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SubjectsMathematics
संख्या रेखा
The Number Line topic in Class 9 Mathematics, within Number Systems, helps students visualise numbers as points on a continuous line. They learn to locate and compare integers, rational numbers, irrational numbers and real numbers, understand their order and relative position, and interpret distance using intervals. The topic also supports the geometric representation of irrational numbers such as √2, making the connection between numerical expressions and their positions on the real number line clear.
Correct answer: A. Between 0 and 1
Explanation: \(\frac{9}{10}=0.9\), so it is greater than 0 and less than 1. Therefore, it lies between 0 and 1 on the number line. Option B is incorrect because \(\frac{9}{10}\) is less than 1. Exam tip: compare the fraction with 0 and 1 first to locate it quickly.
Correct answer: C. 3/4
Explanation: The governing concept is locating and comparing real numbers on an interval. A number lies strictly between 0 and 1 only if it is greater than 0 and less than 1. For option C, 3/4 = 0.75, so 0 < 0.75 < 1; therefore it lies in the required interval. Option A gives 7/5 = 1.4, which is to the right of 1. Option B is −1/2 = −0.5, which lies to the left of 0. Option D, 2, is also greater than 1. On a real number line, the correct point must be right of 0 but left of 1. Only 3/4 meets both inequalities, so option C is unambiguously correct.
Correct answer: A. −3 < −1 < 2
Explanation: The governing concept is comparison of signed real numbers on the number line. On a number line, numbers increase from left to right; a number farther left is smaller, and a number farther right is greater. The point −3 lies to the left of −1, and −1 lies to the left of 2. Hence the increasing order is −3 < −1 < 2, making option A correct. Option B reverses the natural order and places the positive number first. Option C incorrectly claims that −1 is less than −3, although −1 is actually greater than −3. Option D also begins with 2, so it is not an increasing sequence. Comparing positions on the number line is more reliable than judging only the visual size of negative numerals.
Correct answer: A. At 0
Explanation: The square root of a number is the value whose square equals that number. Since \(0^2=0\), we have \(\sqrt{0}=0\). Therefore, it lies at the origin, or 0, on the number line. Choosing 1 confuses it with \(\sqrt{1}=1\); in an exam, first evaluate the square root.
Correct answer: C. 3 and 4
Explanation: The governing idea is comparison with consecutive perfect squares. We know that 3² = 9 and 4² = 16. Since 9 < 14 < 16, taking principal square roots preserves the order and gives 3 < √14 < 4. Hence √14 is located between the integers 3 and 4, so option C is correct. It cannot be between 2 and 3 because every number strictly between 2 and 3 has a square between 4 and 9, whereas 14 is larger than 9. It cannot be between 4 and 5 because 4² is already 16, which is greater than 14. Numerically, √14 is approximately 3.74, confirming the interval.
Correct answer: B. Between −1 and 0
Explanation: −0.6 is negative, so it lies to the left of 0. Its absolute value is less than 1, so it lies to the right of −1. Therefore, −0.6 is between −1 and 0. Option A may seem close, but it represents an interval of positive numbers. Exam tip: Check the position by writing −1 < −0.6 < 0.
Correct answer: D. Between −2 and −1
Explanation: To locate −1.25, compare it with the adjacent integers −2 and −1. Since −2 < −1.25 < −1, the number lies between −2 and −1, so option D is correct. On the number line, −1.25 is 0.75 unit to the right of −2 and 0.25 unit to the left of −1. The negative sign places it to the left of zero, and its magnitude is greater than 1, so it must lie to the left of −1 rather than between −1 and 0. Options A and C are positive intervals and cannot contain a negative number. Option B contains numbers such as −0.5, which are greater than −1, not −1.25.
Correct answer: B. 7
Explanation: On a number line, the number farther to the right is greater. Since 7 lies to the right of 3, 7 is the greater number. Choosing 3 is incorrect because it lies to the left of 7. Exam tip: when comparing numbers on a number line, select the one farther to the right.
Correct answer: C. At the origin, between negative and positive numbers
Explanation: On the number line, 0 represents the origin. It lies to the right of negative numbers and to the left of positive numbers; therefore, calling it the origin is more precise than calling it the geometric ‘center’ of the number line. Exam tip: negative numbers are written to the left of 0 and positive numbers to its right.
Correct answer: C. 4
Explanation: On the number line, numbers smaller than 5 lie to the left of 5. Among the given options, 4 is one less than 5, so it is the correct answer. The numbers 6, 7, and 8 are greater than 5. Exam tip: Numbers increase when moving right on the number line and decrease when moving left.
Correct answer: A. प्रत्येक परिमेय संख्या का संख्या रेखा पर एक अद्वितीय बिंदु होता है।
Explanation: Every rational number, such as \(\frac{1}{2}\), \(-\frac{3}{4}\), or \(2\), is represented by exactly one fixed point on the number line. Option C is incorrect because there are infinitely many rational numbers between any two rational numbers. Exam tip: Numbers to the right on a number line are greater, while numbers to the left are smaller.
Correct answer: C. −3
Explanation: On a number line, numbers to the left of zero are negative. −3 is less than zero, so it is a negative number. In contrast, 2, 4, and 5 lie to the right of zero and are positive numbers. In an exam, identify a negative number by the minus sign (−) before it.
Correct answer: A. संख्या रेखा पर बाईं ओर स्थित संख्या छोटी होती है।
Explanation: On a number line, the value of numbers increases as we move from left to right. Therefore, a number to the left is smaller than a number to the right. Option B states the reverse and is incorrect. Negative numbers lie to the left of 0, and 0 has a fixed position on the number line. Exam tip: Remember: right means greater and left means smaller.
Correct answer: D. 3
Explanation: Positive numbers are greater than zero and lie to the right of zero on the number line. Among the given options, 3 is greater than zero, so it is the correct answer. −4 and −1 are negative, while 0 is neither positive nor negative. Exam tip: to check whether a number is positive, determine whether it is greater than 0.
Correct answer: B. 5
Explanation: The midpoint of two numbers is their average: \((1+9)÷2=10÷2=5\). Therefore, 5 is correct. Choosing 4 or 6 would not place the point at equal distances from both numbers. In an exam, add the two endpoints and divide the sum by 2 to find the midpoint.
Correct answer: C. 3
Explanation: On a number line, numbers to the right of 0 are greater than 0. Among the given options, 3 lies to the right of 0, so it is the correct answer. −1, −2, and −5 lie to the left of 0 and are less than 0. Exam tip: every positive number is greater than 0.
Correct answer: B. शून्य के दाईं ओर
Explanation: 8 is a positive number. On a number line, positive numbers are located to the right of zero, so 8 lies to the right of zero. Negative numbers lie to the left of zero. Exam tip: identify the sign of a number first—positive numbers are placed to the right and negative numbers to the left.
Correct answer: A. −3
Explanation: On the number line, the negative number closer to zero is greater. Since −3 is closer to zero than −7, we have −3 > −7. Exam tip: among negative numbers, the one with the smaller absolute value is greater.
Correct answer: B. 4
Explanation: On the number line, there are 4 units from 0 to 4. Distance is found using the absolute difference: \(|4-0|=4\). Therefore, the correct answer is 4. Remember that distance is always non-negative, so reversing the order still gives 4.
Correct answer: B. To the left
Explanation: On a number line, negative numbers are placed to the left of 0. Therefore, minus2 is located two units to the left of 0. Moving to the right of 0 gives positive numbers, so “To the right” is incorrect. Exam tip: place every negative number to the left of zero.
Correct answer: C. 0
Explanation: On the number line, 0 lies to the left of 1, so 0 is smaller than 1. The numbers 2, 3, and 5 lie to the right of 1 and are greater than 1. For exams, remember that the number farther to the left on a number line is smaller.
Correct answer: B. 6
Explanation: On a number line, the number located farther to the right is greater. Since 6 lies to the right of 2, 6 is the greater number. Exam tip: among positive numbers, moving right on the number line means the value increases.
Correct answer: A. कोई निश्चित संख्या नहीं
Explanation: A number line extends infinitely in both directions, so it has no rightmost or greatest number. A number located to the right of a given number is greater than it. Exam tip: moving right on the number line increases the value, but there is no final right endpoint.
Correct answer: B. 1
Explanation: On a number line, the number located farther to the right is greater. Since 1 lies to the right of −1, 1 is greater. Also, 1 is positive and −1 is negative, and every positive number is greater than every negative number. In an exam, choose the number placed farther to the right on the number line.
Correct answer: B. दाएँ
Explanation: 10 is a positive number. On a number line, positive numbers are located to the right of 0, so 10 will be on the right. Exam tip: negative numbers lie to the left of 0.
