Number line

Correct answer: C. \(-20.5\)

Explanation: For negative numbers, the number farther to the right on the number line is greater. \(-20.5\) lies to the right of \(-21\) because it is closer to zero. Therefore, \(-20.5\) is greater. Although \(-20.75\) is also greater than \(-21\), it is not one of the two numbers being compared. Exam tip: among negative numbers, the number with the greater negative value is smaller.

Correct answer: B. \(-0.007\)

Explanation: For negative numbers, the number closer to zero is greater. \(-0.007\) is closer to zero than \(-0.07\), so \(-0.007 > -0.07\). Choosing \(-0.07\) is a common error because, among negative numbers, the one with the larger magnitude is smaller. Exam tip: write \(-0.07\) as \(-0.070\) before comparing decimal places.

Correct answer: A. There are infinitely many rational and infinitely many irrational numbers between them.

Explanation: Between any two distinct real numbers, there are infinitely many rational and infinitely many irrational numbers. Hence every non-zero interval on the number line contains both types. Exam tip: when you see “two distinct real numbers,” recall the density property.

Correct answer: A. \(-2\)

Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-10+6}{2}=\frac{-4}{2}=-2\). Therefore, \(-2\) is correct. \(2\) may result from ignoring the negative sign, but the sum of \(-10\) and \(6\) is \(-4\). Exam tip: first add both numbers carefully, then divide the result by 2.

Correct answer: A. 21

Explanation: The distance between two numbers on a number line is the absolute value of their difference. Thus, \(|4-(-17)|=|21|=21\). Therefore, 21 is correct. Choosing 20 would result from missing the sign change when subtracting a negative number. Exam tip: always take the absolute value of the difference when finding distance.

Correct answer: B. -30

Explanation: The successor of an integer is obtained by adding 1. Thus, \(-31+1=-30\), so -30 is the correct answer. -32 is the predecessor of -31 because it lies one step to the left of -31 on the number line. Exam tip: moving one step right on a number line increases the number by 1.

Correct answer: B. 19

Explanation: The predecessor of a whole number is exactly 1 less than that number. Therefore, the predecessor of 20 is \(20-1=19\). Since 18 is 2 less than 20, it is not the predecessor. Exam tip: subtract 1 from the given number to find its predecessor.

Correct answer: B. \(19\)

Explanation: The absolute value of a number is its distance from 0 on the number line. Since \(-19\) is 19 units away from 0, \(|-19|=19\). \(-19\) is the number itself, not its absolute value. Exam tip: the absolute value of a negative number is always positive.

Correct answer: A. Between any two distinct real numbers, there are infinitely many rational as well as infinitely many irrational numbers.

Explanation: Real numbers are dense on the number line. For example, between 1 and 2, \(3/2\) is rational while \(\sqrt{2}\) is irrational, and infinitely many more exist. Exam tip: unlike integers, real numbers have no consecutive pair.

Correct answer: C. ( -4 )

Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-7+(-1)}{2}=\frac{-8}{2}=-4\). Therefore, \((-4)\) is the correct answer. \((-5)\) is closer to one of the numbers and is not equally distant from both. Exam tip: add the two numbers and divide by 2 to find their midpoint.

Correct answer: B. \(-2.05\)

Explanation: Write \(-2.5\) as \(-2.50\) to compare the decimals. Since \(-2.05\) is closer to zero and lies to the right of \(-2.50\) on the number line, \(-2.05\) is greater. Choosing \(-2.5\) is incorrect because, among negative numbers, the number with the larger magnitude is smaller. Exam tip: Add trailing zeros when needed before comparing decimals.

Correct answer: B. ( 0 )

Explanation: On the number line, the number to the right is greater.
( -0.0009 ) is a negative number and lies to the left of 0, so 0 is greater. “Both are equal” is incorrect because one number is zero and the other is negative. Exam tip: Zero is always greater than any negative number.

Correct answer: A. 7

Explanation: The distance between two numbers on a number line is the absolute value of their difference. Here, \(\lvert -5-(-12)\rvert=\lvert 7\rvert=7\), so 7 is correct. Getting 8 would result from an incorrect subtraction. Exam tip: a distance is always non-negative.

Correct answer: C. उनके बीच अनंत परिमेय तथा अनंत अपरिमेय संख्याएँ होती हैं।

Explanation: Between any two distinct rational numbers, there are infinitely many rational as well as irrational numbers. Hence C is correct; B is false because irrationals also occur between them. Exam tip: real numbers are dense on the number line.

Correct answer: C. \( 0 \)

Explanation: \(0\) is greater than \(-6\) and less than \(1\), so it lies between the two numbers. \(-7\) and \(-8\) are less than \(-6\), while \(2\) is greater than \(1\). Exam tip: To check whether a number lies between two values, verify that it is greater than the left value and less than the right value.

Correct answer: A. 7

Explanation: On a number line, the midpoint of 3 and 11 is their average: \(\frac{3+11}{2}=\frac{14}{2}=7\). Therefore, 7 is correct. The number 6 is not at an equal distance from 3 and 11. Exam tip: To find the midpoint of two numbers, add them and divide by 2.

Correct answer: B. ( 1.1 )

Explanation: (1.1) can be written as 1.10. Comparing 1.10 and 1.01, the tenths digit is 1 in 1.10 but 0 in 1.01. Therefore, (1.1) is greater. (1.01) is smaller, and the two numbers are not equal. Exam tip: When comparing decimals, add zeros at the end if needed so that corresponding place values can be compared.

Correct answer: B. An irrational number located between 1 and 2

Explanation: Since \(1^2=1\) and \(2^2=4\), \(\sqrt{2}\) lies between 1 and 2. As 2 is not a perfect square, \(\sqrt{2}\) is irrational, not a midpoint or an integer. Exam tip: compare neighbouring squares to locate roots.

Correct answer: A. 6

Explanation: On a number line, the distance between two numbers is the absolute value of their difference: \(\left|-8-(-2)\right|=\left|-6\right|=6\). Therefore, the correct answer is 6. The value 8 is only the magnitude of \(-8\), not the distance between the two numbers. Exam tip: a distance is always non-negative.

Correct answer: B. \( -14.9 \)

Explanation: \( -14.9 \) is greater than \( -15 \) because it lies to the right of \( -15 \) on the number line and is closer to zero. Among negative numbers, the number closer to zero is greater. Thus, \( -15 \) is smaller, and the two numbers are not equal. Exam tip: when comparing negative numbers, the number farther right on the number line is greater.

Correct answer: A. \(-3\)

Explanation: The midpoint of two numbers on a number line is their average: \(\frac{-9+3}{2}=\frac{-6}{2}=-3\). Therefore, \(-3\) is correct. \(-6\) is the sum of the two numbers, not their midpoint. Exam tip: add the two numbers and divide by 2 to find their midpoint.

Correct answer: B. 100

Explanation: The successor of an integer is found by adding 1 to it. Thus, 99 + 1 = 100, so 100 is the correct answer. 101 is the second integer after 99, not its immediate successor. Exam tip: always add 1 to find a successor.

Correct answer: B. -51

Explanation: The predecessor of a number is 1 less than the number. Hence, \(-50-1=-51\). \(-49\) is the successor because it is 1 greater than \(-50\). Exam tip: subtract 1 to find a predecessor.

Correct answer: B. 0.6

Explanation: The absolute value of a number is its distance from 0 on the number line, so it cannot be negative. Hence,

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Correct answer: A. ( -4, -2, -1, 3 )

Explanation: In increasing order, numbers are written from smallest to largest. Among negative numbers, the number farther to the left of zero is smaller. Thus, -4 < -2 < -1 < 3, so the correct order is ( -4, -2, -1, 3 ). In option B, -1 is placed before -2, which is incorrect. Exam tip: On a number line, the number to the left is always smaller.