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M0IITU08 - Straight lines qns

# M0IITU08 - Straight lines qns - Straight Line 1 The...

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1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. The equation of the straight line which passes through the point (1, - 2) and cuts off equal intercepts from axes, is (A) x + y = 1 (B) x - y = 1 (C) x + y + 1 = 0 (D) x - y - 2 = 0 2. A line L is perpendicular to the line 5x - y = 1 and the area of the triangle formed by the line L and coordinate axes is 5 . The equation of the line L is : x + 5y = 5 x + 5y = ± 5 2 x - x - 2 3. In the equation, y - y 1 = m (x - x 1 ) if m & x 1 are fixed & different lines are drawn for different values of y 1 , then The lines will pass through a single point There will be a set of parallel lines There will be one line only None of these 4. For the straight lines given by the equation, (2 + k) x + (1 + k) y = 5 + 7k, for different values of k, which of the following statements is true ? Lines are parallel Lines pass through the point (- 2, 9) (2, - 9) 5. Orthocentre of the triangle whose vertices are (0, 0), (2, - 1) & (1, 3) is (A) 4 7 1 7 , - - 4 7 1 7 , (- 4, - 1) (4, 1) 6. If the lines, ax + by + c = 0, bx + cy + a = 0 and cx + ay + b = 0 be concurrent, then : a 3 + b 3 + c 3 + 3 abc = 0 a 3 3 3 - abc = 0 a 3 3 3 - 3 7. The line joining two point A (2, 0), B (3, 1) is rotated about A in anti clockwise direction through an angle of 15º . The equation of the line in the new position is : 3 x - y - 2 3 = 0 x - 3 y - 2 = 0 3 x + y - 2 x + 3 8. The equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, - 1) . The length of the side of the triangle is : 3 2 2 2 3 9. A point moves so that square of its distance from the point (3, - 2) is numerically equal to its distance from the line 5x - 12y = 13 . The equation of the locus of the point is : 13x 2 + 13y 2 - 83x + 64y + 182 = 0 x 2 + y 2 - 11x + 16y + 26 = 0 x 2 2 - 11x + 16y = 0 Straight Line

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2 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 10. The equation of the lines which passes through the point (3, - 2) & are inclined at 60º to the line 3 x + y = 1 (A) y + 2 = 0, 3 x - y - 2 - 3 3 = 0 (B) x - 3 x - y + 2 + 3 (C) 3 x - y - 2 - 3 (D) None of these 11. The points on the line, x + y = 4 which lie at a unit distance from the line, 4x + 3y = 10, are : (3, 1) , ( - 7, 11) , (7, 11) (- 3, 1) , (- (1, 3) 12. The equation of the bisector of the acute angle between the lines, 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 is 21x + 77y - 101 = 0 11x - 3y + 9 = 0 31x + + - - 13. If the lines y = 3x + 1 & 2y = x + 3 are equally inclined to the line, y = mx + 4 then m = (A) 1 3 2 7 + 1 3 2 7 - 1 3 2 7 ± 1 5 2 7 ± 14. If the slope of a line passing through the point A (3, 2) be 3 4 , then the points on the line which are 5 units away from A, are : (A) (5, 5) ( - 1, - 1) (B) (7, 5) ( - 1, - 1) (C) (5, 7) ( - - 1) (7, 5) (1, 1) 15. The lines ax + by + c = 0, where 3a + 2b + 4c = 0 are concurrent at the point : 1 2 3 4 , 3 4 1 2 , 16. The equations of two equal sides of an isosceles triangle are 7x - y + and x + y - 3 = 0 and the third side passes through the point (1, - 10) . The equation of the third side is : (A) x - - 31 = 0 but not 3x + y + 7 = 0 (B) 3x + y + 7 = 0 but not x - - = 0 (C) 3x + y + 7 = 0 or x - - 31 = 0 Neither 3x + y + 7 nor x - 3y - 17. The value of k for which the lines, 7x - 8y + 5 = 0, 3x - + 5 = 0 and 4x + + k = 0 are concurrent is given by : - 45 44 54 - 54 18. The co-ordinates of the foot of the perpendicular from the point (2, 3) on the line y = 3x + 4 are given by : 37 10 1 10 , - -
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M0IITU08 - Straight lines qns - Straight Line 1 The...

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