1. A two-digit number has its units digit 6 more than the tens digit, and the product of the two digits is 12 less than the number itself. Determine and write down the possible values of the units digit.

2. In a two-digit number, the unit digit is 6 more than the tens digit, and the product of the two digits is 12 less than the number itself. What could the number be?

3. In a two-digit number, the unit digit is 6 more than the tens digit, and the product of the digits is 12 less than the number itself. — Form a quadratic equation with one variable from the given statement.

4. Determine the two-digit number where the unit digit is 6 more than the tens digit, and the product of the two digits is 12 less than the number itself.

5. A two-digit number has its unit digit 6 more than its tens digit, and the product of the two digits is 12 less than the number itself. What is the number?

6. A two-digit number has its unit digit 5 more than its tens digit. Also, the product of the two digits is 14 less than the number itself. Find the number.

7. In a two-digit number, the digit in the tens place is 3 less than the digit in the units place. If the product of its digits is subtracted from the number, the result is 15. What is the digit in the units place of the number?

8. If a two-digit positive number is multiplied by its unit digit, the product is 189, and the tens digit is twice the unit digit, then find the number.

9. In a right-angled triangle, the hypotenuse is 6 cm longer than one of the other two sides and 12 cm longer than the other. Find the area of the triangle.

10. The sum of the digits of a two-digit number is 4. If 18 is subtracted from the number, its digits are reversed. What is the number?

(a) 71 (b) 35 (c) 53 (d) 62

11. From the following cumulative frequency distribution table, prepare a frequency distribution table and determine the mode of the data:

12. If a two-digit positive number is multiplied by its unit digit, the product is 189. Also, the tens digit is twice the units digit. Then determine the digit in the unit place.

13. The weight data of 35 students in Nibedita’s class is as follows: ```html

14. Points \(X\) and \(Y\) are taken on sides \(PQ\) and \(PR\) of triangle \(∆PQR\), respectively. Given: \(PQ = 8\) units, \(YR = 12\) units, \(PY = 4\) units, and the length of \(PY\) is 2 units less than the length of \(XQ\). Determine, with reasoning, whether segment \(XY\) is parallel to side \(QR\).

15. Two friends start a partnership business by investing ₹40,000 and ₹50,000 respectively. They agree that 50% of the profit will be shared equally, and the remaining 50% will be divided in the ratio of their investments. If the first friend’s share of the profit is ₹800 less than the second friend’s share, then what is the first friend’s profit?

16. The dimensions of two cuboids are 4, 6, 4 units and 8, (2h − 1), 2 units respectively. If the volumes of the two cuboids are equal, then what is the value of \(h\)?

17. Two cuboids have dimensions \(4, 6, 4\) units and \(8, 2h - 1, 2\) units, respectively. If the surface areas of both cuboids are equal, then what is the value of \(h\)?

18.

19. Two friends started a joint business with investments of ₹40,000 and ₹50,000 respectively. They agreed that 50% of the profit would be shared equally between them, and the remaining 50% would be divided in proportion to their capital contributions. If the first friend’s profit share is ₹800 less than the second friend’s, calculate the amount received by the first friend.