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MULTIPLE CHOICE QUESTIONS (MCQS), Mark the correct alternative in each of the following questions., 1. The exponent of 2 in the prime factorisation of 144, is, (a) 4, (b) 5, (c) 6, (d) 3, 2. The LCM of two numbers is 1200. Which of the following cannot be their HCF?, (a) 600, (b) 500, (c) 400, (d) 200, 3. If n = 2* x 3* x 5 x 7, then the number of consecutive zeros in n, where n is a natural, number, is, (a) 2, (b) 3, (c) 4, (d) 7, 4. The sum of the exponents of the prime factors in the prime factorisation of 196, is, (c) 4, (a) 1, (b) 2, (d) 6, 5. The number of decimal places after which the decimal expansion of the rational number, 23, will terminate, is, 2 x 5, (a) 1, (b) 2, (c) 3, (d) 4, 6. If p, and p, are two odd prime numbers such that P > P2, then pi- p is, (a) an even number, (c) an odd prime number, 7. If two positive ingeters a and b are expressible in the form a = pq² and b = p°q; p,q, being prime numbers, then LCM (a, b) is, (b) an odd number, (d) a prime number, %3D, (a) pq, (b) p'g, (c) p'q, (d) p'q
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8. In Q. No. 7, HCF (a, b) is, (a) pq, (b) p°q?, (c) p'q, (d) p°q², 3. If two positive integers m and n are expressible in the form m pq and n = p'q, where, P.q are prime numbers, then HCF (m, n)=, %3D, %3D, (b) pq², (c) p'q, (d) p*q', (a) pq, 10. If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a=, (d) 1, (a) 2, (b) 3, (c) 4, 11. The HCF of 95 and 152, is, (d) 38, (a) 57, 12. If HCF (26, 169) = 13, then LCM (26, 169) =, (a) 26, (b) 1, (c) 19, (b) 52, (c) 338, (d) 13, 13. If a = 2 x 3, b = 2 x 3 x 5, c = 3" x 5 and LCM (a, b, c) = 2° x 3 x 5, then n=, %3D, (a) 1, (b) 2, (c) 3, (d) 4, 14587, 14. The decimal expansion of the rational number, 1250, will terminate after, (a) one decimal place, (c) three decimal place, 15. If p and q are co-prime numbers, then p and q are, (b) two decimal place, (d) four decimal place, (a) coprime, (b) not coprime, (c) even, (d) odd, 16. Which of the following rational numbers have terminating decimal?, 16, 7., (i), 225, (ii), 18, (iii), 21, (iv), 250, (a) (i) and (ii), 17. If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then, the least prime factor of a + b, is, (a) 2, (b) (ii) and (iii), (c) (i) and (iii), (d) (i) and (iv), (b) 3, (c) 5, (d) 10, 18. 3.27 is, (a) an integer, (b) a rational number, (c) anatural number, (d) an irrational number, 19. The smallest number by which 27 should be multiplied so as to get a rational number, is, (a) 27, (b) 3/3, (c) 3, (d) 3, 20. The smallest rational number by which, should be multiplied so that its decimal, expansion terminates after one place of decimal, is, 3, (a), 10, (b), 3, (d), 100, 10, (c) 3
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21. If n is a natural number, then 92 - 42n is always divisible by, (c) both 5 and 13, (a) 5, (b) 13, (d) None of these, [Hint: 92-42 is of the form a - which is divisible by both a -b and a+b., So, 92 - 42" is divisible by both 9-4 = 5 and 9 + 4 = 13.], %3D, 22. If n is any natural number, then 6" - 5" always ends with, (a) 1, (b) 3, (c) 5, (d) 7, [Hint: For any neN, 6" and 5" end with 6 and 5 respectively. Therefore, 6"-5", always ends with 6-5 = 1.], 23. The LCM and HCF of two rational numbers are equal, then the numbers must be, (d) equal, (a) prime, (b) co-prime, (c) composite, 24. 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, (a) 203400, (b) 194400, (c) 198400, (d) 205400, 25. The remainder when the square of any prime number greater than 3 is divided by 6, is, (a) 1, (b) 3, (c) 2, (d) 4, [Hint: Any prime number greater than 3 is of the form 6k +1, where k is a natural, number and (6k + 1) = 36k + 12k +1 = 6k (6k + 2) +1], %3D, !!, 26. For some integer m, every even integer is of the form, (b) m +1, (a) m, (c) 2m, (d) 2m + 1, 27. For some integer q, every odd integer is of the form, (b) q+ 1, (a) 9, (c) 29, (d) 2q+ 1, 28. n-1 is divisible by 8, if n is, (a) an integer, (b) a natural number, (c) anodd integer, (d) an even integer, 33, will terminate after, 29. The decimal expansion of the rational number, 2 x 5, (b) two decimal places, (a) one decimal place, (c) three decimal places(d)more than 3 decimal places, 30. If two positive integers a and b are written as a = r'y and b = xy ; x, y are prime, %3D, numbers, then HCF (a, b) is, (a) xy, (b) xy?, (c) 'y, (d) x*y