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.
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Here are the solutions to the questions: SECTION B (10 Marks) 21. The following expressions are either undefined or indeterminate: (0)/(0), (100)/(0), (0)/(100), (0)/(0) (0)/(0) is indeterminate. (100)/(0) is undefined. (0)/(100) = 0, which is neither undefined nor indeterminate. Therefore, the statement is false. Answer: False 22. The equation x^2 + 1 = 0 have no solution in the set of real numbers, R x^2 = -1. The square of any real number cannot be negative. Therefore, there are no real solutions. Answer: True 23. ((2)/(5))^-3 = ((5)/(2))^3 Using the property ((a)/(b))^-n = ((b)/(a))^n. ((2)/(5))^-3 = ((5)/(2))^3. Answer: True 24. If a is an even number, then 3a^3 + 3 is an odd number. If a is even, then a^3 is even. 3a^3 is (odd × even) = even. 3a^3 + 3 is (even + odd) = odd. Answer: True 25. The quadratic equation 2 + 6sqrt(2)y + 9y^2 has two equal roots. Rearrange the equation: 9y^2 + 6sqrt(2)y + 2 = 0. For two equal roots, the discriminant B^2 - 4AC must be 0. Here, A=9, B=6sqrt(2), C=2. B^2 - 4AC = (6sqrt(2))^2 - 4(9)(2) = (36 × 2) - 72 = 72 - 72 = 0 Since the discriminant is 0, the equation has two equal roots. Answer: True 26. There are infinitely many integers between 5.3 and 5.37. Integers are whole numbers. There are no integers between 5.3 and 5.37. Answer: False 27. _b (M + N) = _b M + _b N The correct logarithm property is _b (MN) = _b M + _b N. The given statement is incorrect. Answer: False 28. (1)/(2)x - 3 = 0 is a linear equation in one variable. This equation is of the form ax + b = 0, where a = (1)/(2) and b = -3. It has one variable (x) raised to the power of 1. Answer: True 29. We use the determinant of a quadratic equation to determine its nature of roots. The discriminant* (b^2 - 4ac) is used to determine the nature of roots for a quadratic equation. The term "determinant" is used for matrices. Answer: False 30. 5y - 4x = 0 is neither a quadratic equation nor a linear equation? The equation 5y - 4x = 0 is a linear equation in two variables (x and y). Therefore, the statement that it is neither* is false. Answer: False Send me the next one 📸