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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. 4
Explanation: On a number line, the reflection of a number about zero is its additive inverse. Since -4 is 4 units to the left of zero, its reflection is 4 units to the right of zero, i.e. 4. The option -4 represents the original point, not its reflection. Exam tip: the reflection of x about zero is -x.
Correct answer: A. Moves to the right
Explanation: On a number line, adding a positive number means moving to the right from the starting number. For example, adding 3 to 2 means moving 3 steps right from 2 to reach 5. Moving left represents subtraction or adding a negative number. Exam tip: numbers increase to the right and decrease to the left.
Correct answer: B. Moving to the left
Explanation: On a number line, subtracting a positive number means moving to the left. For example, \(5-3=2\): starting at 5 and moving 3 steps left reaches 2. Moving right represents addition. Exam tip: for subtraction, count the required number of steps to the left from the starting number.
Correct answer: B. 6
Explanation: Absolute value represents a number’s distance from 0 on the number line. The distance of \(-6\) from 0 is 6 units, so \(|-6|=6\). \(-6\) is the original number, not its absolute value. Exam tip: the absolute value of a negative number is positive.
Correct answer: B. Dense
Explanation: Rational numbers are dense on the number line. Between any two distinct rational numbers, there are infinitely many rational numbers; for example, their average is also a rational number lying between them. Hence, “finite” is incorrect. Exam tip: When asked for a rational number between two rationals, use their average.
Correct answer: A. Between −2 and −3
Explanation: \(-5/2=-2.5\). On the number line, \(-2.5\) is greater than \(-3\) and less than \(-2\), so it lies between \(-2\) and \(-3\). The interval between \(-4\) and \(-5\) contains numbers that are more negative. Exam tip: for negative numbers, the more negative value lies farther to the left on the number line.
Correct answer: A. -3
Explanation: The absolute value of -3 is 3, while the absolute value of 2 is 2. Since 3 is greater than 2, -3 has the greater absolute value. “Both are equal” is incorrect because the two numbers are not at the same distance from zero. Exam tip: remove the negative sign when finding absolute value, then compare the distances from zero.
Correct answer: A. -1, 0, 2, 3
Explanation: In increasing order, numbers are arranged from the smallest to the largest. On the number line,
-1 lies to the left of 0, so it is the smallest, followed by 0, 2, and 3. Therefore, the correct order is
-1, 0, 2, 3. In option B, 0 is placed before -1, so it is not an increasing order. Exam tip: A number farther left on the number line is smaller.
Correct answer: B. Arranging numbers from largest to smallest
Explanation: In decreasing order, numbers are arranged from the largest to the smallest. For example, 3, 2, 1, 0 is in decreasing order. Option A goes from the smallest to the largest, so it represents increasing order. Exam tip: Compare the first and last terms to identify the order quickly.
Correct answer: B. Values increase as we move to the right
Explanation: On a number line, a number placed to the right has a greater value than a number placed to its left. For example, \,3\, is to the right of \,−2\,, so \,3 > −2\,. Option A reverses this direction. Exam tip: moving right on a number line always means moving to a greater value.
Correct answer: B. \(\sqrt{5}\)
Explanation: Numbers to the right of 0 are positive. Hence a point \(\sqrt{5}\) units to the right of 0 represents \(\sqrt{5}\), not \(-\sqrt{5}\). Exam tip: distance is always positive; use direction to decide the sign.
Correct answer: A. The statement is correct because \(-\frac{5}{2}=-2.5\).
Explanation: \(-\frac{5}{2}=-2.5\). The gap from \(-3\) to \(-2\) is 1 unit, so \(-2.5\) is 0.5 unit from each endpoint. In exams, remember that more negative numbers lie further left.
Correct answer: B. 0
Explanation: 0 is greater than -2 and less than 3, so \(-2 < 0 < 3\). Hence, 0 lies strictly between the two numbers. Although 3 is an endpoint, it is not between -2 and 3. Exam tip: on a number line, values increase from left to right.
Correct answer: B. 0 के बाईं ओर एक इकाई
Explanation: On a number line, numbers to the left of 0 are negative. Therefore, -1 represents the point one unit to the left of 0. One unit to the right of 0 is +1, so that option is incorrect. Exam tip: Values increase as you move right on a number line and decrease as you move left.
Correct answer: B. -5
Explanation: On a number line, the number to the right is greater. Since -5 lies to the right of -8 and is closer to zero, -5 is greater. -8 is smaller because it lies further to the left. Exam tip: Among negative numbers, the number closer to zero is greater.
Correct answer: B. 8
Explanation: The successor of an integer is obtained by adding 1 to it. Therefore, the successor of 7 is 7 + 1 = 8. Here, 6 is the predecessor of 7, while 9 is the successor of 8. Exam tip: add 1 for a successor and subtract 1 for a predecessor.
Correct answer: A. -1
Explanation: The predecessor of an integer is the number exactly 1 less than it. Therefore, the predecessor of 0 is \(0-1=-1\). \(1\) is the successor of 0, while \(-2\) is the predecessor of \(-1\). Exam tip: subtract 1 to find a predecessor and add 1 to find a successor.
Correct answer: C. -2
Explanation: The midpoint of two numbers is their average: \(\frac{-6+2}{2}=\frac{-4}{2}=-2\). Therefore, \(-2\) is the correct answer. \(-3\) is not equally distant from \(-6\) and \(2\). Exam tip: To find a midpoint on a number line, add the two numbers and divide by 2.
Correct answer: B. -2
Explanation: On the number line, -2 lies to the right of -4 and to the left of -1. Since \(-4 < -2 < -1\), the correct answer is -2. Note that -5 is smaller than -4, while 0 and 2 are greater than -1. Exam tip: Write the numbers as an inequality to check whether a number lies between them.
Correct answer: A. -9
Explanation: The absolute value of -9 is 9, whereas the absolute value of 6 is 6. Since 9 > 6, -9 has the greater absolute value. As 6 is positive, its absolute value remains 6. Exam tip: absolute value is the distance from 0 on the number line, so it is never negative.
Correct answer: B. -7, -3, 2
Explanation: In increasing order, numbers are arranged from smallest to greatest. On the number line, -7 lies to the left of -3, and -3 lies to the left of 2. Therefore, the correct order is -7, -3, 2. In option A, -3 is placed before -7, which is incorrect. Exam tip: Among negative numbers, the number with the greater absolute value is smaller.
Correct answer: B. 6
Explanation: The distance between two numbers on a number line is their absolute difference: \(|-4-(-10)|=|6|=6\). Therefore, the correct answer is 6. The value 14 comes from adding the magnitudes of the two numbers, not from their distance. Exam tip: always use \(|a-b|\) to find distance on a number line.
Correct answer: B. It is an irrational real number located between 1 and 2.
Explanation: \(\sqrt{2}\) is irrational but real, so it has a definite point on the number line. Since \(1^2<2<2^2\), it lies between 1 and 2. Exam tip: irrational does not mean non-real.
Correct answer: B. -1
Explanation: On a number line, moving left means subtracting. Therefore, moving 3 steps left from 2 gives \(2-3=-1\). The number 0 would be reached by moving only 2 steps left from 2. Exam tip: add when moving right and subtract when moving left.
Correct answer: C. 0
Explanation: On a number line, the number farther to the right is greater. Since 0 lies to the right of -1, -3, and -6, it is the greatest number. Although -1 is the greatest negative number here, it is still less than 0. Exam tip: Among negative numbers, the number closer to zero is greater.
