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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: B. 1.15
Explanation: 1.15 is greater than 1.1 and less than 1.2, since \(1.1 < 1.15 < 1.2\). Therefore, it lies between the two numbers on the number line. 1.05 is a close distractor, but it is less than 1.1. Exam tip: Compare decimals by writing them to the same number of decimal places if needed.
Correct answer: B. -1/2
Explanation: \(-\frac{1}{2}=-0.5\), whereas \(-\frac{1}{3}\approx -0.333\). On the number line, \(-0.5\) lies to the left of \(-0.333\), so \(-\frac{1}{2}\) is smaller. They are not equal because their values are different. Exam tip: Among negative numbers, the number farther to the left on the number line is smaller.
Correct answer: D. All real numbers
Explanation: Every point on the number line represents a real number, and every real number has a definite position on it. Real numbers include both rational and irrational numbers. Exam tip: real numbers = rational numbers + irrational numbers.
Correct answer: B. 2
Explanation: On the number line, the integers strictly between -2 and 3 are -1, 0, 1 and 2. Therefore, 2 is the correct option. -3 lies to the left of -2, while 3 and 4 are not less than 3. Exam tip: “Between” usually excludes the two endpoint numbers.
Correct answer: A. Increasing value of numbers
Explanation: On a number line, the value of numbers increases as we move from left to right. For example, \(3\) and then \(4\) lie to the right of \(2\). Values decrease when we move left. Exam tip: numbers on the right are greater, while numbers on the left are smaller.
Correct answer: B. 10
Explanation: The successor of an integer is 1 greater than the number. Therefore, the successor of 9 is 9 + 1 = 10. Here, 8 is the predecessor of 9, while 11 is 2 greater than 9. Exam tip: add 1 to a number to find its successor.
Correct answer: B. -16
Explanation: The predecessor of a number is 1 less than that number. Thus, \(-15-1=-16\), so -16 is correct. -14 is the successor of -15 because it is 1 greater. Exam tip: subtract 1 for a predecessor and add 1 for a successor.
Correct answer: A. -1
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-8+6}{2}=\frac{-2}{2}=-1\). Therefore, the correct answer is \(-1\). The value \(-2\) is not the average of the two numbers. Exam tip: add the two numbers and divide by 2 to find their midpoint.
Correct answer: B. 14
Explanation: The distance between two numbers on a number line is the absolute value of their difference: \(|9-(-5)|=|14|=14\). Therefore, the correct answer is 14.
Although -14 may arise from subtracting in the opposite order, a distance can never be negative. Exam tip: always take the absolute value of the difference when finding distance.
Correct answer: B. 1.45
Explanation: 1.45 is greater than 1.4 and less than 1.5, since 1.40 < 1.45 < 1.50. Therefore, it lies between 1.4 and 1.5 on the number line. 1.6 is greater than 1.5, while 1.3 and 1.2 are less than 1.4. Exam tip: Add zeros at the end of decimals when needed to compare the same number of decimal places.
Correct answer: B. 7/8
Explanation: The correct answer is \(7/8\), because \(3/4=6/8\) and \(1=8/8\). Thus, \(6/8 < 7/8 < 8/8\), so \(7/8\) lies between \(3/4\) and 1. While \(2/3\) is less than \(3/4\), \(5/4\) is greater than 1. Exam tip: Convert fractions to a common denominator to compare them quickly.
Correct answer: B. एक परिमेय संख्या
Explanation: For any two distinct rational numbers, their average \(\frac{a+b}{2}\) is rational and lies between them. Hence B is correct. A whole number need not lie between them. Exam tip: use the average to identify a rational number between two rationals.
Correct answer: B. 11
Explanation: The absolute value of a number is its distance from 0 on the number line. Since -11 is 11 units away from 0, \(|-11|=11\). Option -11 is the original number, not its absolute value. Exam tip: the absolute value of a negative number is its positive counterpart.
Correct answer: B. Positive numbers
Explanation: All numbers to the right of 0 on a number line are positive, such as 1, 2, and \(\frac{1}{2}\). Negative numbers lie to the left of 0. Exam tip: values increase as you move to the right on a number line.
Correct answer: A. 2
Explanation: On a number line, subtraction means moving to the left. Starting at 5 and moving 3 steps left gives 4, then 3, and finally 2. Therefore, the correct answer is 2. Option 8 would be obtained by adding 3 to 5, not subtracting it. Exam tip: move right for addition and left for subtraction on a number line.
Correct answer: B. -3
Explanation: On a number line, subtracting 7 from 4 means moving 7 steps to the left from 4. This lands at -3, so the correct answer is -3. The value 3 would be obtained from 7 minus 4, not from 4 minus 7. Exam tip: in subtraction, move left by the number being subtracted.
Correct answer: A. \(-\frac{3}{5}\)
Explanation: \(-\frac{3}{5}\) is negative but greater than \(-1\), so it lies between \(-1\) and \(0\). In contrast, \(-\frac{5}{3}<-1\). Exam tip: among negative numbers, the one closer to 0 is greater.
Correct answer: B. -1
Explanation: Among negative integers, the number farther to the right on the number line is greater. Here,
displaystyle -1 > -4 > -6 > -8
Therefore, -1 is the greatest integer. The numbers -4, -6 and -8 lie to the left of -1 on the number line, so they are smaller. Exam tip: among negative numbers, the number closest to zero is greater.
Correct answer: A. -10
Explanation: On a number line, the number farther to the left is smaller.
-10 lies to the left of -9.5 because it is more negative, so -10 is smaller. Although -9.5 is negative, it is closer to zero and hence greater than -10. Exam tip: Among negative numbers, the number with the greater magnitude is smaller.
Correct answer: A. -2
Explanation: The midpoint of two numbers on a number line is their average: \(\frac{2+(-6)}{2}=\frac{-4}{2}=-2\). Therefore, \(-2\) is correct. \(-3\) is not the average of the two numbers. Exam tip: include the negative sign while adding the numbers, then divide by 2.
Correct answer: B. 2
Explanation: The distance between two numbers on a number line is the absolute value of their difference. Thus, \(\left|\frac{1}{2}-\left(-\frac{3}{2}\right)\right|=\left|\frac{4}{2}\right|=2\). Therefore, the correct answer is 2. While \(-2\) may arise as a signed displacement in some order, distance can never be negative. Exam tip: always use absolute value when finding distance on a number line.
Correct answer: A. -8
Explanation: On a number line, the reflection of a number about zero is its additive inverse. Since 8 is 8 units to the right of zero, its reflection is 8 units to the left of zero, i.e., -8. The number 8 is not its own reflection; only 0 reflects to itself. Exam tip: for reflection about zero, change the sign of the number.
Correct answer: B. -5
Explanation: The distance of a number from 0 is its absolute value.
\(|6|=6\) and \(|-5|=5\). Since 5 is less than 6, -5 is closer to 0. “Both are equally distant” would be correct only for opposite numbers such as 5 and -5. Exam tip: compare absolute values to decide which number is closer to zero.
Correct answer: B. 101
Explanation: The successor of an integer is obtained by adding 1 to it. Therefore, 100 + 1 = 101. While 99 is the predecessor of 100, 102 is two integers after 100. Exam tip: add 1 to find a successor.
Correct answer: C. \(-\frac{1}{2}\)
Explanation: The midpoint of two numbers \(a\) and \(b\) is \(\frac{a+b}{2}\). Therefore, the midpoint of \(-1\) and \(0\) is \(\frac{-1+0}{2}=-\frac{1}{2}\). \(\frac{1}{2}\) is the midpoint between 0 and 1, so it is not correct here. Exam tip: on a number line, a midpoint is equally distant from both numbers.
