CBSE Maths › Class 10 PYQs › Real Numbers

Real Numbers: 4 marks Questions (CBSE Class 10)

2 different 4 marks questions on Real Numbers from CBSE Class 10 Maths board exams 2022–2026, newest first.

1 mark (104)2 marks (48)3 marks (49)4 marks (2)

Q384 marksCase StudyReal Numbers CBSE 2024 · Standard 30/3/1

Teaching Mathematics through activities is a powerful approach that enhances students’ understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number, the last student got 173250.
Now, Mukta asked some questions as given below to the students :
(i) What is the least prime number used by students ? (1)
(ii) How many students are in the class ? (2)
OR What is the highest prime number used by students ? (2)
(iii) Which prime number has been used maximum times ? (1)

Show answer & solution

Answer: (i) 3 (ii) 7; OR 11 (iii) 5

$173250 = 2 \times 86625 = 2 \times 3^{2} \times 5^{3} \times 7 \times 11$ .
The teacher's 2 accounts for the factor 2; the students multiplied by $3, 3, 5, 5, 5, 7, 11$ .
(i) Least prime used by students = 3.
(ii) Number of primes used = 2 + 3 + 1 + 1 = 7, so there are 7 students.
OR: Highest prime used = 11.
(iii) 5 is used the maximum number of times (three times).

Also asked in: 2024 Standard 30/3/2, 2024 Standard 30/3/3

Q374 marksCase StudyReal Numbers CBSE 2023 · Basic 430/4/1

Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought 36 apples and 60 bananas and decided to distribute fruits equally among all.
Based on the above information, answer the following questions :
(i) How many guests Khushi can invite at the most ? (1)
(ii) How many apples and bananas will each guest get ? (1)
(iii) (a) If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most ? (2)
OR (b) If the cost of 1 dozen of bananas is ₹ 60, the cost of 1 apple is ₹ 15 and cost of 1 mango is ₹ 20, find the total amount spent on 60 bananas, 36 apples and 42 mangoes. (2)

Show answer & solution

Answer: (i) 12 (ii) 3 apples and 5 bananas (iii) (a) 6 OR (b) ₹ 1680

(i) $36 = 2^{2} \times 3^{2}$ , $60 = 2^{2} \times 3 \times 5$ ; HCF $= 2^{2} \times 3 = 12$ guests.
(ii) Apples: $36 \div 12 = 3$ ; bananas: $60 \div 12 = 5$ .
(iii) (a) $42 = 2 \times 3 \times 7$ ; HCF(36, 60, 42) $= 2 \times 3 = 6$ guests.
(iii) (b) Bananas: 60 = 5 dozen, cost $5 \times 60 = ₹ 300$ ; apples: $36 \times 15 = ₹ 540$ ; mangoes: $42 \times 20 = ₹ 840$ .
Total $= 300 + 540 + 840 = ₹ 1680$ .

Also asked in: 2023 Basic 430/4/2, 2023 Basic 430/4/3

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