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Phoenix Institute of Mathematics, Preliminary Examination, Std: Mathematics (12th), Date : 24/Jan/2022, , Subject: Mathematics & Statistics, , Time: 30Hrs, Max Marks: 25, , Section A (MCQ & VSA Questions), Q.1, Select and write the correct answer:, (i) Which of the following represents coincident lines, A) x² + xy + y² = 0 B) x² + 2xy - y² = 0, C) x² + xy - y² = 0 D) 2x² + 4xy + 2y² = 0, (ii) Find separate equation of lines represented by x² - y² - 3x + 3y = 0, A) x + y = 3 and y = -2, B) x + y = -3 and x - y = 0, C) x + y = 3 and x - y = 0 D) x = -2 and x - y = 3, Q.2, Answer the following:, (i) What is a degree of equation?, (ii) Find the combined equation of the following pair of lines: 2x + y = 0 and 3x – y = 0, (iii) Find the acute angle between lines represented by x² + 3xy + y² = 0, Section B (2 MARKS EACH), Attempt any Four:, Find the separate equations of the lines represented by following equation: x² + 2(cosec α)xy + y² = 0, Q.3, Find k if: The sum of the slopes of the lines given by 3x² + kxy - y² = 0 is zero., Q.4, Find the separate equation of lines represented by: 5x² – 3y² = 0, Q.5, Find the acute angle between lines represented by: x² + xy = 0, Q.6, Find the acute angle between lines represented by: 2x² - 6xy + y² = 0, Q.7, Show that lines represented by 3x² - 4xy - 3y² = 0 are perpendicular to each other., Q.8, Section C (3 MARKS EACH), Attempt any Two:, Find the combined equation of lines passing through the origin and each of which making angle 60°, Q.9, with the Y- axis., If line x + 2 = 0 coincides with one of the lines represented by the equation x² + 2xy + 4y + k = 0, Q.10, then show that k = -4., Prove that the combined equation of the pair of lines passing through the origin and perpendicular to, Q.11, the lines represented by ax² + 2hxy + by² = 0 is bx² - 2hxy + ay² = 0, Section D (4 MARKS EACH), Attempt any One:, Find the combined equation of the pair of lines passing through the origin and perpendicular to the, Q.12, lines represented by 3x² + 2xy – y² = 0., Q.13, Prove that the product of lengths of perpendiculars drawn from P (x₁, y₁) to the lines represented by, ax² + 2hxy + by² = 0 is, , 4, , 3, , 8, , 6, , 4, , -------- All the Best -------Page 1 of 2