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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: C. 7
Explanation: On a number line, numbers to the right of 6 are greater than 6. Among the given options, 7 lies to the right of 6, so it is the correct answer. The numbers 5, 4, and 3 are all less than 6. Exam tip: Moving to the right on a number line increases the value of numbers.
Correct answer: B. 0
Explanation: On a number line, the number farther to the right is greater. Since 0 lies to the right of -4, 0 is greater. Although -1 is greater than -4, it is still less than 0. Exam tip: Zero is greater than every negative number.
Correct answer: B. 2
Explanation: On a number line, the number farther to the right is greater. The number 2 lies to the right of -7, so 2 is greater. Although 0 and -1 are also options, neither is one of the two numbers being compared. Exam tip: Any positive number is greater than any negative number.
Correct answer: C. 7
Explanation: On a number line, numbers less than 8 lie to the left of 8. Among the given options, 7 is to the left of 8, so it is the correct answer. The numbers 9, 10, and 11 are greater than 8 and lie to its right. Exam tip: on a number line, a number farther left is smaller and a number farther right is greater.
Correct answer: B. 15
Explanation: On a number line, the number farther to the right is greater. Since 15 lies to the right of -15, 15 is greater. Although both numbers are equally far from 0, the positive number 15 is greater than the negative number -15. Exam tip: When comparing a positive and a negative number, the positive number is greater.
Correct answer: A. 0
Explanation: The midpoint of two numbers is their average: \(\frac{1+(-1)}{2}=\frac{0}{2}=0\). Therefore, the midpoint of 1 and -1 is 0. The numbers 1 and -1 are the endpoints, not the midpoint. Exam tip: The midpoint of opposite numbers \(a\) and \(-a\) is always 0.
Correct answer: C. -8
Explanation: On the number line, -8 lies to the right of -9, so -8 is greater than -9. Among negative numbers, the number closer to zero is greater; therefore, -10, -11, and -12 are not correct. Exam tip: When comparing negative numbers, the number farther to the right on the number line is greater.
Correct answer: B. 5
Explanation: On a number line, the number farther to the right is greater. Since 5 is greater than -3, 5 lies to the right of -3. Therefore, option B is correct; -3 lies to the left. Exam tip: Moving right on a number line increases the numerical value.
Correct answer: B. -2
Explanation: On a number line, the number to the right is greater. Since -2 lies to the right of -7 and is closer to zero, -2 is greater. “Both are equal” is incorrect because -7 and -2 are different integers. Exam tip: Among negative numbers, the number closer to zero is greater.
Correct answer: D. There is no smallest negative number
Explanation: Negative numbers extend infinitely to the left on the number line. For any negative number, subtracting 1 gives an even smaller negative number; therefore, there is no smallest negative number. Although -10 is smaller than -1, -11 is smaller than -10. Exam tip: Among negative numbers, the number farther to the left is smaller.
Correct answer: C. Both are equally distant
Explanation: On the number line, 3 and -3 lie on opposite sides of zero but at the same distance from it. Their distances from zero are given by their absolute values: \(|3|=3\) and \(|-3|=3\). Therefore, both are equally distant from zero. Exam tip: Use the absolute value to find a number’s distance from zero.
Correct answer: C. 0
Explanation: On a number line, values increase as we move to the right. Since 0 is greater than -1, it lies to the right of -1. The numbers -2, -3 and -4 are less than -1, so they lie to its left. Exam tip: A number positioned farther to the right on the number line always has the greater value.
Correct answer: B. 9
Explanation: On a number line, the number located farther to the right is greater. Since 9 lies to the right of 4, 9 is greater. Option C is incorrect because the two numbers are not equal. Exam tip: For positive numbers, values increase as you move to the right on the number line.
Correct answer: A. -5
Explanation: On a number line, the number farther to the left is smaller. Since -5 lies to the left of 1, -5 is smaller. Option B is incorrect because 1 is to the right and is greater; the two numbers are not equal. Exam tip: when comparing numbers on a number line, the number on the left is the smaller one.
Correct answer: A. 1
Explanation: The left neighbor of a number on the number line is 1 less than that number. Therefore, 2 - 1 = 1, so the correct answer is 1. The number 3 is the right neighbor of 2, not the left neighbor. In an exam, subtract 1 to find the left neighbor.
Correct answer: B. -3
Explanation: On a number line, moving one step to the right increases the number by 1. Therefore, the number immediately to the right of -4 is -3. While -5 is to the left of -4, -2 and 0 are more than one unit to its right. Exam tip: Add 1 to an integer to find its right neighbour.
Correct answer: B. -1
Explanation: Among negative integers, the number farther to the right on the number line is greater. -1 is closest to zero and lies to the right of every other negative integer, so it is the greatest negative integer. Numbers such as -5, -10, and -100 lie to the left of -1 and are smaller. Exam tip: For negative numbers, the one closer to zero is greater.
Correct answer: A. 5
Explanation: The integers strictly between 0 and 6 are 1, 2, 3, 4, and 5, so there are 5 integers. Option B (6) would result from including one of the endpoints, 0 or 6. In such questions, remember that “between” excludes the two given endpoints.
Correct answer: B. 2
Explanation: The opposite of a number lies at the same distance from zero on the other side of the number line. Therefore, the opposite of -2 is 2. The number -1 is not the same distance from zero, and 0 has no opposite side. Exam tip: To find the opposite of a number, change its sign.
Correct answer: A. -7
Explanation: The opposite of a number lies at the same distance from 0 on the other side of the number line. Since 7 is 7 units to the right of 0, its opposite is -7, which is 7 units to the left. The number 7 itself is not its opposite; it is the given number. Exam tip: To find the opposite of a non-zero number, change its sign; the opposite of 0 is 0.
Correct answer: B. 0
Explanation: On the standard number line, 0 is the origin, with positive numbers to its right and negative numbers to its left. Therefore, 0 is the central reference point. The points 1 and -1 are each one unit away from 0, while 10 is farther away. Exam tip: The origin of a number line is always marked as 0.
Correct answer: B. -6
Explanation: On the number line, -6 lies to the right of -9 and is closer to zero, so -6 is greater. The distractor -9 is smaller because it lies farther to the left. Exam tip: Among negative numbers, the number closer to zero is greater.
Correct answer: B. 9
Explanation: On a number line, values decrease as we move to the left. The number immediately to the left of 10 is 9, so the correct answer is 9. Numbers 11 and 12 lie to the right of 10, while 10 itself is at the same point. Exam tip: smaller numbers are placed to the left and larger numbers to the right.
Correct answer: B. -7
Explanation: On a number line, numbers increase as we move to the right. One step to the right of -8 is -7, so -7 is correct. -9 lies to the left of -8, while 0 and -6 are not its immediate neighbours. Exam tip: To find the integer immediately to the right of a number, add 1.
Correct answer: A. 3
Explanation: On a number line, the number positioned farther to the left is smaller. Since 3 lies to the left of 8, 3 is smaller; 8 lies to the right and is therefore greater. Exam tip: moving right on a number line increases the value, while moving left decreases it.
