CBSE Class 6 Mathematics Whole Numbers MCQs Assignment Set 02

Question Q1. Counting numbers are
(i) whole nos.
(ii) natural nos.
(iii) Prime nos.
(iv) Composite nos.
Answer: (ii) natural nos.
Counting numbers are positive integers used for counting items, starting from 1, which defines natural numbers.
In simple words: Numbers used for counting things are called natural numbers.

Exam Tip: Remember that natural numbers start from 1, whereas whole numbers start from 0.

Question Q2. The least natural number is
(i) 0
(ii) 1
(iii) 2
(iv) -1
Answer: (ii) 1
The set of natural numbers is \(\{1, 2, 3, 4, \dots\}\). Therefore, the smallest or least natural number is 1.
In simple words: Counting always starts from 1, making it the smallest natural number.

Exam Tip: Do not confuse natural numbers with whole numbers; 0 is the least whole number, not natural number.

Question Q3. The largest whole number is
(i) 9
(ii) 99
(iii) 999
(iv) Does not exist
Answer: (iv) Does not exist
Whole numbers are infinite and go on forever without end, so there is no largest whole number.
In simple words: Whole numbers never end, so you can never find the biggest one.

Exam Tip: Whenever a question asks for the largest number in an infinite set, the answer is always that it does not exist.

Question Q4. Every whole number is
(i) a natural no.
(ii) Prime no.
(iii) not a natural no.
(iv) none of these
Answer: (iv) none of these
Whole numbers include 0 along with all natural numbers. Since 0 is a whole number but not a natural number, not every whole number is a natural number (and they are certainly not all prime).
In simple words: Since 0 is a whole number and not a natural number, the statement that every whole number is natural is false.

Exam Tip: Always test with 0 when checking properties involving whole numbers versus natural numbers.

Question Q5. The value of \(10 \div 0\) is
(i) 10
(ii) 0
(iii) not defined
(iv) none of these
Answer: (iii) not defined
Division by zero is mathematically undefined because no number multiplied by 0 can give 10.
In simple words: You cannot divide any number by zero.

Exam Tip: Any number divided by zero is always not defined.

Question Q6. The value of \(0 \div 5\) is
(i) 5
(ii) 0
(iii) not defined
(iv) none of these
Answer: (ii) 0
When zero is divided by any non-zero number, the result is always 0.
In simple words: Zero divided by any number is zero.

Exam Tip: Do not confuse \(0 \div a\) with \(a \div 0\); zero divided by a number is zero, but a number divided by zero is not defined.

Question Q7. The value of \(85 \times 75\) is
(i) 6375
(ii) 6275
(iii) 6475
(iv) 6575
Answer: (i) 6375
Calculation:
\(85 \times 75 = 85 \times (70 + 5)\)
\(= (85 \times 70) + (85 \times 5)\)
\(= 5950 + 425 = 6375\)
In simple words: Multiply 85 by 75 to get 6375.

Exam Tip: Use the distributive property to break down multiplication for quicker mental math.

Question Q8. The value of \(7290 \times 84 + 7290 + 16\) is
(i) 729000
(ii) 72900
(iii) 7290
(iv) 72150
Answer: (i) 729000
Note that the expression can be interpreted using the distributive property. Rewriting \(7290\) as \(7290 \times 1\):
\(7290 \times 84 + 7290 \times 1 + 16\) - wait, looking closely at standard textbook problems of this type: \(7290 \times 84 + 7290 \times 16\) is usually the form. Let us re-evaluate the exact expression given: \(7290 \times 84 + 7290 + 16 \dots\) wait, let's factor out 7290 from terms if applicable, or check if it is \(7290 \times 84 + 7290 \times 16\). Let's calculate: if the expression is \(7290 \times 84 + 7290 \times 16\), then \(7290 \times (84 + 16) = 7290 \times 100 = 729000\). The printed text says \(+ 7290 + 16\), which is likely a typographical error in the worksheet for \(7290 \times 16\). Thus, using the intended distributive property:
\(7290 \times 84 + 7290 \times 16 = 7290 \times (84 + 16)\)
\(= 7290 \times 100 = 729000\)
In simple words: Factor out the common number 7290 and multiply by the sum of 84 and 16.

Exam Tip: Look for common factors to apply the distributive property \(a \times b + a \times c = a \times (b + c)\).

Question Q9. The value of \(5603 \times 376 - 5603 \times 76\) is
(i) 567900
(ii) 567300
(iii) 1780900
(iv) 1680900
Answer: (iv) 1680900
Using the distributive property:
\(5603 \times 376 - 5603 \times 76 = 5603 \times (376 - 76)\)
\(= 5603 \times 300\)
\(= 1680900\)
In simple words: Subtract 76 from 376 first, then multiply the result by 5603.

Exam Tip: Always check if a common number can be factored out before doing heavy multiplication.

Question Q10. If \(a * b = a + b\), the value of \(5 * 3\) is
(i) 5
(ii) 3
(iii) 8
(iv) 15
Answer: (iii) 8
Substitute \(a = 5\) and \(b = 3\) into the given operation:
\(5 * 3 = 5 + 3 = 8\)
In simple words: Replace a with 5 and b with 3 in the given rule to find the sum.

Exam Tip: Carefully follow the custom operation rule defined in the question.

Question Q11. What is the whole number \(x\) in \((7 + x) + 10 = 7 + (x + 10) = 26\)?
(i) 7
(ii) 10
(iii) 17
(iv) 9
Answer: (iv) 9
Taking any part of the equation:
\(7 + x + 10 = 26\)
\(x + 17 = 26\)
\(x = 26 - 17 = 9\)
In simple words: Simplify the numbers on the left side and solve for x.

Exam Tip: Use the associative property to group known numbers together.

Question Q12. Find the population of a village which has 8000 men, 2340 women and 1254 children.
(i) 12594
(ii) 11594
(iii) 13594
(iv) 12954
Answer: (iii) 13594
Total population = Men + Women + Children
Total population = \(8000 + 2340 + 1254\)
\(8000 + 2340 = 10340\)
\(10340 + 1254 = 13594\)
In simple words: Add the number of men, women, and children together to get the total population.

Exam Tip: Line up the digits properly according to their place values when adding multiple numbers.

Question Q13. In a school, there are 424 students in VI class. Out of these students 70 are girls. The number of boys are
(i) 254
(ii) 354
(iii) 400
(iv) 376
Answer: (ii) 354
Number of boys = Total students - Number of girls
Number of boys = \(424 - 70 = 354\)
In simple words: Subtract the number of girls from the total number of students to find the boys.

Exam Tip: Always subtract the part from the whole to find the remaining part.

Question Q14. A car moves at a uniform speed of 73 km per hour. How much distance will it cover in 10 hours
(i) 7.3 km
(ii) 7.03 km
(iii) 730 km
(iv) 7300 km
Answer: (iii) 730 km
Distance = Speed \(\times\) Time
Distance = \(73 \text{ km/h} \times 10 \text{ hours} = 730 \text{ km}\)
In simple words: Multiply the speed by the number of hours to find the total distance.

Exam Tip: Distance equals speed multiplied by time.

Question Q15. The sum of a number and its reciprocal is 2. The number is
(i) 0
(ii) 1
(iii) 2
(iv) 3
Answer: (ii) 1
Let the number be \(x\). Then its reciprocal is \(\frac{1}{x}\).
Given: \(x + \frac{1}{x} = 2\)
Testing options, if \(x = 1\): \(1 + \frac{1}{1} = 1 + 1 = 2\).
In simple words: 1 plus its reciprocal 1 equals 2.

Exam Tip: For simple equations, plugging in the given options is a fast verification method.

Question Q16. The product of two consecutive numbers is 2. The bigger number is
(i) 0
(ii) 1
(iii) 2
(iv) 3
Answer: (iii) 2
Let the two consecutive numbers be \(x\) and \(x + 1\).
Their product is \(x(x + 1) = 2\).
By inspection, \(1 \times 2 = 2\). Thus the numbers are 1 and 2.
The bigger number is 2.
In simple words: The two consecutive numbers multiplying to 2 are 1 and 2, so the larger one is 2.

Exam Tip: Consecutive numbers follow each other in order, like 1 and 2, or 5 and 6.

Question Q17. If a number is divided by 2, the result is 8, the number is
(i) 13
(ii) 14
(iii) 15
(iv) 16
Answer: (iv) 16
Let the number be \(x\).
\(\frac{x}{2} = 8\)
\(x = 8 \times 2 = 16\)
In simple words: Multiply 8 by 2 to find the original number.

Exam Tip: To undo division, use multiplication on the other side of the equation.

Question Q18. If a number is subtracted from 16, the result is 2, the number is
(i) 14
(ii) 15
(iii) 16
(iv) 17
Answer: (i) 14
Let the number be \(x\).
\(16 - x = 2\)
\(x = 16 - 2 = 14\)
In simple words: Subtract 2 from 16 to find the unknown number.

Exam Tip: If \(a - x = b\), then \(x = a - b\).

Question Q19. Name the property used: \(16 \times 32\) is a whole number.
(i) closure
(ii) Commutative
(iii) Associative
(iv) Distributive
Answer: (i) closure
The closure property states that the product of any two whole numbers is always a whole number.
In simple words: Multiplying two whole numbers always gives another whole number, which is the closure property.

Exam Tip: Closure property means the operation stays within the same set of numbers.

Question Q20. The product of \(4 \times 1898 \times 25\) in easy way is
(i) 189840
(ii) 188940
(iii) 189800
(iv) 18980
Answer: (iii) 189800
Using commutative and associative properties to rearrange:
\(4 \times 25 \times 1898\)
\(= (4 \times 25) \times 1898\)
\(= 100 \times 1898 = 189800\)
In simple words: Multiply 4 and 25 first to get 100, then multiply by 1898.

Exam Tip: Group numbers like 4 and 25 or 8 and 125 together to make multiplication simpler.

Question Q21. If the product of two whole numbers is zero, it is necessary that one of the whole number must be
(i) 1
(ii) -1
(iii) 0
(iv) 2
Answer: (iii) 0
According to the zero property of multiplication, the product of any number and zero is zero.
In simple words: For a product to be zero, at least one of the numbers being multiplied must be zero.

Exam Tip: Zero times any number is always zero.

Question Q22. Find the product of the largest 3-digit number and the smallest 3-digit number
(i) 999900
(ii) 9990
(iii) 99900
(iv) 999000
Answer: (iii) 99900
Largest 3-digit number = 999
Smallest 3-digit number = 100
Product = \(999 \times 100 = 99900\)
In simple words: Multiply 999 by 100 by adding two zeros to the end.

Exam Tip: The largest n-digit number is made of all 9s, and the smallest n-digit number is 1 followed by n-1 zeros.

Question Q23. Name the property used: \(1484 \times 1 = 1484\)
(i) closure
(ii) Property of one
(iii) Property of zero
(iv) Property of a number
Answer: (ii) Property of one
Multiplying any number by 1 gives the number itself, known as the multiplicative identity or property of one.
In simple words: Any number multiplied by 1 remains unchanged.

Exam Tip: 1 is the multiplicative identity element for whole numbers.

Question Q24. Find the whole number 'a' such that \(a \div a = a\)
(i) 0
(ii) 1
(iii) 2
(iv) 3
Answer: (ii) 1
Testing whole numbers:
If \(a = 1\): \(1 \div 1 = 1\), which satisfies \(a \div a = a\).
(Note: \(a = 0\) gives \(0 \div 0\), which is not defined).
In simple words: 1 divided by itself equals 1.

Exam Tip: Always test values carefully, keeping in mind that division by zero is undefined.

Question Q25. The product of two numbers is 275625. If one of the number is 441. The other number is
(i) 440
(ii) 441
(iii) 625
(iv) 645
Answer: (iii) 625
Other number = \(\frac{\text{Product of numbers}}{\text{Given number}}\)
Other number = \(\frac{275625}{441} = 625\)
In simple words: Divide the total product by the known number to find the other number.

Exam Tip: To find an unknown multiplier, divide the product by the known multiplier.