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MULTIPLE CHOICE QUESTIONS (MCQ@s), , , , Mark the correct alternative in each of the following:, , 1. Lisa variable line such that the algebraic sum of the distances of the points (1, 1), (2, 0) and, (0, 2) from the line is equal to zero. The line L will always pass through, , (a) (1,1) (b) (2,1) (c) (1, 2) (d) none of these

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23.132, , 2., , . The distance between the orthoc, , . The equation of the straight line whi, , MATHEMATICS,, , The acute angle between the medians drawn from the acute angles of a right aNgleg, , ne x (=) . (b) cos ;) (0) cos*(2) (d) cos*(2), , entre and circumcentre of the triangle with Verticas, , 34/3 6), , , , 2 2, (b) V2 () 3+V3 (d) none of these, , ch passes through the point a 4, 3) such that the, portion of the line between the axes is divided internally by the point in the ratio 5:3 is, , (a) 9x-20y+96 = 0 (b) 9x + 20y = 24, (c) 20x + 9y +53 = 0 (d) none of these, , The point which divides the join of (1, 2) and (3, 4) externally in the ratio 1:1, , (1, 2).(2, 1) ma, , (a) 0, , (a) lies in the III quadrant (b) lies in the II quadrant, , (c) lies in the I quadrant (d) cannot be found, , A line passes through the point (2, 2) and is perpendicular to the line 3x+y=3,, , Its y-intercept is [NCERT EXEMPLAR}, , (a) 1/3 (b) 2/3 (c) 1 (d) 4/3, , If the lines ax +12y +1 = 0,bx+13y+1 = Oand cx +14y+1 = 0 are concurrent, then, ~ a,b, carein, , (a) HP. (b) G.P. (c) A.P. (d) none of these, , 10., , 11., , 13., , . The number of real values of 4 for which the lines x -2y + 3=0, Ax + 3y+1=0 and, , 4x —2y + 2 =Oare concurrent is, (a) 0 (b) 1 (c) 2 (d) Infinite, , . The equations of the sides AB,BC and CA of AABC are y—x=2,x+2y=1 and, , 3x + y +5 =0 respectively. The equation of the altitude through B is, (a) x-3y+1 = 0 (b) x-3y+4 = 0 (c) 3x-y+2 = 0 (d) none of these, , If pj and py are the lengths of the perpendiculars from the origin upon the lines, x sec 6 + y cosec @ =a and x cos 0 —y sin 0 =a cos 2 @ respectively, then, , 2 2, (a) 4p," +p." = a (b) py? + 4p,” =@, , 2, , 2 2, (c) py +Py =a (d) none of these, , Area of the triangle formed by the points ((a+ 3)(a+4),a+ 3), ((a+ 2) (a+ 3) ,(at 9), and ((a +1) (a+ 2),(a+1)) is, , 2:, (a) 25a (b) 5a? (c) 2402 (d) none of these, Ifa+b +c =0, then the family of lines 3ax + by +2c = 0 pass through fixed point, (a) (2, 2/3) (b) (2/3, 2) (c) (-2, 2/3) (d) none of these, , The line segment joining the points (— 3, - 4) and (1, — 2) is divided by y-axis in the ratio, (a) 1:3 (b) 2:3 (©) 3:1 (a) 3:2, , Scanned with CamScanner

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THE STRAIGHT LINES 23,133, , , , , , , , , , 19., , 20., , 21., , 24,, 25., , 26., 27,, , 28., , . If the point (5, 2) bisects the intercept of a line be, , . The area of a triangle with vertices at (4) — Oe 2) and (4),- 3) is Hani, , (a) 17 (b) 16 (0) 15) | (@) none of these, , . The line segment j joining the points (i, ) and (=2, 1) is divided by ihe line 3x+4y=7i in, , the ratio, , 40) oy asa i i @yseal ital anaes, ween the axes, then its equation is, (@) 5+ 2Y520,() 2x+5y=20) (@)5x-2y=20 (a) 22- 5y=20_, , A(6, 3) B(- 3,5),C (4,~2) and D(z, 32) ane, ADBC: ‘A ABC = 1:2, then x, is equal to, , , , , , , , i (a) 11/8 (b) 8/11 ay 3 | @. none Sf these, wie P| be the ee of the Papeete from the origin on the line x/a + ‘y/o = 1 then, abi 2, (a) p? =a7 +b (b) p? at wit ot-ti1@ none of these, ie yD poi Bo, , The equation of the line passing thtougt (1,5) and Pereeaicaay to the tne, 3x-5Sy+7 =0is, , (a) 5x + 3y—20=0 (b)' 3x- Sy+7=0 (c) 3x-—5y+6=0 (d) BEE oy ATE O., The figure formed by the lines ax + by+c= 0i is, (a) arectangle: (b) a square (c) a rhombus (d) none of these, , Two vertices of a triangle are(— 2, —1) and (3, 2) and third vertex lies on the line x + an =5. it, o area of the triangle is 4 square units, then the third vertex is, , a) (0,5) or, (4,1) (b) (2, 3) or, (1,4) (c) G, 0) or, (4:1) (d) (0,5) or, (1, 4), , .. The inclination of the straight line passing through the point (— 3, 6) and the mid point of, , the line joining the point (4, —5) and (— 2, 9) is, , , , (a) 0/4 (b) x/6 (c) x/3 (Aa) 32/4, Distance between the lines 5x + 3y —7 =O and 15x + 9y +14 =Ois, 35 iid 35, , = tS c d), ©) a © 3 Ja 3 faa © sr, The angle between the lines 2x —y + 3=Oand x + 2y+ 3=Ois, (a) 90° (b) 60° (c) 45° (d) 30°, The value of A for which the lines 3x + 4y =5,5x + 4y =4andd x + 4y = 6meetata pointis, (a) 2 (b) 1 (c) 4 (d) 3, , Three vertices of a parallelogram taken in order are (—1, — 6), (2, —5) and (7, 2). The fourth, vertex is, , (a) (1, 4) (b) (4,1) (c) (1) (d) (4, 4), , The centroid of a triangle is (2, 7) and two of its vertices are ( 4, 8) and (— 2, 6). The third, vertex is, , (a) (0, 0) Coe) (c) (7,4) (d) (7,7), , Ifthe lines x +g =0, y— 2 =Oand 3x + 2y +5 = Oare concurrent, then the value of qwill be, (a) 1 (b) 2 (c) 3 (a) 5, , Scanned with CamScanner

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23.134 MATHEMATICg, \, , 29,, , iH, , , , , , i 5 . The vertices of a triangle are 6 0), (0, 6) and (6, 6). The distance between its circumcent,, and centroidis ;, , , , 32., 33,, 34., 35., 36., , 37), , 38., , 39,, , 40., , 41., , 42,, , 43,, , "The medians AD and BE of a triangle with vertices A (0,b), B(0, 0) and C (a,, : e, , Perpendicular to each other, if | |, , BH iehigbs ea sk @hygtmeNED ih, , , , , e |equatio ‘of the line with slope ~ 3/2 and which is concurrent with the ling, Sye7=Oand x+5y-1-0i6 He |, , , , |) (b) bx 42y-2 = 0, "1" d) none of these, , , , , , , ty, , a) 22) b) 2 1) V2 “@1, , A point equidistant from the line 4x+ 3y +10 = 0,5x—12y +26 = 0 and 7x + 24y-50 = 9;,, , | i [NCERT EXEMPL Aj,, @ (=) ) G1) (c) (0, 0) (a) (0,1), The tatio in‘ Which the line 3x+4y+2=0 divides the distance between’ the''ling, , , , - 8x+4y+5=Oand 3x+4y-5 =0is (NCERT EXEMPLAR), © (a) 1:2 (b) 3:7 (0) 2:3 (d) 2:5 ui, The coordinates of the foot of the perpendicular from the point (2, 3) on the ling, ‘x+y-11=0are [NCERT EXEMPLAR}, (a) (6,5) (b) 6, 6) (c) (-5, 6) (a) (6,5) ; :, The reflection of the point (4, —13) about the line5x + y + 6 =0is [NCERT EXEMPLAR], (a) (-1,-14) (b) (3, 4) (c) (0, 0) (d) (1, 2) | i, The inclination of the line x —y + 3 = Owith positive direction of x-axis, is \, (a) 45° (b) 135° (c) -45° (d) -135° i de, [NCERT EXEMPLAR], The two lines a,x + byy = cy and a)x + byy = cy are perpendicular if | [NCERT EXEMPLAR], (a) a4.) +byby =0 (b) ayby =Ayby ~ (c) ayby + Agbg =0 > (A) ay by + and, =0, The ‘coordinates of the foot of the perpendicular from the point (2, 3) on the line, x+y—11£0are [NCERT EXEMPLAR], (a) (-6,5) (b) 6, 6) (c) (-5, 6) (a) (6,5) The coordinates of the image of the point (2, 3) in the line mirror x + y—11 = O are, (a) (5, 6) (b) (9,8) (c) (8,9) (d) (-8, -9), The intercept cut-off by a line from y-axis is twice than from x-axis and the line passes, through the point (1, 2). The equation of the line is [NCERT EXEMPLAR], (a) 2x+y=4 (b) 2x+y+4=0 (c) 2x-y=4 (d) 2x-y+4=0, A line passes through the point P (1, 2) such thatits intercept between the axes is bisectedat, P.The equation of the line is [NCERT EXEMPLAR], , (a) x+2y=5 (b) x-y+1=0 (c) x+y-3=0 (d) 2x+y-4=0, , The reflection of the point (4, —13) about the line5x + y + 6 =Ois [NCERT EXEMPLAR}, @(-1-19 (3,4) (© 0,0) (a) (1,2), , A point moves such that its distance from the point (4, 0) is half that of its distance from the, line x =16. the locus of the point is [NCERT EXEMPLAR], (a) 3x74 4y" =192 (b) 4x74 3y* =192 (c) x7+ y =12 (d) none of these, , One vertex of the equilateral triangle with centroid at the origin and one side asx + ¥ -220, is [NCERT EXEMPLAR], , (a) (-1, -1) (b) (2, 2) (c) (-2,-2) (d) (2, -2), , Scanned with CamScanner

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48,, , 49., , THE, , gTRAIGHT LINES 23.135, , qhe coordinates of the foot of perpendicular from the point (2, 3) on the line y = 3x + 4 are, given by rane (2,3) on ay ore Aa, , 7d ) 6) (- 1 37 aH INCERT EXEMPLAR], @) | 40’ 10 10’ al (c) (2. -10) hoi) (3.-3), , If the coordinates of the middle point of ‘the portion of a line interc epted between the, , " coordinate axes are(3, 2), then the equation of theline willbe [NCERT EXEMPLAR], , (a) 2x+ 3y =12 (b) 3x+2y=12. (©) 4x—3y =6 (d) 5x —-2y =40, , , Equations of diagonals of the square formed by the lines x=0,y=0,x=1 and y=1, , aS [NCERT EXEMPLAR], , ‘a yar yaxtl (b) y=x,x+y=2 (©) 2y=x,x+y=5 (A) y=22,y=2x11, , For apecifyin ing a straight line, how many geometrical’ parameters’ should be, tH || [NCERT EXEMPLAR], @1 (b) 2 (c) 3 ‘(d) 4 i |, The point (4, 1) undergoes the following two successive transformations:, , (i) Reflection about the line y = x a ETAT CS,, , ., Gi) Translation through a distance of 2 units along the positive ‘axis, Then the coordinates:, , 50,, , 51,, , 52., , , , , , , , of the point are [NCERT EXEMPLAR], (a) (4, 3) (b) (3, 4) (c) (1, 4) (d) (7/2,7/2) |, The tangent of the angle between the lines whose intercepts on the axes are a, -bandb, —a, respectively, is [NCERT EXEMPLAR], fa) a2 —b? 6) b? -a? ( b?-a d, , 7 a c) Dab (d) none of these, , If the line - - =1 passes through the points (2, — 3) and(4, —5), then (a, b) =, , (a) (1,1) (b) (-1,1) (c) (1, -1) (d) (-1, -1), , [NCERT EXEMPLAR], The distance between the lines y = mx + cy and y =mx + ¢9,is [NCERT EXEMPLAR], @ 2 gy tal Be @) Iya, , Vi+m2 Vl+m V1 +m?, , The equations of the lines passing through the point (1, 0) and at a distance a from the, , origin are, , _ @ V3x+y-V3 =0 (b) V3xty+V3 =0, , 55., , (0) xt V3y-V3 =0 (d) none of these [NCERT EXEMPLAR], , . The equations of the lines which pass through the point (3, —2)and are inclined at 60° to the, , lineV3x+y =1are [NCERT EXEMPLAR], (a) y+2=0, V3x-y-2-3V3 =0 (b) x-2=0, V3x-y+2+3V3 =0, , , , (0) ¥3x-y-2+ 3V3 =0 (d) none of these, The distance of the point of intersection of the lines 2x-3y+5=Oare 3x+ 4y =0 from the, line5x-2y =0,is [NCERT EXEMPLAR], (a) 130 ) 3 (2. (a) none of these, 17/29 7429 7, . Slopes of lines which cuts off intercepts of equal lengths on the coordinate axes are, 1 d) +V3, (a) 0 eae (c) +1 (, ) ) +75, , [NCERT EXEMPLAR], , Scanned with CamScanner