Find the HCF of 28m'n and 63mn

Here are the solutions to the questions: 15. Find the HCF of 28m^n and 63m^n. Step 1: Find the HCF of the numerical coefficients, 28 and 63. Prime factors of 28 = 2^2 × 7 Prime factors of 63 = 3^2 × 7 The greatest common factor of 28 and 63 is 7. Step 2: Find the HCF of the variable parts. The common variable part is m^n. Step 3: Combine the HCF of the numerical and variable parts. HCF(28m^n, 63m^n) = 7m^n. The correct option is B. The HCF is 7m^n. 16. 65% of those who tried out to belong to a football team made it. If 13 players made it to the team, how many tried out? Step 1: Let x be the total number of players who tried out. We are given that 65\% of x is 13. 0.65x = 13 Step 2: Solve for x. x = (13)/(0.65) x = (1300)/(65) x = 20 The correct option is D. 20 players tried out. 17. A fruit vendor has 54 apples. She sells 17 apples in the morning and 12 in the evening. How many apples does she have left? Step 1: Calculate the total number of apples sold. Apples sold = 17 + 12 = 29 Step 2: Subtract the sold apples from the initial total. Apples left = 54 - 29 = 25 The correct option is B. She has 25 apples left. 18. In a village, the numbers of person infected with Bird Flu in 2018 were 75. In 2021, 105 persons were infected. Find the ratio of those infected in 2018 and those in 2021. Step 1: Write the ratio as 2018 : 2021. Ratio = 75 : 105 Step 2: Simplify the ratio by dividing both numbers by their greatest common divisor. Divide both by 5: 15 : 21 Divide both by 3: 5 : 7 The correct option is D. The ratio is 5 : 7. 19. Convert the Denary number 73 to a binary number. Step 1: Use repeated division by 2 and record remainders. 73 ÷ 2 = 36 R 1 36 ÷ 2 = 18 R 0 18 ÷ 2 = 9 R 0 9 ÷ 2 = 4 R 1 4 ÷ 2 = 2 R 0 2 ÷ 2 = 1 R 0 1 ÷ 2 = 0 R 1 Step 2: Read the remainders from bottom to top. The binary number is 1001001_2. The correct option is A. The binary number is 1001001_2. 20. Richard spent 35.3% of his money on provision, 28.7% on transport and 15.5% on textbooks. What percentage of his money is left? Step 1: Calculate the total percentage spent. Total spent = 35.3\% + 28.7\% + 15.5\% = 79.5\% Step 2: Subtract the total percentage spent from 100%. Percentage left = 100\% - 79.5\% = 20.5\% The correct option is B. 20.5\% of his money is left. 21. Convert the denary number 73 to a binary number. Step 1: Use repeated division by 2 and record remainders. 73 ÷ 2 = 36 R 1 36 ÷ 2 = 18 R 0 18 ÷ 2 = 9 R 0 9 ÷ 2 = 4 R 1 4 ÷ 2 = 2 R 0 2 ÷ 2 = 1 R 0 1 ÷ 2 = 0 R 1 Step 2: Read the remainders from bottom to top. The binary number is 1001001_2. The correct option is A. The binary number is 1001001_2. 22. Calculate the negative difference between 35 and 49. Step 1: Calculate the difference between 49 and 35. Difference = 49 - 35 = 14 Step 2: Find the negative of this difference. Negative difference = -14 The correct option is B. The negative difference is -14. 23. Evaluate 79^2 - 24^2. Step 1: Use the difference of squares formula: a^2 - b^2 = (a-b)(a+b). 79^2 - 24^2 = (79 - 24)(79 + 24) Step 2: Perform the operations inside the parentheses. (79 - 24) = 55 (79 + 24) = 103 Step 3: Multiply the results. 55 × 103 = 5665 The correct option is A. The value is 5665. 24. Factorise the expression 3dh - 15hk. Step 1: Identify the common factors in both terms. The common numerical factor is 3. The common variable factor is h. So, the common factor is 3h. Step 2: Factor out the common factor. 3dh - 15hk = 3h(d) - 3h(5k) = 3h(d - 5k) The correct option is C. The factorised expression is 3h(d - 5k). 25. Calculate the area of a cuboid of length 11 cm, breadth 9 cm and height 5 cm. The question asks for "area" but the options are in cm^3, which are units for volume. Given the options, it is highly probable that the question intended to ask for the volume of the cuboid. Step 1: Identify the dimensions. Length l = 11 cm Breadth b = 9 cm Height h = 5 cm Step 2: Calculate the volume of the cuboid. Volume = l × b × h Volume = 11 cm × 9 cm × 5 cm Volume = 495 cm^3 The correct option is B. The volume is 495 cm^3. 26. How many notebooks sold at N150.00 each can a father purchase for N2550.00 for his ward? Step 1: Divide the total money by the cost per notebook. Number of notebooks = N2550.00N150.00 Step 2: Perform the division. Number of notebooks = 17 The correct option is C. He can purchase 17 notebooks. 27. Reduce (105)/(225) to a fraction in its lowest term. Step 1: Find the greatest common divisor (GCD) of the numerator and denominator. Both 105 and 225 are divisible by 5. (105 ÷ 5)/(225 ÷ 5) = (21)/(45) Step 2: Continue dividing by common factors. Both 21 and 45 are divisible by 3. (21 ÷ 3)/(45 ÷ 3) = (7)/(15) The correct option is B. The fraction in its lowest term is (7)/(15). 28. Change 7 to a number in percentage. If the question literally means to convert the integer 7 to a percentage, the answer is 7 × 100\% = 700\%. This is not among the options. Given option C is 87(1)/(2)\%, it is highly probable that the question intended to ask for the percentage equivalent of (7)/(8). Step 1: Convert the fraction (7)/(8) to a percentage. Percentage = (7)/(8) × 100\% Step 2: Calculate the percentage. Percentage = 0.875 × 100\% = 87.5\% Percentage = 87(1)/(2)\% The correct option is C. The percentage is 87(1)/(2)\%. 29. The number 10,080,008 can be interpreted in words as: Step 1: Break down the number by place value. 10,000,000 Ten Million 80,000 Eighty Thousand 8 Eight Step 2: Combine the parts. Ten Million, Eighty Thousand and Eight. The correct option is B. The number is Ten Million, Eighty Thousand and Eight. 30. Which of the following angles is an obtuse angle? Step 1: Recall the definition of an obtuse angle. An obtuse angle is an angle that measures greater than 90^ but less than 180^. Step 2: Evaluate each option. A. 89^ is an acute angle (less than 90^). B. 92^ is an obtuse angle (greater than 90^ and less than 180^). C. 184^ is a reflex angle (greater than 180^). D. 0.237^ is an acute angle. The correct option is B. 92^ is an obtuse angle. 31. Express 117 as a product of its prime factors. Step 1: Divide 117 by the smallest prime numbers. 117 ÷ 3 = 39 39 ÷ 3 = 13 13 ÷ 13 = 1 Step 2: Write the prime factorization. 117 = 3 × 3 × 13 = 3^2 × 13 The correct option is D. The prime factors are 3^2 × 13. 32. Calculate the area of the triangle below: The diagram shows a right-angled triangle with a base of 8 cm and a height of 6 cm. Step 1: Identify the base and height. Base b = 8 cm Height h = 6 cm Step 2: Apply the formula for the area of a triangle. Area = (1)/(2) × base × height Area = (1)/(2) × 8 cm × 6 cm Area = 4 cm × 6 cm Area = 24 cm^2 The correct option is D. The area of the triangle is 24 cm^2. 33. Solve the simultaneous equations: (i) a + 6b = 13 (ii) 5a - 6b = 7 Adding the two given equations results in 6a = 20, so a = (10)/(3), which is not an integer. Since all options are integers, there is likely a typo in equation (ii). If equation (ii) was 5a - 6b = -7, then the solution would match option C. Assuming this typo: (i) a + 6b = 13 (ii) 5a - 6b = -7 Step 1: Add equation (i) and equation (ii) to eliminate b. (a + 6b) + (5a - 6b) = 13 + (-7) 6a = 6 Step 2: Solve for a. a = (6)/(6) = 1 Step 3: Substitute a=1 into equation (i) to solve for b. 1 + 6b = 13 6b = 13 - 1 6b = 12 b = (12)/(6) = 2 The correct option is C (assuming the typo in equation (ii) as 5a - 6b = -7). The solutions are a = 1 and b = 2. 34. Factorize the expression y^2 + 10y - 24 = 0. Step 1: Find two numbers that multiply to -24 and add to 10. The two numbers are 12 and -2, because 12 × (-2) = -24 and 12 + (-2) = 10. Step 2: Rewrite the middle term using these numbers and factor by grouping. y^2 + 12y - 2y - 24 = 0 y(y + 12) - 2(y + 12) = 0 (y + 12)(y - 2) = 0 Step 3: Solve for y. y + 12 = 0 y = -12 y - 2 = 0 y = 2 The correct option is B. The solutions are y = -12 or y = 2. Last free one today — make it count tomorrow, or type /upgrade for unlimited.