Class 10 Ch-1 Real Numbers MCQ TEST/QUIZ Post author:KeyIndia Education Post published:September 21, 2022 Post category:Aptitude / CBSC Maths Class 10th / NCERT / TEST/QUIZ Post comments:0 Comments 0% 2 votes, 5 avg 4 Created on August 10, 2022 By KeyIndia EducationCBSC/NCERT CLASS X MATHS Class 10 Ch-1 Real Numbers MCQ TEST/QUIZ 1 / 21 1. The prime factorisation of 96 is A. 2^6 B. 2^4 × 32 C. 2^4 × 3 D. 2^5 × 3 The prime factorisation of 96 is:96 = 2 × 2 × 2 × 2 × 2 × 3 = 25 × 3 2 / 21 2. The sum or difference of two irrational numbers is always A. rational B. irrational C. not determined D. rational or irrational 3 / 21 3. Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy A. 0 ≤ r < b B. 0 < r ≤ b C. 0 < r < b D. 1 < r < b Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy 0 ≤ r < b. 4 / 21 4. For any two positive integers a and b, HCF (a, b) × LCM (a, b) = A. (a × b)/2 B. a × b C. 1 D. a/b For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b. 5 / 21 5. The decimal expansion of 22/7 is A. Non-terminating and repeating B. None of the above C. Non-terminating and Non-repeating D. Terminating 22/7 = 3.14285714286.. 6 / 21 6. n² – 1 is divisible by 8, if n is A. an even integer B. an odd integer C. an integer D. a natural number We know that an odd number in the form (2Q + 1) where Q is a natural number ,so, n² -1 = (2Q + 1)² -1= 4Q² + 4Q + 1 -1= 4Q² + 4QSubstituting Q = 1, 2,…When Q = 1,4Q² + 4Q = 4(1)² + 4(1) = 4 + 4 = 8 , it is divisible by 8.When Q = 2,4Q² + 4Q = 4(2)² + 4(2) =16 + 8 = 24, it is also divisible by 8 .When Q = 3,4Q² + 4Q = 4(3)² + 4(3) = 36 + 12 = 48 , divisible by 8It is concluded that 4Q² + 4Q is divisible by 8 for all natural numbers.Hence, n² -1 is divisible by 8 for all odd values of n. 7 / 21 7. The multiplication of two irrational numbers is: A. Rational number B. Maybe rational or irrational C. None D. Irrational number The multiplication of two irrational numbers is maybe rational or irrational. 8 / 21 8. For some integer m, every even integer is of the form A. m + 1 B. 2m + 1 C. 2m D. m For some integer m, every even integer is of the form 2m. 9 / 21 9. The largest number that divides 70 and 125, which leaves the remainders 5 and 8, is: A. 65 B. 25 C. 15 D. 13 70 – 5 = 65 and 125 – 8 = 117 10 / 21 10. The decimal expansion of 22/7 is A. None of the above B. Non-terminating and repeating C. Terminating D. Non-terminating and Non-repeating 22/7 = 3.14285714286.. 11 / 21 11. HCF of 26 and 91 is: A. 15 B. 19 C. 11 D. 13 The prime factorisation of 26 and 91 is;26 = 2 x 1391 = 7 x 13Hence, HCF (26, 91) = 13 12 / 21 12. If p and q are integers and is represented in the form of p/q, then it is a: A. Natural number B. Even number C. Rational number D. Whole number 13 / 21 13. The values of the remainder r, when a positive integer a is divided by 3 are A. Only 1 B. 0, 1, 2 C. Only 0 or 1 D. 1, 2 According to Euclid’s division lemma,a = 3q + r, where 0 ≤ r < 3 and r is an integer.Therefore, the values of r can be 0, 1 or 2. 14 / 21 14. Using Euclid’s division algorithm, the HCF of 231 and 396 is A. 33 B. 21 C. 13 D. 32 396 > 231Using Euclid’s division algorithm,396 = 231 × 1 + 165231 = 165 × 1 + 66165 = 66 × 2 + 3366 = 33 × 2 + 0 15 / 21 15. If set A = {1, 2, 3, 4, 5,…} is given, then it represents: A. Rational Numbers B. Natural numbers C. Whole numbers D. Complex numbers If set A = {1, 2, 3, 4, 5,…} is given, then it represents natural numbers. 16 / 21 16. The addition of a rational number and an irrational number is equal to: A. Rational number B. Both C. None of the above D. Irrational number The addition of a rational number and an irrational number is equal to irrational number. 17 / 21 17. For some integer n, the odd integer is represented in the form of: A. n B. 2n + 1 C. n + 1 D. 2n Since 2n represents the even numbers, hence 2n + 1 will always represent the odd numbers. Suppose if n = 2, then 2n = 4 and 2n + 1 = 5. 18 / 21 18. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is A. 2 B. 4 C. 3 D. 1 117 > 65117 = 65 × 1 + 5265 = 52 × 1 + 1352 = 13 × 4 + 0Therefore, HCF(65, 117) = 13According to the given,65m – 117 = 1365m = 117 + 1365m = 130m = 130/65 = 2 19 / 21 19. The decimal expansion of the rational number 23/(22 . 5) will terminate after A. one decimal place B. three decimal places C. more than 3 decimal places D. two decimal places 23/(22 . 5) = (23 × 5)/(22 . 52) = 115/(10)2 = 115/100 = 1.15Hence, 23/(22 . 5) will terminate after two decimal places. 20 / 21 20. Which of the following is not irrational? A. (3 + √7) (3 – √7) B. 3√7 C. (3 + √7) D. (3 – √7) we solve, (3 + √7) (3 – √7), we get;(3 + √7) (3 – √7) = 32 – (√7)2 = 9 – 7 = 2 [By a2 – b2 = (a – b) (a + b)] 21 / 21 21. The least number that is divisible by all the numbers from 1 to 5 is: A. 80 B. 70 C. 90 D. 60 Explanation: The least number will be LCM of 1, 2, 3, 4, 5.Hence, LCM (1, 2, 3, 4, 5) = 2 x 2 x 3 x 5 = 60 Your score isThe average score is 15% LinkedIn Facebook VKontakte 0% Restart quiz Send feedback Please Share This Share this content Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window You Might Also Like Class 10 Chapter 15 Probability TEST/QUIZ September 21, 2022 Class 10 Science Chapter 1 Chemical Reactions and Equations| MCQ Test June 9, 2022 CLASS 9: THE FUNDAMENTAL UNIT OF LIFE FILL IN THE BLANKS QUESTIONS November 20, 2021 Leave a Reply Cancel replyCommentEnter your name or username to comment Enter your email address to comment Enter your website URL (optional) Save my name, email, and website in this browser for the next time I comment.
