In questions 1 to 17, only one of the four options is correct. Write the correct one. Q1: Every integer less than 0 has the sign (a) + (b) - (c) × (d) ÷
Solution:
Ans: (b) The numbers -1, -2, -3, -4, ....... are referred to as negative integers.
All negative integers are less than zero.
Q2: The integer '5 units to the right of 0 on the number line' is (a) +5 (b) -5 (c) +4 (d) - 4
Solution:
Ans: (a)
Q3: The predecessor of the integer -1 is (a) 0 (b) 2 (c) -2 (d) 1
Solution:
Ans: (c) The number which comes immediately before a particular number is called its predecessor. To find the predecessor of a number, subtract one from the given number. So, predecessor of -1 = -1 -1 = -2
Q4: Number of integers lying between -1 and 1 is (a) 1 (b) 2 (c) 3 (d) 0
Solution:
Ans: (a) Integer that comes between -1 and 1 is 0.
Q5: Number of whole numbers lying between -5 and 5 is (a) 10 (b) 3 (c) 4 (d) 5
Solution:
Ans: (d) We know that, whole numbers are starts from 0. Then, number of whole numbers between -5 and 5 are 0, 1, 2, 3, and 4.
Q6: The greatest integer lying between -10 and -15 is (a) -10 (b) -11 (c) -15 (d) -14
Solution:
Ans: (b) In case of negative integer, small number is greater.
Q7: The least integer lying between -10 and -15 is (a) -10 (b) -11 (c) -15 (d) -14
Solution:
Ans: (d) In case of negative integer, big number is smaller.
Q8: On the number line, the integer 5 is located (a) to the left of 0 (b) to the right of 0 (c) to the left of 1 (d) to the left of -2
Solution:
Ans: (b)
Q9: In which of the following pairs of integers, the first integer is not on the left of the other integer on the number line? (a) (-1, 10) (b) (-3, -5) (c) (-5, -3) (d) (-6, 0)
Solution:
Ans: (b)
Q10: The integer with negative sign (-) is always less than (a) 0 (b) -3 (c) -1 (d) -2
Solution:
Ans: (a) Negative integers are always comes left to the 0, so negative integers are always less than 0.
Q11: An integer with positive sign (+) is always greater than (a) 0 (b) 1 (c) 2 (d) 3
Solution:
Ans: (a) Positive integers are always coming right to the 0, so positive integers always greater than 0.
Q12: The successor of the predecessor of -50 is (a) -48 (b) -49 (c) -50 (d) -51
Solution:
Ans: (c) The successor of a whole number is the number obtained by adding 1 to it. To find the predecessor of a number, subtract one from the given number. So, predecessor of - 50 = - 50 - 1 = - 51 Then, successor of - 51 = - 51 + 1 = 50
Q13: The additive inverse of a negative integer (a) is always negative (b) is always positive (c) is the same integer (d) zero
Solution:
Ans: (b)
Q14: Amulya and Amar visited two places A and B respectively in Kashmir and recorded the minimum temperatures on a particular day as -4°C at A and -1°C at B. Which of the following statement is true? (a) A is cooler than B (b) B is cooler than A (c) There is a difference of 2°C in the temperature (d) The temperature at A is 4°C higher than that at B.
Solution:
Ans: (a) We know that, in case of negative integer, big number is smaller.
Q15: When a negative integer is subtracted from another negative integer, the sign of the result (a) is always negative (b) is always positive (c) is never negative (d) depends on the numerical value of the integers
Q16: The statement "When an integer is added to itself, the sum is greater than the integer" is (a) always true (b) never true (c) true only when the integer is positive (d) true for non-negative integers
Solution:
Ans: (c) For example : consider the positive integer 5 = 5 + 5 = 10 In positive integer the sum is greater than the integer. But in negative integer -4 = -4 + (-4) = - 4 - 4 = - 8 In negative integer the sum is less than the integer.
Q17: Which of the following shows the maximum rise in temperature? (a) 0°C to 10°C (b) -4°C to 8°C (c) -15°C to -8°C (d) -7°C to 0°C
Solution:
Ans: (b) In the above question, the most temperature is risen in option B. The difference between two temperatures = 8 - (-4) = 8 + 4 = 12ºC
In questions 18 to 39, state whether the given statements are true (T) or false (F) : Q18: The smallest natural number is zero.
Solution:
False. We know that, natural numbers start from 1, so smallest natural number is 1.
Q19: Zero is not an integer as it is neither positive nor negative.
Solution:
False. Zero is an integer even though it is neither positive nor negative.
Q20: The sum of all the integers between -5 and -1 is -6.
Solution:
False. The sum of all integers between -5 and -1 = -4 -3 -2 = -9
Q21: The successor of the integer 1 is 0.
Solution:
False. The successor of a whole number is the number obtained by adding 1 to it. Successor of 1 = 1 + 1 = 2
Q22: Every positive integer is larger than every negative integer.
Solution:
True. Every positive integer is always larger than every negative integer. Positive integers are always coming right to the 0, so positive integers always greater than 0.
Q23: The sum of any two negative integers is always greater than both the integers.
Solution:
False. In negative integer = -4 + (-6) = - 4 - 6 = - 10 In negative integer the sum is less than both the integer.
Q24: The sum of any two negative integers is always smaller than both the integers.
Solution:
True. In negative integer = -6 + (-7) = - 6 - 7 = - 13 In negative integer the sum is less than both the integer.
Q25: The sum of any two positive integers is greater than both the integers.
Solution:
True. Example: consider the two positive integer 11 and 21 Sum of two integers = 11 + 21 = 32 Therefore, sum of any two positive integers is greater than both the integers.
Q26: All whole numbers are integers.
Solution:
True. Whole numbers start from 0, 1, 2, 3.... so it contains 0 and other positive integers. Hence, all whole numbers are integers.
Q27: All integers are whole numbers.
Solution:
False. Whole numbers start from 0, 1, 2, 3.... Whole numbers can not be negative integers, but integers are both positive and negative numbers. Therefore, all integers are not whole numbers.
Q28: Since 5 > 3, therefore -5 > -3
Solution:
False. In case of negative integer, the bigger number is smaller. So, - 5 < -3
Q29: Zero is less than every positive integer.
Solution:
True.
Zero is always less than positive integer and greater than negative integer.
Q30: Zero is larger than every negative integer.
Solution:
True. Zero is always less than positive integer and greater than negative integer.
Q31: Zero is neither positive nor negative.
Solution:
True. Zero is neither positive nor negative.
Q32: On the number line, an integer on the right of a given integer is always larger than the integer.
Solution:
True. By observing the number line below, we can say that an integer on the right of a given integer is always larger than the integer.
Q33: -2 is to the left of -5 on the number line.
Solution:
False. -2 is to the right of the number line.
Q34: The smallest integer is 0.
Solution:
False. As we know that, 0 is greater than negative integers. So, 0 is not smallest integer.
Q35: 6 and -6 are at the same distance from 0 on the number line.
Solution:
True.
From the above number line we can say that, 6 and -6 are at the same distance of 6 units from 0 on the number line.
Q36: The difference between an integer and its additive inverse is always even.
Solution:
True. Example: Consider an integer 5. Its additive invers is -5 Difference between an integer and its additive inverse = 5 - (-5) = 5 + 5 = 10
Q37: The sum of an integer and its additive inverse is always zero.
Solution:
True. Example: Consider an integer 8. Its additive invers is -8 Sum of an integer and its additive inverse = 8 + (-8) = 8 - 8 = 0
Q38: The sum of two negative integers is a positive integer.
Solution:
False. Sum of two negative integers is always negative. Example: Consider two negative integers - 8 and - 10. Sum of two negative integers = - 8 + (-10) = - 8 - 10 = - 18
Q39: The sum of three different integers can never be zero.
Solution:
False. Example: Consider 3 different integers 5, 10 and -15. Sum of 3 integers = 5 + 10 + (-15) = 5 + 10 - 15 = 15 - 15 = 0 Therefore, the sum of three different integers can be zero.
In questions 40 & 41, fill in the blanks to make the statements true: Q40: On the number line, -15 is to the _______ of zero.
Solution:
On the number line, -15 is to the left of zero. Negative integers are always left to the number zero, thus they are less than 0.
Q41: On the number line, 10 is to the _______ of zero.
Solution:
On the number line, 10 is to the right of zero. Positive integers are always right to the number zero, thus they are greater than zero.
Q42: The additive inverse of 14 is _______.
Solution:
-14 Additive inverse of an integer is obtained by changing the sign of the integer. ∴ Additive inverse of 14 is -14.
Q43: The additive inverse of -1 is _______.
Solution:
1
Q44: The additive inverse of 0 is _______.
Solution:
0
Q45: The number of integers lying between -5 and 5 is _______.
Solution:
9 The integers lying between -5 and 5 are -4, -3, -2, -1, 0, 1, 2, 3, 4 i.e., 9 in number.
Q46: (-11) + (-2) + (-1) = _______.
Solution:
-14 (-11) + (-2) + (-1) = -11 - 2 -1 = -14
Q47: _______ + (-11) + 111 = 130
Solution:
30
Q48: (-80) + 0 + (-90) = _______
Solution:
-170 (-80) + 0 + (-90) = -80 + 0 - 90 = -170
Q49: _______ -3456 = -8910
Solution:
-5454
In questions 50 to 58, fill in the blanks using <, = or > : Q50: (-11) + (-15) _______ 11 + 15
Q59: Match the items of Column I with that of Column II:
Solution:
(i) ➝ (B), (ii) ➝ (E), (iii) ➝ (B), (iv) ➝ (A), (v) ➝ (B) (i) The additive inverse of +2 is -2. (ii) The greatest negative integer is -1. (iii) The greatest negative even integer is -2. (iv) The smallest integer 0 is greater than every negative integer. (v) Predecessor and successor of -1 are -2 and 0 respectively. ∴ Sum = -2 + 0 = -2
Q61: If we denote the height of a place above sea level by a positive integer and depth below the sea level by a negative integer, write the following using integers with the appropriate signs: (a) 200 m above sea level (b) 100 m below sea level (c) 10 m above sea level (d) sea level
Q62: Write the opposite of each of the following: (a) Decrease in size (b) Failure (c) Profit of Rs.10 (d) 1000 A.D. (e) Rise in water level (f) 60 km south (g) 10 m above the danger mark of river Ganga (h) 20 m below the danger mark of the river Brahmaputra (i) Winning by a margin of 2000 votes (j) Depositing Rs.100 in the Bank account (k) 20°C rise in temperature.
Solution:
(a) Increase in size. (b) Success. (c) Loss of ₹ 10 (d) 1000 BC (e) Fall in water level. (f) 60 km north. (g) 10 m below the danger mark of river Ganga. (h) 20 m above the danger mark of the river Brahmaputra. (i) Losing by a margin of 2000 votes. (j) Withdrawing ₹ 100 from the Bank account. (k) 20°C fall in temperature.
Q63: Temperature of a place at 12:00 noon was +5°C. Temperature increased by 3°C in first hour and decreased by 1°C in the second hour. What was the temperature at 2:00 pm?
Solution:
Temperature at 12 : 00 noon = + 5°C ∴ Temperature at 1 : 00 p.m. = 5°C + 3°C = 8°C And temperature at 2 : 00 p.m. = 8°C - 1°C = 7°C
Q64: Write the digits 0, 1, 2, 3, ..., 9 in this order and insert '+' or '-' between them to get the result 3.
Solution:
The digits can be written as 0 - 1 - 2 - 3 - 4 - 5 - 6 + 7 + 8 + 9 = 3
Q65: Write the integer which is its own additive inverse.
Solution:
0 is the integer which is its own additive inverse.
Q66: Write six distinct integers whose sum is 7.
Solution:
1 + 2 + 3 + 6 + (-2) + (-3) = 7 ∴ The six distinct integers are 1, 2, 3, 6, -2 and -3.
Q67: Write the integer which is 4 more than its additive inverse.
Solution:
Let x be the required integer. According to question, x = 4 + (-x), where (-x) is the additive inverse of x. ⇒ x = 4 - x ⇒ x + x = 4 => 2x = 4 => x = 2 ∴ The required integer is 2.
Q68: Write the integer which is 2 less than its additive inverse.
Solution:
Let the required integer be x. According to question, x = (-x) - 2, where -x is the additive inverse of x. ⇒ x = -x - 2 ⇒ x + x = -2 ⇒ 2x = -2 ⇒ x = -1
Q69: Write two integers whose sum is less than both the integers.
Solution:
We can take any two negative integers, i.c., -2 and -4. ∴ Sum = -2 + (-4) = -2 - 4 = -6, which is less than both -2 and -4.
Q70: Write two distinct integers whose sum is equal to one of the integers.
Solution:
Two distinct integers whose sum is equal to one of the integer, then one must be 0 in them. Let us take 0 and 4. ∴ Sum =0 + 4 = 4.
Q71: Using number line, how do you compare (a) two negative integers? (b) two positive integers? (c) one positive and one negative integer?
Solution:
Since, the integer lying on right is greater than the integer lying on left. ∴ In all of the given cases (a), (b) and (c), we can compare by using the number line by observing which one of the given integers lie on the right or left.
Q72: Observe the following : 1 + 2 - 3 + 4 + 5 - 6 - 7 + 8 - 9 = -5 Change one '-' sign as '+' sign to get the sum 9.
Solution:
On observing the given expression, 1 + 2 - 3 + 4 + 5 - 6 - 7 + 8 - 9 = -5, we noticed that (-7) should be replaced by (+7) to get a result of 9. Thus, 1 + 2 - 3 + 4 + 5 - 6 + 7 + 8 - 9 = (1 + 2 + 4 + 5 + 7 + 8) - (3 + 6 + 9) = 27 - 18 = 9
Q73: Arrange the following integers in the ascending order : -2, 1, 0, -3, +4, -5
Solution:
Ascending order of given integers is, -5, -3, -2, 0, 1, 4
Q74:Arrange the following integers in the descending order : -3, 0, -1, -4, -3, -6
Solution:
Descending order of given integers is, 0, -1, -3, -4, -6
Q75: Write two integers whose sum is 6 and difference is also 6.
Solution:
We have, 6 + 0 = 6, 6 - 0 = 6 ∴ The required two integers are 6 and 0.
Q76: Write five integers which are less than -100 but greater than -150.
Solution:
The required five integers which are less than -100 but greater than -150 are -101, -102, -103, -104 and -105.
Q77: Write four pairs of integers which are at the same distance from 2 on the number line.
Solution:
There are many pairs of integers which are at the same distance from 2 i.e., (1, 3), (0, 4), (-1, 5) and (-2, 6)
Q78: The sum of two integers is 30. If one of the integers is -42, then find the other.
Solution:
Let the required integer be x. According to question, x + (-42) = 30 ⇒ x - 42 = 30 ⇒ x = 30 + 42 = 72
Q79: Sum of two integers is -80. If one of the integers is -90, then find the other.
Solution:
Let the required integer be x. According to question, x + (-90) = -80 ⇒ x - 90 = - 80 ⇒ x = -80 + 90 = 10
Q80: If we are at 8 on the number line, in which direction should we move to reach the integer (a) -5 (b) 11 (c) 0?
Solution:
(a) If we are at 8 on the number line, then to reach the integer -5, we must move towards the left on the number line. (b) If we are at 8 on the number line, then to reach the integer 11, we must move towards the right on the number line. (c) If we are at 8 on the number line, then to reach the integer 0, we must move towards the left on the number line.
Q81: Using the number line, write the integer which is (a) 4 more than -5 (b) 3 less than 2 (c) 2 less than -2
Solution:
(a) We want to know an integer 4 more than -5. So, we start from -5 and proceed 4 steps to the right, then we obtain -1 as shown below. Hence, 4 more than -5 is -1. (b) We want to know an integer 3 less than 2. So, we start from 2 and proceed 3 steps to the left, then we obtain -1 as shown below. Hence, 3 less than 2 is -1. (c) We want to know an integer 2 less than -2. So, we start from -2 and proceed 2 steps to the left, then we obtain -4 as shown below. Hence, 2 less than -2 is -4.
1. What are positive and negative integers and how do I tell them apart?
Ans. Positive integers are whole numbers greater than zero (1, 2, 3...), while negative integers are less than zero (-1, -2, -3...). Zero is neither positive nor negative. On a number line, positive integers appear to the right of zero and negative integers to the left, making them easy to identify visually.
2. How do I add and subtract integers with different signs in CBSE exams?
Ans. When adding integers with different signs, subtract the smaller absolute value from the larger and keep the sign of the larger number. For subtraction, change the sign of the integer being subtracted and follow addition rules. For example, 5 + (-3) = 2 and 5 - (-3) = 8. This approach works consistently across all integer operations.
3. What's the difference between absolute value and integer value?
Ans. Absolute value is the distance of a number from zero, always positive or zero (denoted |x|). Integer value refers to the actual number itself, which can be positive or negative. For instance, |-5| = 5, but the integer value of -5 remains -5. Understanding this distinction is crucial for solving integer problems accurately.
4. Why do two negative integers multiply to give a positive answer?
Ans. Multiplying two negative integers yields a positive result because negation reverses twice. Think of it as reversing direction twice: you end up facing the original direction. For example, (-3) × (-4) = 12. This pattern holds because the product of same-signed numbers is always positive, while opposite signs produce negative results.
5. How should I use number lines to solve integer problems for my TET preparation?
Ans. Number lines visually represent integer operations: start at the first number, then move right for positive values and left for negative values. For addition, count steps forward; for subtraction, count backward. This concrete method helps clarify integer concepts and prevents errors. Refer to visual worksheets and mind maps on EduRev to practise this technique effectively.
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