifying (√5 + √6)²

(a) 12 + 5√30

(b) 13 + 2√33

(c) 11 - 2√30

(d) 11 + 2√30

► (d) 11 + 2√30

2. Find the remainder when 67⁹⁹ is divided bt 7

(a) 1

(b) 6

(c) 4

(d) 2

► (a) 1

3. All the integers are

(a) whole numbers

(b) rational numbers

(c) irrational numbers

(d) natural numbers

► (b) rational numbers

4. The rational number between 1 and 2 is

(a) 3/2

(b) 7/2

(c) 5/2

(d) 1/2

► (a) 3/2

5. (256)3/4 = ____

(a) 128

(b) 32

(c) 26

(d) 64

► (d) 64

6. Between 3 and 4 there are

(a) 10,000 rational numbers

(b) 1000 rational numbers

(c) Infinitely many rational numbers

(d) 500 rational numbers

► (c) Infinitely many rational numbers

7. The value of 49^1/2 is equal to———

(a) 1/49

(b) 49

(c) 7

(d) 1/7

► (c) 7

8. Which of the following is an irrational number ?

(a) 4/55

(b) 2.31312345….

(c) 1.404040…..

(d) 1.11

► (b) 2.31312345….

9. Which of the following statement is true

(a) x⁰ = 1/x

(b) x⁰ = x

(c) x⁰ = 0

(d) x⁰ = 1

► (d) x⁰ = 1

10. Which of the following statement about real numbers is false ?

(a) Closed with respect to operation of algebra

(b) Associative law of multiplication

(c) Distributive law of multiplication with respect to addition

(d) Closed with respect to commutative law of addition

► (a) Closed with respect to operation of algebra

11. A rational number between √3 and √5 is

(a) 1/2(√3 -√ 5)

(b) 1/2(√3 + √5)

(c) 2.1

(d) 3.1

► (c) 2.1

12. Which of the following statements is false?

(a) Rational numbers have a terminating or non terminating repeating decimal form.

(b) Irrational numbers can be written in the form p/q where q is non zero and both p, q are integers

(c) Rational numbers can be written in the form p/q where q is non zero and both p,q are integers

(d) Every number on the number line is either rational or irrational, there’s no third alternative

► (b) Irrational numbers can be written in the form p/q where q is non zero and both p, q are integers

13. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is completely divided by 2 the quotient is 33. The other number is:

(a) 66

(b) 130

(c) 132

(d) 196

► (c) 132

14. (2√3 +√3) is equal to

(a) 2√6

(b) 6

(c) 3√3

(d) 4√6

► (c) 3√3

15. The ratio of the circumference of a circle to the diameter of the circle is.

(a) An integer

(b) A rational number

(c) An irrational number

(d) A whole number

► (c) An irrational number

16. Insert one rational number between 2 and 3.​

(a) (2+3)/2

(b) (2-3)/2

(c) (2 x 3)/2.

(d) 2 x 2 + 3 x 3

► (a) (2+3)/2

17. p/q is a rational number, so p and q must be

(a) Any two integers

(b) One of them positive and the other negative

(c) Both natural numbers

(d) Both integers but q must be non zero

► (d) Both integers but q must be non zero

18. Which of the following is not a rational number:

(a) √2

(b) √4

(c) √9

(d) √16

► (a) √2

19. If  a = 1/ (3-2√2)  &  b =  1/ ( 3+2√2)  then the value of a2 +b2 is :-

(a) 34

(b) 35

(c) 36

(d) 37

► (a) 34

20. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is      

(a) 10

(b) 100

(c) 504

(d) 2520

► (d) 2520

21. What should be added to -5/4 to get -1?

(a) -1/4

(b) 1/4

(c) 1

(d) -3/4

► (b) 1/4

22. The product of two numbers is -20/9. If one of the numbers is 4, find the other. 

(a) –5/9

(b) 3/11 

(c) 12/39

(d) –9/11

► (a) –5/9