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![[Post New]](/templates/default/images/icon_minipost_new.gif) posted on 14 Feb 2008 10:27:24 IST
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Mathematics For Class XI
Straight Lines
for school prepration Questions keep getting added here on regular intervals. Please do keep checking this section. | (Q.1) The equations of the lines through the point (3, 2) which make angles of 45° with the line x ? 2y = 3 are | | ( 0 Marks ) |
(A) 3x ? y = 7 and x + 3y = 9 (B) x ? 3y = 7 and 3x + y = 9 (C) x ? y = 3 and x + y = 2 (D) None of these View Answer | (Q.2) Let PS be the median of the triangle with vertices P(2,2), Q(6,-1) and R(7,3). The equation of the line passing through (1,-1) and parallel to PS is | | ( 1 mark ) |
(A) 2x ? 9y ? 7 = 0 (B) 2x ? 9y ? 11 = 0 (C) 2x + 9y ? 11 = 0 (D) 2x + 9y + 7 = 0 View Answer (Q.3) A line through A (? 5, ? 4) meets the line x + 3y + 2 = 0, 2x + y + 4 = 0 and x ? y ? 5 = 0 at B, C and D respectively. If  + =  , then the equation of the line is | | ( 1 mark ) |
(A) 2x + 3y + 22 = 0 (B) 5x ? 4y + 7 = 0 (C) 3x ? 2y + 3 = 0 (D) None of these View Answer (Q.4) The lines x + 2y ? 5 = 0, 2x ? 3y + 4 = 0, 6x + 4y ? 13=0 are
| | ( 1 mark ) |
(A) are concurrent (B) form a right angled triangle (C) form an isosceles triangle (D) form an equilateral triangle View Answer | (Q.5) The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is ?1 is | | ( 1 mark ) |
(A)  (B)  (C)  (D)  View Answer | (Q.7) Find the equation of the angle bisectors of the angle between the coordinate axes. | | ( 1 mark ) |
View Answer | (Q.8) Write the distance formula. | | ( 1 mark ) |
View Answer | (Q.9) Find a point on the X-axis which is equidistant from the points (5, 6) and (7, 8). | | ( 1 mark ) |
View Answer (Q.10) Find the distance between the parallel lines  and  | | ( 1 mark ) |
View Answer (Q.11) Find the distance of the point (5,-2) from the line  . | | ( 1 mark ) |
View Answer (Q.12) Find the value of p so that the three lines  ,  and  may intersect at one point. | | ( 1 mark ) |
View Answer (Q.13) Find the equation of the straight line which makes an angle of  with the positive direction of X axis and cuts an intercept of + 6 on the Y axis. | | ( 1 mark ) |
View Answer | (Q.14) What is the slope of a vertical line and a horizontal line? | | ( 1 mark ) |
View Answer (Q.15) What is the relation between the slopes of two lines when they are
(i) Parallel (ii) Perpendicular | | ( 1 mark ) |
View Answer | (Q.16) The equation of the straight line which passes through the point (1, ?2) and cuts off equal intercepts from axes, is.? | | ( 1 mark ) |
(A) x + y = 1 (B) x ? y = 1 (C) x + y + 1 = 0 (D) x ? y ? 2 = 0 View Answer | (Q.17) A triangle ABC is right angled at A has points A and B as (2, 3) and (0, ?1)respectively. If BC = 5, then point C may be | | ( 1 mark ) |
(A) (?4, 2) (B) (4, ?2) (C) (0, 4) (D) (0, ?4) View Answer | (Q.18) The vertices of a triangle ABC are A(1, 1), B(4, ? 2) and C(5, 5) respectively. Then equation of perpendicular dropped from C to the internal bisector of angle A is | | ( 1 mark ) |
(A) y ? 5 = 0 (B) x ? 5 = 0 (C) 2x + 3y ?7 = 0 (D) None of these View Answer (Q.19) If (?2, 6) is the image of the point (4, 2) with respect to line L = 0, then equation of the line.
| | ( 1 mark ) |
(A) 3x ? 2y + 5 (B) 3x ? 2y + 10 (C) 2x + 3y ? 5 (D) 6x ? 4y ? 7 View Answer | (Q.20) The straight line y = x ? 2 rotates about a point where it cuts the x-axis and becomes perpendicular to the straight line ax + by + c = 0. Then its equation is | | ( 1 mark ) |
(A) ax + by + 2a = 0 (B) ax ? by ? 2a = 0 (C) bx + ay ? 2b = 0 (D) ay ? bx + 2b = 0 View Answer | (Q.21) A line through the point A (2, 0), which makes an angle of 30º with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15º. The equation of the straight line in the new position is | | ( 1 mark ) |
(A) (2 ?  ) x ? y ? 4 + 2 = 0 (B) (2 ? ) x + y ? 4 + 2= 0 (C) (2 ? ) x ? y + 4 + 2 = 0 (D) None of these View Answer | (Q.22) Let the perpendiculars from any point on the line 7x + 56y = 0 upon 3x + 4y = 0 and 5x ? 12y = 0 be p and p', then | | ( 1 mark ) |
(A) 2p = p' (B) p = 2p' (C) p = p' (D) None of these View Answer | (Q.23) D is a point on AC of the triangle with vertices A (2, 3), B (1, ?3), C (?4, ?7) and BD divides triangle ABC into two triangles of equal area. The equation of the line drawn through B at right angles to BD is | | ( 1 mark ) |
(A) y ? 2x + 5 = 0 (B) 2y ? x + 5 = 0 (C) y + 2x ? 5 = 0 (D) 2y + x ? 5 = 0 View Answer | (Q.24) The distance of the line 2x + y = 3 from the point (?1, 3) in the direction whose slope is 1, is | | ( 1 mark ) |
(A)  (B)  (C)  (D)  View Answer | (Q.25) The equation of a straight line, which passes through the point (a, 0) and whose perpendicular distance from the point (2a, 2a) is a, is. | | ( 1 mark ) |
(A) 3x ? 4y ? 3a = 0 (B) x ? a = 0 (C) both (a) and (b) (D) Neither of (a) and (b) View Answer (Q.26) The larger of the two angles made with the x axis of a straight line drawn through (1, 2) so that it intersects x + y = 4 at a point distant  from (1, 2) is | | ( 1 mark ) |
(A) 105° (B) 75° (C) 60° (D) 15° View Answer | (Q.27) The equation to a pair of opposite sides of a parallelogram are x2 ? 5x + 6 = 0 and y2 ? 6y + 5 = 0. The equations to its diagonals are | | ( 1 mark ) |
(A) x + 4y = 13 and y = 4x ? 7 (B) 4x + y = 13 and 4y = x ? 7 (C) 4x + y = 13 and y = 4x ? 7 (D) y ? 4x = 13 and y + 4x = 7 View Answer (Q.28) Two lines are given (x ? 2y)2 + k (x ? 2y) = 0. The value of k, so that the distance between them is 3, is
| | ( 1 mark ) |
(A) k = 0 (B)  (C)  (D) k = 3 View Answer | (Q.29) If the middle points of the sides BC, CA and AB of the triangle ABC be (1, 3), (5, 7) and (?5, 7) then the equation of the side AB is | | ( 1 mark ) |
(A) x ? y ? 2 = 0 (B) x ? y + 12 = 0 (C) x + y ? 12 = 0 (D) None of these View Answer | (Q.30) The equation of the line parallel to the line 2x ? 3y = 1 and passing through the middle point of the line segment joining the points (1, 3) and (1, ?7), is | | ( 1 mark ) |
(A) 2x ? 3y + 8 = 0 (B) 2x ? 3y = 8 (C) 2x ? 3y + 4 = 0 (D) 2x ? 3y = 4 View Answer | (Q.31) The equation of a line passing through the point of intersection of the lines x + 5y + 7 = 0, 3x + 2y ? 5 = 0, and perpendicular to the line 7x + 2y ? 5 = 0, is given by | | ( 1 mark ) |
(A) 2x ? 7y ? 20 = 0 (B) 2x + 7y ? 20 = 0 (C) ?2x + 7y ? 20 = 0 (D) 2x + 7y + 20 = 0 View Answer | (Q.32) If perpendiculars are drawn from, origin to the straight lines x + 3y = 3 and 2x + 3y = 5, then the equation of the line joining the feet of these perpendiculars is | | ( 1 mark ) |
(A) 2x + 3y = 5 (B) 3x ? 2y = 0 (C) 33x ? 61y + 45 = 0 (D) 117x ? 150y = 39 View Answer (Q.33) Let  be fixed angle. If  , then Q is obtained from P by | | ( 1 mark ) |
(A) clockwise rotation around origin through an angle  (B) anticlockwise rotation around origin through an angle (C) reflection in the line through origin with slope tan (D) reflection in the line through origin with slope tan (/2) View Answer | (Q.34) Find the ratio in which the line joining (2, 3) and (4, 1) divides the line joining (1, 2) and (4, 3). | | ( 4 Marks ) |
View Answer | (Q.36) Find the equation of the line joining the points (- 3, - 1) and (2, 3).Also find the equation of the other line which is perpendicular to this line and passing through the point (5, 2). | | ( 4 Marks ) |
View Answer (Q.37) If the angle between two lines is  and the slope of one of the lines is  , find the slope of the other line.
| | ( 4 Marks ) |
View Answer | (Q.38) Find the equation of the line that cuts off equal intercepts on the coordinate axes and passes through the point (3, 4). | | ( 4 Marks ) |
View Answer (Q.39) If p is the measure of the perpendicular segment from the origin on the line whose intercepts on the axes are a and b, show that | | ( 4 Marks ) |
View Answer | (Q.40) By using the concept of the equation of a line, prove that the three points (3,0), (-2,-2) and (8,2) are collinear. | | ( 4 Marks ) |
View Answer (Q.41) Show that the path of a moving point such that its distances from two lines and  are equal is a straight line. | | ( 4 Marks ) |
View Answer | (Q.42) Which of the lines 2x + 7y - 9 = 0 and 4x ? y +11 = 0 is farther from the point (3,4)? | | ( 4 Marks ) |
View Answer | (Q.43) If the lines 7x + y ? 3 = 0, 5x + ky ? 5 = 0 and 8x ? y ? 2 = 0 are concurrent, then find the value of k. | | ( 4 Marks ) |
View Answer | (Q.44) Assuming that straight lines work as the plane mirror for a point, find the image of the point (1, 2) in the line 2x + 3y ? 5 = 0. | | ( 4 Marks ) |
View Answer | (Q.45) A line passes through (2, 4) and the sum of the intercepts on the axes is 12. Find the equation of the line. | | ( 4 Marks ) |
View Answer (Q.46) A line forms a triangle in the first quadrant with the coordinate axes. If the area of the triangle is 54 sq. units and the perpendicular drawn from the origin to the line makes an angle of  with the X-axis, find the equation of the line. | | ( 4 Marks ) |
View Answer (Q.47) Find the equations of the straight lines which passes through the origin and trisect the portion of the straight line  , which is
intercepted between the axes. | | ( 6 Marks ) |
View Answer (Q.48) Prove that the product of the lengths of the perpendiculars drawn from the points  and  to the line  is  . | | ( 6 Marks ) |
View Answer (Q.49) Find the equation of the straight line which passes through the point (-2, 3) and making an angle of  with the X axis. Also find the points on the line which are at the distance of
(i) 3 units (ii) 5 units from the point (-2, 3). | | ( 6 Marks ) |
View Answer (Q.50) Find the equation of the straight line which passes through the origin and making an angle of  with the line 3x + 4y = 2. | | ( 6 Marks ) |
View Answer
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