16. Practice Question Set B — Moderate / Exam Level

B1. (Unit Digit — Combined Powers) Find the unit digit of (127)^173 + (56)^43. (a) 1 (b) 3 (c) 5 (d) 7

B2. (HCF of Three Numbers) Find the HCF of 144, 180, and 192. (a) 6 (b) 12 (c) 24 (d) 36

B3. (HCF–LCM Relation) The LCM of two numbers is 495 and their HCF is 5. If one of the numbers is 45, find the other. (a) 45 (b) 55 (c) 65 (d) 75

B4. (Number of Factors) Find the number of factors of 1,800. (a) 24 (b) 30 (c) 36 (d) 40

B5. (Remainder — Cyclicity of Remainders) Find the remainder when 2^100 is divided by 7. (a) 1 (b) 2 (c) 4 (d) 6

B6. (Last Two Digits) Find the last two digits of 17^400. (a) 01 (b) 17 (c) 21 (d) 89

B7. (Remainder of a Square) A number, when divided by 5, gives a remainder of 3. What is the remainder when its square is divided by 5? (a) 1 (b) 2 (c) 3 (d) 4

B8. (HCF with Remainder Condition) Find the largest number that divides 245 and 1,029, leaving a remainder of 5 in each case. (a) 8 (b) 16 (c) 32 (d) 64

B9. (Sum Formula + Remainder) The sum of the first 15 natural numbers is divided by 8. Find the remainder. (a) 0 (b) 2 (c) 4 (d) 6

B10. (Even Factors) If N = 2³ × 3² × 5, how many factors of N are even? (a) 12 (b) 16 (c) 18 (d) 20

B11. (LCM with Remainder Condition) Find the smallest number which, when divided by 6, 9, and 12, leaves a remainder of 4 in each case. (a) 36 (b) 40 (c) 44 (d) 48

B12. (Remainder via Cyclicity) Find the remainder when 7^84 is divided by 5. (a) 1 (b) 2 (c) 3 (d) 4

B13. (Ratio, HCF, LCM) Two numbers are in the ratio 3:4. Their HCF is 5. Find their LCM. (a) 15 (b) 30 (c) 60 (d) 90

B14. (Trailing Zeros in Factorial) Find the number of zeros at the end of 100!. (a) 20 (b) 22 (c) 24 (d) 26

B15. (Smallest Number Divisible by Given Numbers) Find the smallest 4-digit number exactly divisible by 12, 15, and 18. (a) 1080 (b) 1170 (c) 1260 (d) 990

B16. (Unit Digit — Combined Powers) Find the unit digit of 18^47 + 24^36. (a) 6 (b) 7 (c) 8 (d) 9

B17. (HCF of Three Numbers) Find the HCF of 210, 315, and 462. (a) 7 (b) 21 (c) 35 (d) 42

B18. (LCM — Three-Number Word Problem) Three measuring rods are 45 cm, 50 cm, and 75 cm long. Find the least length of cloth that can be measured an exact whole number of times using any one of the rods. (a) 225 cm (b) 450 cm (c) 900 cm (d) 1350 cm

B19. (Remainder — Large Power) Find the remainder when 5^203 is divided by 7. (a) 1 (b) 2 (c) 3 (d) 5

B20. (Last Two Digits) Find the last two digits of 63^75. (a) 07 (b) 27 (c) 43 (d) 69

B21. (Odd Factors) Find the number of odd factors of 2² × 3³ × 5² × 7. (a) 12 (b) 18 (c) 24 (d) 36

B22. (Indices) Simplify: 16^0.75 (a) 4 (b) 6 (c) 8 (d) 16

B23. (Negative Indices) Simplify: (2^(−3) × 2⁷) ÷ 2^(−2) (a) 16 (b) 32 (c) 64 (d) 128

B24. (Base Conversion) Convert 37 (base 10) to base 5. (a) 120 (b) 121 (c) 122 (d) 132

B25. (Trailing Zeros) Find the number of trailing zeros in 250!. (a) 58 (b) 60 (c) 62 (d) 64

B26. (Missing Digit — Divisibility by 11) Find the smallest value of digit x for which the number 4823x1 is divisible by 11. (a) 3 (b) 5 (c) 6 (d) 9

B27. (Ratio, HCF, LCM) The ratio of two numbers is 5:6 and their LCM is 480. Find their HCF. (a) 8 (b) 12 (c) 16 (d) 20

B28. (HCF with Remainder Condition) Find the largest number that divides 70 and 125, leaving remainders 5 and 8 respectively. (a) 5 (b) 13 (c) 15 (d) 26

B29. (Number Series — Wrong Number) Find the wrong number in the series: 2, 5, 10, 17, 26, 37, 50, 64 (a) 17 (b) 26 (c) 50 (d) 64

B30. (HCF–LCM of Co-prime Numbers) The product of two co-prime numbers is 117. Find their LCM. (a) 9 (b) 13 (c) 39 (d) 117