CBSE Class 7 Mathematics Integers MCQs Set 09

Mathematics Objective Questions and Answers: Chapter 01 Integers

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Multiple Choice Questions

Question 1: The additive identity of integers is:
(a) 1
(b) 0
(c) -1
(d) None of these
Show Answer & Explanation

Answer: (b) 0

Explanation:
1. Adding 0 to any integer leaves it unchanged, so 0 is the additive identity.

Teacher's Note:
1. The additive identity is the number that adds nothing.
2. For multiplication the identity is 1.

Question 2: The multiplicative identity of integers is:
(a) +1
(b) 0
(c) -1
(d) None of these
Show Answer & Explanation

Answer: (a) +1

Explanation:
1. Multiplying any integer by 1 gives the same integer.

Teacher's Note:
1. The multiplicative identity does not change the number it multiplies.
2. 0 would make every product 0.

Question 3: The integer which is its own additive inverse is:
(a) -1
(b) +1
(c) None of these
(d) 0
Show Answer & Explanation

Answer: (d) 0

Explanation:
1. 0 + 0 = 0, so 0 is its own additive inverse; no other integer has this property.

Teacher's Note:
1. Additive inverse of a is -a.
2. -a = a only when a = 0.

Question 4: The value of 5(10 - 9) is:
(a) only 5
(b) only 5 × 10 - 5 × 9
(c) both 5 and 5 × 10 - 5 × 9
(d) neither of these
Show Answer & Explanation

Answer: (c) both 5 and 5 × 10 - 5 × 9

Explanation:
1. 5(10 - 9) = 5 × 1 = 5, and 5 × 10 - 5 × 9 = 50 - 45 = 5, so both forms are equal.

Teacher's Note:
1. This is the distributive property of multiplication over subtraction.
2. Always check both forms numerically.

Question 5: The absolute value of -6 is:
(a) -6
(b) 6
(c) 0
(d) 1/6
Show Answer & Explanation

Answer: (b) 6

Explanation:
1. The absolute value is the distance from zero on the number line, which is 6.

Teacher's Note:
1. Absolute value is never negative.
2. Both -6 and 6 are 6 units from zero.

Question 6: The property shown by 4 + (-7) = (-7) + 4 is:
(a) commutative
(b) closure
(c) associative
(d) distributive
Show Answer & Explanation

Answer: (a) commutative

Explanation:
1. Changing the order of two integers does not change their sum, which is the commutative property.

Teacher's Note:
1. Commutative: a + b = b + a.
2. Associative involves regrouping three numbers.

Question 7: The property shown by [-7 + (-8)] + 9 = -7 + [(-8) + 9] is:
(a) closure
(b) commutative
(c) distributive
(d) associative
Show Answer & Explanation

Answer: (d) associative

Explanation:
1. The grouping of three integers is changed but the order is the same, so it is the associative property.

Teacher's Note:
1. Associative: (a + b) + c = a + (b + c).
2. Both sides here equal -6.

Question 8: The sum of two integers is always an integer. This property is called:
(a) commutative
(b) associative
(c) closure
(d) distributive
Show Answer & Explanation

Answer: (c) closure

Explanation:
1. Staying inside the set after the operation is the closure property.

Teacher's Note:
1. Integers are closed under addition, subtraction and multiplication.
2. They are not closed under division.

Question 9: If a and b are integers (b not 0), then a ÷ b:
(a) is always an integer
(b) may or may not be an integer
(c) is never an integer
(d) is always positive
Show Answer & Explanation

Answer: (b) may or may not be an integer

Explanation:
1. For example 6 ÷ 3 = 2 is an integer but 3 ÷ 6 = 1/2 is not.

Teacher's Note:
1. One counter-example is enough to disprove closure.
2. So integers are not closed under division.

Question 10: The value of (-40) ÷ 10 is:
(a) -4
(b) 4
(c) -400
(d) -30
Show Answer & Explanation

Answer: (a) -4

Explanation:
1. A negative number divided by a positive number gives a negative quotient: 40 ÷ 10 = 4, so the answer is -4.

Teacher's Note:
1. Unlike signs give a negative quotient.
2. Like signs give a positive quotient.

Question 11: The value of 60 ÷ (-6) is:
(a) 10
(b) -360
(c) 54
(d) -10
Show Answer & Explanation

Answer: (d) -10

Explanation:
1. Positive ÷ negative gives a negative result: 60 ÷ 6 = 10, so -10.

Teacher's Note:
1. Divide the numbers first, then fix the sign.
2. Unlike signs give a negative sign.

Question 12: The value of (-49) ÷ (-7) is:
(a) -7
(b) 42
(c) 7
(d) -56
Show Answer & Explanation

Answer: (c) 7

Explanation:
1. Negative ÷ negative is positive: 49 ÷ 7 = 7.

Teacher's Note:
1. Like signs give a positive quotient.
2. Check by multiplying: 7 × (-7) = -49.

Question 13: The value of 13 ÷ [(-4) + 3] is:
(a) 13
(b) -13
(c) 1/13
(d) -7
Show Answer & Explanation

Answer: (b) -13

Explanation:
1. The bracket is (-4) + 3 = -1, so 13 ÷ (-1) = -13.

Teacher's Note:
1. Evaluate the bracket first.
2. Dividing by -1 only changes the sign.

Question 14: The value of [(-48) ÷ 12] ÷ 4 is:
(a) -1
(b) 1
(c) -16
(d) -48
Show Answer & Explanation

Answer: (a) -1

Explanation:
1. (-48) ÷ 12 = -4, and -4 ÷ 4 = -1.

Teacher's Note:
1. Work left to right inside the brackets first.
2. Check: -1 × 4 × 12 = -48.

Question 15: The value of 0 ÷ (-14) is:
(a) -14
(b) 14
(c) not defined
(d) 0
Show Answer & Explanation

Answer: (d) 0

Explanation:
1. Zero divided by any non-zero integer is 0.

Teacher's Note:
1. 0 ÷ a = 0 for a not equal to 0.
2. Division by 0 is the undefined case.

Question 16: Which of the following is the correct value of |18 - 8| ?
(a) 26
(b) -10
(c) 10
(d) 8
Show Answer & Explanation

Answer: (c) 10

Explanation:
1. 18 - 8 = 10 and the absolute value of 10 is 10.

Teacher's Note:
1. Simplify inside the bars first.
2. Then remove the sign if negative.

Question 17: The value of |-5 - 4| is:
(a) -9
(b) 9
(c) 1
(d) -1
Show Answer & Explanation

Answer: (b) 9

Explanation:
1. -5 - 4 = -9, and |-9| = 9.

Teacher's Note:
1. Do the arithmetic inside the bars before taking the absolute value.
2. The result of absolute value is never negative.

Question 18: The value of -|3 - 2| is:
(a) -1
(b) 1
(c) 5
(d) -5
Show Answer & Explanation

Answer: (a) -1

Explanation:
1. |3 - 2| = |1| = 1, and the minus sign outside makes it -1.

Teacher's Note:
1. The sign outside the bars is applied after the absolute value.
2. Do not confuse a minus outside the bars with one inside them.

Question 19: Arranged in ascending order, the integers -20, 13, 4, 0, -5, +5 are:
(a) 0, 4, 5, 13, -5, -20
(b) 13, 5, 4, 0, -5, -20
(c) -5, -20, 0, 4, 5, 13
(d) -20, -5, 0, 4, 5, 13
Show Answer & Explanation

Answer: (d) -20, -5, 0, 4, 5, 13

Explanation:
1. Negative numbers come first, with the larger magnitude being smaller, then 0 and the positives.

Teacher's Note:
1. On the number line numbers increase to the right.
2. -20 is the smallest and 13 is the greatest.

Question 20: Which temperature is higher: -2°C or -4°C ?
(a) -4°C
(b) both are equal
(c) -2°C
(d) cannot be compared
Show Answer & Explanation

Answer: (c) -2°C

Explanation:
1. -2 lies to the right of -4 on the number line, so it is greater.

Teacher's Note:
1. Among negatives the smaller magnitude is greater.
2. -2 > -4.

Question 21: A monkey sits on step 1 of a tank. The water is at step 9. He jumps 3 steps down and then 2 steps up, repeatedly. In how many jumps does he reach the water level?
(a) 9
(b) 11
(c) 10
(d) 12
Show Answer & Explanation

Answer: (b) 11

Explanation:
1. Start at step 1. After jump 1: 4; jump 2: 2; jump 3: 5; jump 4: 3; jump 5: 6; jump 6: 4; jump 7: 7; jump 8: 5; jump 9: 8; jump 10: 6.
2. Jump 11 is 3 steps down: 6 + 3 = 9, the water level.
3. So he needs 11 jumps.

Teacher's Note:
1. Track the net movement of a pair of jumps.
2. Check whether the next single jump reaches the target before completing the pair.

Question 22: From step 9, a monkey climbs 4 steps up and then 2 steps down in every move. In how many jumps does he reach step 1 (the top)?
(a) 5
(b) 4
(c) 6
(d) 8
Show Answer & Explanation

Answer: (a) 5

Explanation:
1. Jump 1: step 5; jump 2: step 7; jump 3: step 3; jump 4: step 5; jump 5: step 1.

Teacher's Note:
1. Up here means towards step 1, so up 4 changes the step number by -4.
2. The last jump (an up jump) reaches the top before any down jump is needed.

Question 23: In a test, +3 marks are given for each correct answer and -2 for each incorrect answer. Ram scored 20 marks with 12 correct answers. The number of incorrect answers is:
(a) 4
(b) 6
(c) 10
(d) 8
Show Answer & Explanation

Answer: (d) 8

Explanation:
1. 12 correct answers give 36 marks. Marks lost = 36 - 20 = 16, so incorrect answers = 16 ÷ 2 = 8.

Teacher's Note:
1. Find the marks from correct answers first.
2. The shortfall is due to the negative marking.

Question 24: In a test, +3 marks are given for each correct answer and -2 for each incorrect answer. Mohan scored -5 marks with 7 correct answers. The number of incorrect answers is:
(a) 8
(b) 10
(c) 13
(d) 15
Show Answer & Explanation

Answer: (c) 13

Explanation:
1. 7 correct answers give 21 marks. To reach -5 he lost 26 marks, so incorrect answers = 26 ÷ 2 = 13.

Teacher's Note:
1. Total = marks for correct + marks for incorrect.
2. 21 + (-2) × 13 = -5.

Question 25: Marks are +5 for a correct answer and -2 for an incorrect one. A student gets four correct and six incorrect answers out of 10. The score is:
(a) 32
(b) 8
(c) 20
(d) -8
Show Answer & Explanation

Answer: (b) 8

Explanation:
1. 4 × 5 + 6 × (-2) = 20 - 12 = 8.

Teacher's Note:
1. Multiply the number of answers by the marks per answer.
2. Then add the positive and negative totals.

Question 26: Marks are +5 for a correct answer and -2 for an incorrect one. A student gets five correct and five incorrect answers. The score is:
(a) 15
(b) 25
(c) 10
(d) -15
Show Answer & Explanation

Answer: (a) 15

Explanation:
1. 5 × 5 + 5 × (-2) = 25 - 10 = 15.

Teacher's Note:
1. Use the same method for each student.
2. Unattempted questions give 0 marks.

Question 27: A company earns a profit of Rs. 11 per bag of white cement and a loss of Rs. 6 per bag of grey cement. It sells 4000 white bags and 8000 grey bags. Its result is:
(a) a profit of Rs. 4000
(b) a loss of Rs. 92000
(c) a profit of Rs. 92000
(d) a loss of Rs. 4000
Show Answer & Explanation

Answer: (d) a loss of Rs. 4000

Explanation:
1. Profit = 4000 × 11 = 44000; loss = 8000 × 6 = 48000. Net = 44000 - 48000 = -4000, a loss of Rs. 4000.

Teacher's Note:
1. Treat profit as positive and loss as negative.
2. Add the two totals.

Question 28: A company earns Rs. 11 profit per white cement bag and has a loss of Rs. 6 per grey cement bag. If it sells 1100 grey bags, the number of white bags needed for neither profit nor loss is:
(a) 500
(b) 660
(c) 600
(d) 1100
Show Answer & Explanation

Answer: (c) 600

Explanation:
1. Loss on grey = 1100 × 6 = 6600. White bags needed = 6600 ÷ 11 = 600.

Teacher's Note:
1. No profit and no loss means the two amounts cancel.
2. Check: 600 × 11 = 6600.

Question 29: A boy has Rs. 350 in his account and deposits Rs. 40 every day for 10 days. The amount at the end of 10 days is:
(a) Rs. 390
(b) Rs. 750
(c) Rs. 400
(d) Rs. 850
Show Answer & Explanation

Answer: (b) Rs. 750

Explanation:
1. Deposits = 40 × 10 = 400. Total = 350 + 400 = 750.

Teacher's Note:
1. Add the total deposits to the opening balance.
2. Multiplication first, then addition.

Question 30: At 12 noon the temperature is 10°C and it falls by 2°C every hour. At what time will it be -8°C?
(a) 9 pm
(b) 6 pm
(c) 8 pm
(d) 10 pm
Show Answer & Explanation

Answer: (a) 9 pm

Explanation:
1. Total fall = 10 - (-8) = 18°C. Time = 18 ÷ 2 = 9 hours after noon, i.e. 9 pm.

Teacher's Note:
1. Find the total change first, then divide by the rate.
2. Noon plus 9 hours is 9 pm.

Question 31: At 12 noon the temperature is 10°C and it falls by 2°C every hour. The temperature at midnight is:
(a) -10°C
(b) -12°C
(c) -24°C
(d) -14°C
Show Answer & Explanation

Answer: (d) -14°C

Explanation:
1. In 12 hours the fall is 24°C. 10 - 24 = -14.

Teacher's Note:
1. Midnight is 12 hours after noon.
2. Subtract the total fall from 10.

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Chapter 01 Integers Objective Questions & Solutions for Class 7 Mathematics

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