Real Number Problems And Solutions

Given below are the Class 10 Maths Problems for Real Numbers
a. HCF and LCM problems
b. Prime Factorisation Problems
c. Division Problems
d. Multiple Choice Problems
e. Word Problems
Question 1
In a seminar, the number of participants in Hindi, English and Mathematics are 60, 84 and 108, respectively. Find the minimum number of rooms required if in each room the same numbers of participants are to be seated and all of them being in the same subject.

Question 2
If the HCF of 657 and 963 is expressible in the form $657x + 963 \times (-15)$, find x.

Question 3
Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.

Question 4
Find the greatest umbers that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.
Question 5
Find the greatest number which divides 2011 and 2623 leaving remainder 9 and 5 respectively.
Question 6
Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.
Question 7
Find the smallest number which when increased by 17 is exactly divisible by both 520 and 468.
Question 8
A circular field has a circumference of 360km. Three cyclists start together and can cycle 48, 60 and 72 km a day, round the field. When will they meet again?
Question 9
If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, then the product of two numbers is.
Question 10
The HCF of two numbers is 145 and their LCM is 2175. If one number is 725, find the other.
Question 11
If two positive integers a and b are written as
$a = x^3y^2$ and $b = xy^3$ . x, y are prime numbers, then HCF (a, b) is
(A) $xy$
(B) $xy^2$
(D) $x^2y^2$

Question 12
If two positive integers p and q can be expressed as
p = ab2 and q a3 a, b being prime numbers, then LCM (p, q) is
(A) ab
(C)  a3b2
(D) a3b3

Question 13
If HCF (26, 169) = 13, then LCM (26, 169) =?
Question 14
If 3 is the least prime factor of number a and 7 is the least prime factor of numbers b, then the least prime factor of a + b, is.

Question 15
Euclid's Division Lemma states that if p and q are any two positive integers, then there exist unique integers r and s such that
(A) $p = qr + s, 0 \leq s < q$
(B) $p = qr + s, 0 < s \leq q$
(C) $p= qr + s, 0 \leq r < q$
(D) $p = qr + s, 0 < r \leq q$
Question 16
Two tankers contain 583 litres and 242 litres of petrol respectively. A container with maximum capacity is used which can measure the petrol of either tanker in exact number of litres. How many containers of petrol are there in the first tanker.

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Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20