THE EDUTECH
CBSE Class 10 Maths Chapter 1 – Real Numbers Important
Objective Questions
Introduction to Real Numbers Guys
1. What should be that least number that should be added to 1056 so that the number is divisible by 23??
(A) 0
(B) 3
(C) 2
(D) 1
The answer is this (C) 2
Solution: We have,
23) 1056 (45
1035
−−−−
21
−−−−
On dividing 1056 by 23, we got the 21 as the remainder.
⇒ If we add 23 - 21 = 2 to the dividend 1056, we will get a number completely divisible
by 23.
∴ Required number = (23 - 21) = 2
2. The difference between the two numbers is 1365. On dividing the larger number by the smaller, we have
Will get 6 as quotient and 15 as the remainder. What is the smaller number?
(A) 360
(B) 295
(C) 270
(D) 240
Answer is : (c) 270
Solution: Let the smaller number be x.
⇒ Larger number = (x+1365)
⇒x+1365=6x+15
⇒5x=1350
⇒x=270
∴hence,The Larger number is (270 + 1365) = 1635
and smaller number is 270.
3. Euclid’s division lemma states that “Given positive integers a and b, there exist unique
integers q and r satisfying a=bq+r". Which of the following is true for r or remainder?
(A) r>a
(B) r<0
(C) 0≤r<b
(D) r>b
Answer: (C) 0≤r<b
Solution: Euclid's division lemma:
Given that two positive integers a and b, there exist unique integers q and r satisfying a = bq + r
where 0≤r<b
Basically, it can be observed that the remainder can never be more than the divisor, and is a
non-negative integer.
4. two positive integers a and b, when divided by 7 and 6 respectively, leave remainders p and q respectively.
What will be the maximum value of p + q?
(A)5
(B)6
(C)12
(D) 11
Answer is: (D) 11
Written by Ayush Tiwari at The Edutech
