Class 10 Most Important Questions
Chapter -1
VVI MCQs.
1. The decimal expansion of 22/7 is
(a) Terminating
(b) Non-terminating and repeating
(c) Non-terminating and Non-repeating
(d) None of the above
2. For some integer n, the odd integer is represented in the form of:
(a) n
(b) n + 1
(c) 2n + 1
(d) 2n
3. HCF of 26 and 91 is:
(a) 15
(b) 13
(c) 19
(d) 11
4. Which of the following is not irrational?
(a) (3 + √7)
(b) (3 – √7)
(c) (3 + √7) (3 – √7)
(d) 3√7
5. The addition of a rational number and an irrational number is equal to:
(a) rational number
(b) Irrational number
(c) Both
(d) None of the above
6. The multiplication of two irrational numbers is:
(a) irrational number
(b) rational number
(c) Maybe rational or irrational
(d) None
7. If p and q are integers and is represented in the form of p/q, then it is a:
(a) Whole number
(b) Rational number
(c) Natural number
(d) Even number
8. The largest number that divides 70 and 125, which leaves the remainders 5 and 8, is:
(a) 65
(b) 15
(c) 13
(d) 25
9. The least number that is divisible by all the numbers from 1 to 5 is:
(a) 70
(b) 60
(c) 80
(d) 90
10. For some integer m, every even integer is of the form
(a) m
(b) m + 1
(c) 2m
(d) 2m + 1
11. Using Euclid’s division algorithm, the HCF of 231 and 396 is
(a) 32
(b) 21
(c) 13
(d) 33
12. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is
(a) 4
(b) 2
(c) 1
(d) 3
13. The prime factorisation of 96 is
(a) 25 × 3
(b) 26
(c) 24 × 3
(d) 24 × 32
14. n² – 1 is divisible by 8, if n is
(a) an integer
(b) a natural number
(c) an odd integer
(d) an even integer
15. For any two positive integers a and b, HCF (a, b) × LCM (a, b) =
(a) 1
(b) (a × b)/2
(c) a/b
(d) a × b
VVI Short
Q.1: Use Euclid’s division lemma to show that the square of any positive integer is either of form 3m or 3m + 1 for some integer m.
Q.2: Express each number as a product of its prime factors:
(i) 140
(ii) 156
(iii) 3825
(iv) 5005
(v) 7429
Q.3: Given that HCF (306, 657) = 9, find LCM (306, 657).
Q.4: Prove that 3 + 2√5 is irrational.
Q.5: Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
(i) 13/3125 (ii) 17/8 (iii) 64/455 (iv) 15/1600
Q.6: The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p/q what can you say about the prime factors of q?
(i) 43.123456789
(ii) 0.120120012000120000. . .
Q.7: Check whether 6n can end with the digit 0 for any natural number n.
Q.8: What is the HCF of the smallest prime number and the smallest composite number?
Q.9: Using Euclid’s Algorithm, find the HCF of 2048 and 960.
Q.10: Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.
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