Questions & Answers: "Number System: Place Value, Comparison and Operations"

Complete guide to "Number System: Place Value, Comparison and Operations" for Math students. Below you will find important questions and model answers to help you prepare.

15 Questions

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Question 1

1 Mark

All points shown on the given number-line are at equal distances. l(UR) - l(QT) = ?

Diagram for Question 1

Options

Option A is correct

l(RS)

Option B

l(TU)

Option C

l(QR)

Option D

l(SQ)

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Question 2

1 Mark

Which of the two options given below are incorrect statements?

Options

Option A is correct

All integers are not real numbers.

Option B

Some rational numbers are integers.

Option C is correct

All rational numbers are integers.

Option D

Some integers are not whole numbers.

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Question 3

1 Mark

By how much is the greatest of the following numbers is greater than the smallest of the given numbers.

Diagram for Question 3

Options

Option A Diagram for Option A
Option B Diagram for Option B
Option C Diagram for Option C
Option D is correctDiagram for Option D
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Question 4

1 Mark

If (17 × 19 × 4) ÷ m = 161.5 then find the value of ‘m’.

Options

Option A

0.6

Option B

7.0

Option C

0.8

Option D is correct

8.0

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Question 5

1 Mark

Which of the following is an irrational number?

Options

Option A

3.14

Option B Diagram for Option B
Option C is correct

π

Option D Diagram for Option D
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Question 6

1 Mark

Which of the following statement is correct?

Diagram for Question 6

Options

Option A is correct

statement A

Option B

statement B

Option C

statement C

Option D

statement D

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Question 7

1 Mark

Find the incorrect statement from the following: (a) Every prime number is a natural number. (b) Every rational number is a real number. (c) Sum of any two prime numbers is an even number. (d) HCF of twin prime numbers is 1.

Options

Option A

a

Option B

b

Option C is correct

c

Option D

d

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Question 8

1 Mark

Using the digit only once, from one-digit prime number form the greatest and smallest 4-digit number. Which of the following options will not divide the difference between these numbers completely?

Options

Option A

3

Option B

5

Option C

9

Option D is correct

7

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Question 9

1 Mark

I had to give Rs. 7 change to Rickshaw uncle. I had enough coins of Rs. 1, Rs. 2, Rs. 5. Then in how many ways can I pay him?

Options

Option A is correct

6 ways

Option B

3 ways

Option C

5 ways

Option D

4 ways

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Question 10

1 Mark

Which of the following are the factors of the polynomial x² + x – 72

Options

Option A is correct

(x – 8) (x + 9)

Option B

(x + 9) (x + 8)

Option C

(x – 8) (x – 9)

Option D

(x – 9) (x + 8)

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Question 11

1 Mark

Which of the following are the factors of 16x⁴ – 81 [Select the correct alternatives]

Options

Option A

(4x + 9) (4x – 9)

Option B is correct

(4x² + 9) (4x² – 9)

Option C is correct

(4x² + 9) (2x + 3) (2x – 3)

Option D

(2x + 3)² (2x – 3)

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Question 12

1 Mark

Find the value of m if

Diagram for Question 12

Options

Option A

2

Option B

3

Option C

4

Option D is correct

5

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Question 13

1 Mark

Which of the following are the factors of the polynomial.

Diagram for Question 13

Options

Option A Diagram for Option A
Option B is correctDiagram for Option B
Option C Diagram for Option C
Option D Diagram for Option D
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Question 14

1 Mark

The difference between the smallest natural number and the greatest negative integer is the square root of one of the following numbers given in the alternatives. Find the number.

Options

Option A

2

Option B

1

Option C is correct

4

Option D

9

Explanation

The smallest natural number is 11. The greatest negative integer is −1-1. The difference between them is 1−(−1)=1+1=21 - (-1) = 1 + 1 = 2. This difference is the square root of the number we need to find. Let the number be xx. Then x=2\sqrt{x} = 2. Squaring both sides, x=22=4x = 2^2 = 4.

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Question 15

1 Mark

Find the value of 31×32×30×33+1\sqrt{31\times32\times30\times33+1}

Options

Option A

990

Option B

923

Option C

1021

Option D is correct

991

Explanation

Let the given expression be E=31×32×30×33+1E = \sqrt{31\times32\times30\times33+1}. We can rearrange the terms as E=30×31×32×33+1E = \sqrt{30\times31\times32\times33+1}. Let x=30x = 30. Then the expression becomes E=x(x+1)(x+2)(x+3)+1E = \sqrt{x(x+1)(x+2)(x+3)+1}. We can group the terms: E=[x(x+3)][(x+1)(x+2)]+1E = \sqrt{[x(x+3)][(x+1)(x+2)]+1}. This simplifies to E=(x2+3x)(x2+3x+2)+1E = \sqrt{(x^2+3x)(x^2+3x+2)+1}. Let y=x2+3xy = x^2+3x. Substituting yy into the expression, we get: E=y(y+2)+1E = \sqrt{y(y+2)+1} E=y2+2y+1E = \sqrt{y^2+2y+1} E=(y+1)2E = \sqrt{(y+1)^2} E=∣y+1∣E = |y+1| Since x=30x=30, y=302+3(30)=900+90=990y = 30^2+3(30) = 900+90 = 990. Therefore, E=∣990+1∣=991E = |990+1| = 991. Thus, the value of the expression is 991991.

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