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Assertion (A): There are infinite number of lines which pass through (2, 14)Reason(R): A linear equation in two variables has infinitely many solutions.a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion(A).c) Assertion (A) is true but Reason (R) is false.d) Assertion (A) is false but Reason (R) is trueSECTION BSection B consists of 5 questions of 2 marks each.21. Write the expanded form of (7𝑎 − 3𝑏)3[ OR ]Factorize 8𝑥3 − 27𝑦3.22. Without plotting the points indicate the quadrant in which they will lie, ifa) the ordinate is 5 and abscissa is 3b) the abscissa is – 5 and ordinate is 323. Find the measure of an angle which is 26° more than its complement .24. In the given figure, find PM (Give reasons)25. Find the possible expressions for the length and breadth of the rectangle whose area is given by4𝑎2 + 4𝑎 − 3.[ OR ]Using suitable identity find the value of (29)3.

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Assertion (A): There are infinite number of lines which pass through (2, 14)Reason(R): A linear equation in two variables has infinitely many solutions.a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion(A).c) Assertion (A) is true but Reason (R) is false.d) Assertion (A) is false but Reason (R) is trueSECTION BSection B consists of 5 questions of 2 marks each.21. Write the expanded form of (7𝑎 − 3𝑏)3[ OR ]Factorize 8𝑥3 − 27𝑦3.22. Without plotting the points indicate the quadrant in which they will lie, ifa) the ordinate is 5 and abscissa is 3b) the abscissa is – 5 and ordinate is 323. Find the measure of an angle which is 26° more than its complement .24. In the given figure, find PM (Give reasons)25. Find the possible expressions for the length and breadth of the rectangle whose area is given by4𝑎2 + 4𝑎 − 3.[ OR ]Using suitable identity find the value of (29)3.

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Solution

Sure, here are the answers to your questions:

  1. The answer is (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion(A). While it's true that there are infinite lines that can pass through a single point, and a linear equation in two variables has infinitely many solutions, these two facts are not directly related.

  2. The expanded form of (7a - 3b)³ is 343a³ - 441a²b + 189ab² - 27b³.

    The factorization of 8x³ - 27y³ is (2x - 3y)(4x² + 6xy + 9y²).

  3. If the ordinate is 5 and abscissa is 3, the point will lie in the first quadrant. If the abscissa is -5 and ordinate is 3, the point will lie in the second quadrant.

  4. The measure of an angle which is 26° more than its complement is 58°. This is because the complement of an angle is 90° - the angle. So if x is the angle, x = 90° - x + 26°. Solving for x gives x = 58°.

  5. Without the figure, I can't provide the value of PM.

  6. The possible expressions for the length and breadth of the rectangle whose area is given by 4a² + 4a - 3 are (2a + 1) and (2a - 3) or (2a + 3) and (2a - 1).

    The value of (29)³ using the identity (a+b)³ = a³ + 3a²b + 3ab² + b³ is 24389.

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