This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Solve Question 6. The units digit of a perfect square can only be 0, 1, 4, 5, 6, or 9. Checking the given options: (a) 6: Can be a units digit of a perfect square (e.g., 4^2 = 16). (b) 1: Can be a units digit of a perfect square (e.g., 1^2 = 1). (c) 9: Can be a units digit of a perfect square (e.g., 3^2 = 9). (d) 8: Cannot be a units digit of a perfect square. The correct option is (d). (d) 8 Step 2: Solve Question 7. The number of non-perfect square numbers between n^2 and (n+1)^2 is given by the formula 2n. Here, n = 25. Number of numbers between 25^2 and 26^2 is 2 × 25 = 50. The correct option is (b). (b) 50 Step 3: Solve Question 8. The sum of the first n odd natural numbers is n^2. The series 1+3+5+... to n terms represents the sum of the first n odd natural numbers. Therefore, the sum is equal to n^2. The correct option is (c). (c) n^2 Step 4: Solve Question 9. The square of an even number is always an even number. This means its units digit must be 0, 4, or 6. Let's check the options: (a) 196: Units digit is 6. sqrt(196) = 14. Since 14 is an even number, 196 is the square of an even number. (b) 441: Units digit is 1. sqrt(441) = 21. Since 21 is an odd number, 441 is the square of an odd number. (c) 625: Units digit is 5. sqrt(625) = 25. Since 25 is an odd number, 625 is the square of an odd number. (d) 529: Units digit is 9. sqrt(529) = 23. Since 23 is an odd number, 529 is the square of an odd number. The correct option is (a). (a) 196 Step 5: Solve Question 10. The square of an odd number is always an odd number. This means its units digit must be 1, 5, or 9. Let's check the options: (a) 2116: Units digit is 6. This is an even number. sqrt(2116) = 46, which is an even number. (b) 3844: Units digit is 4. This is an even number. sqrt(3844) = 62, which is an even number. (c) 1369: Units digit is 9. This is an odd number. sqrt(1369) = 37. Since 37 is an odd number, 1369 is the square of an odd number. (d) 2500: Units digit is 0. This is an even number. sqrt(2500) = 50, which is an even number. The correct option is (c). (c) 1369 Send me the next one 📸