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8:03 PMY @, , Co © B tl B Sal, , Mathematics NDA NA Guide Exam a, , , , Level |, 1. The distance of the point @2, 3) from the line, x is, @5v2 wavs @av5 | @ 58, , 2, The equation of the straight line joining the origin to, the point of intersection of y—x+7=0 and, , , , , , y+ 2x-2=0is, (a) 3x4 4y (h) Bar dy, (© 4r-3y=0 (@) 4x+3y=0, , #, , The equation of the straight line which is, perpendicular to y = x and passes through (3, 2) is, , (@)x- y=5, @x+y=1, , , , , , , , 4, The angle between the straight lines x — y/3 = 5and, Vax+ y= Tis, (a) 90° (b) 60° (©) 75° (4) 30°, , 5. What is the perpendicular distance of the point (x, »), from x-axis? (NDA 2012 1), @x (bo) y lz! @lyl, , 6. In what ratio is the line y ~ x + 2= 0 divides the line, joining the points (3, -1) and (8, 9)?, @1:2 2:1 ©2:3 @a:4, For what value of &, are the lines x+2y-9=0 and, he + 4y +5 Oparallel? (NDA 2011 1), @2 (b)-1 @1 @o, Equation of the straight line making equal intercepts, on the axes and passing through the point (2, 4) is, (a) 4x- y—4=0 (b) 2x+ y~8=0, (x+y-6=0 (@) x+2y-10=0, The angle between the lines 2x—y+3=0 and, x+2y+3=0is, (@) 90" 60" (e) 45° (@ 30°, 10, What is the equation of a line through (0, 1) and making, an angle with the y-axis equal to the inclination of the, i with x-axis? (NDA 2012, yx=y41, (@ None of these, 11. The point moves such that the area of the triangle, formed by it with the points (1, 5) and (3, -7) is, 21 sq units. The locus of the point is, (a) 6x+ y-32=0 (b) Gx - y+ 52=0, ()x+ Gy - 32=0 (@) Gxr~ y~32=0, 12. If pis the length of the perpendicular drawn from the, origin to the line 2+ ‘ =1, then which one of the, a, , 2, , , , e, , , , , , , , line x= y, , , , , , following is correct? (NDA 2011 I,, , The Straight Line, , 22, Thei, , yer, ae, 23, Ifthe, , , , , , , , , i, ee, Oat, 13. The value of } for which the lines 3x+4y=, , 4and ix+4y = 6 meet at a point is, , @)1 4 @3, 14, Distance between the lines 5x+3y-7=0 and, , ‘a, 1 38 a, a OM On On, 15. If © 4, 5) is one vertex and 7x~- y+8=0 is one, diagonal of a square, then the equation of second, diagonal is, (a) x+ 3y=21 (b) 2x — 3y, (x+Ty=31 (d) 2x + 3y = 21, , 16. What is the equation of the line passing through, , , , , , , , , , , , f@), , , , , , , , , , (2,9) and parallel to Y-axis? (NDA 2011 I), )Y, @xX, 17. Two straight lines x- 3y—2=Oand 2x-6y—6=0, (NDA 20111), , (a) never intersect, , (b) intersect at a single point, , (©) intersect at infinite number of points, , (@) intersect at more than one points (but finite, number of points), , 18. If the lines 3x+4y+1=0, Sr+ay+3=0 and, 2x + y-1=Oare concurrent , then 4 is equal to, (@)-8 @)8 a @-4, , 19. Two consecutive sides of a parallelogram are, 4x+5y=0 and 7x+2y=0. One diagonal of the, parallelogram is 11x + 7y = 9. If the other diagonal is,, ax + by +¢=0, then, (a)a=-1,b=-1,, , , , 2, , (b) a=1,b=-1,c=0, , , , @a=-1, -1, @)a=1b=1ec=1, , 20. The length of perpendicular from the point, (acosa,asina) upon the straight line, y=xtana+c,e>0,is, faye (b) esin?a, © ccosa (@) esec*o, , 21. If the straight lines x-2y=Oand kx+y=1 intersect, , at the point ( 3h then what is the value of #?, 2 (NDA 2010 I), @-1/2, , f@1 b)2 @u2, , 497

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8:03 PMY @, , EO, , [se Pe ee mT, , Mathematics NDA NA Guide Exam a, , , , The Straight Line, , 22. The image of the point (4, ~3) with respect to the line, yeris, @C4-3) OGB4) E43) @E3,4), 23, Ifthe mid-point between the points (a + 6,a ~ 6)and, a, b)lies on the line ax + dy = &, what is the value, of? (NDA 2012.), (@alb Bath — (ab @a-b, , 24, Equation of a line passing through (1,~ 2) and, perpendicular to the line 3x —5y + 7= is, (a) dx + 3y+1=0 (b) x + 5y+1=0, (©) 5x - 3) — (d) ax—5y+1=0, , 15. What is the distance between the lines 3x + 4y =9, , , , , , , , and Gx + 8y=18? (NDA 2012), @o (b) 3 units, (©) 9 units (@) 18 units, , SEU PeRsG Ay anGa Ns petpiaeatie 6 BGs, , ~ y=3, then what is one <s and g,, ue Rl (NDA 2009, , One fans, , 7. The acute angle which the perpendicular from origin, on the line 7x~ 3y = 4 makes with the x-axis is, (NDA 2012.0, , (a) zero (b) positive but not 2/4, (©) negative @nia, , 28. The equation of the line passing through (~1, ~ 2)and, having a slope of 4, , , , , , (a) Ty +10 4x, , , , 4.10, ()xesy+ d) 4x + Ty =10, Ox F947 (d) 4x + Ty, , 29. The perpendicular form of the straight line, Vix + 2y = Tis, , @y =, B. 2. B2, OF pret OR, , 30. The x-intercept and the y-intercept of the line, Bx —7= 6y, respectively are, , , , , , jt, (and =, 5 a8, (c) 2 ana $, OF 7, , , , 31. The line through the points (4, 3) and (2, 5) cuts off, intercepts of lengths & and jt on the axes. Which one, , of the following is correct? (NDA 2009), (@a>e A <p, a> -" @ise, , , , 82. The lines, , , , and * +> =1,wher p#—q are, a Pp, , pa, (a) parallel for all values of p and q, (©) perpendicular for all values of p and q, , int, , 3, , 36., , 38., , 3, , 40., , a1., , 4:, , 8, , 4., , 5., , 7., , g, , 8, , 497, , ra., (p+9), , Pa., (p-9),, Pq pa, (p+ a) (+a), , ‘The lines 4x + 4y=1, 8x 3y= 2and y=Oare, (a) sides of an isosceles triangle, , () concurrent, , (©) parallel, , (@) sides of an equilateral triangle, , Which one of the following is the nearest point on the, line 8x — 4y = 25 from the origin?, , (1-7) )3.-4), , C58) (3,4), , Which one of the following is the reflection of the, point (4, 8)on the line x + y= 02, , (4.3) (), (3,4) am,, , ‘Wie ote a the llpvine ie eo acthonantia ot the, , , , , , (©) not parallel and meet at (, , , , (@) not parallel and meet at, , , , , , , , triangle whose sides are x= 0,y = 1andx+ y, (a) (1,1) g (0,1), CLO a) (0-1), What is the gradient of the coplanar and, , non-intersecting line which lies midway between the, Hines 9+ 6y ~7= and Bx + 2y + 6, , ws = @) 3 =, , , , , , @ -3, , 3, it oie the length of the a from the origin, , on the straight line x+ 2b), value of 6?, , , , 'p, then what is the, (NDA 2007 1), , ©) p, , , , 1 1, @s oO;, If the mid-point of the section of a straight line, intercepted between the axes is (1, 1), then what is, the equation of this line?, , (@) 2e+y=3 (b) 2x-y=1, , (x-y=0 @xty=2, , What is the equation of the line which passes, through (4,-5) and is parallel to the line, Br+4y+5=0?, , (a) Sx— 4y-32=0, (0) 4x 3y= 31 (@) 3x4 4y-8=0, , ‘The lines (p+ 2q)x+(p—3q) y= p-4q for different, values of pand q pass through the fixed point given, hy which one of the following?, , “ey og, of? 3) «(? 3), , What is the angle between the two straight lines, , , , (b) 3x4 4y+8=0, , , , , , , , , y=(2-V3)x+5and y=(2+ ins-3?, (a) 60° (b) 4, (©) 30° (is

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8:04PMY @, , EO, , [se Pe ee mT, , Mathematics NDA NA Guide Exam a, , , , 498, , Level Il, , 1. The equation of straight line through the, intersection of the lines x- 2y=1andx+ 3y =2and, parallel to 3x+4y= is, (a) dx + dy +5=0 () Bx + dy - 1, (©) ax+4y-5=0 (@) 3x4 4y +6, , If we reduce ax+9y+7=0 to the, xeosa + y sina = p, then the value of p is, , az v7 7, , Or, , sy wt ors, , |. Equation to the straight line cutting off an intercept,, 2 from the negative direction of the axis of y and, inclined at 30° to the positive direction of axis of x, is, (a) y+ x-V¥3=0 ) y-x42=0, (© y-Vix-2=0 (@ V3y—2+ W3=0, , |. The three straight lines ax + by =¢, bx + cy =a and, are collinear, if, , a @)cta=b, , =0 @atb=c, What are the coordinates of the foot of the, perpendicular from the point (2, 8) on the line, xty-l= (NDA 2011 1, M29) O66 OF56) M5), . What is the equation of the line joining the origin, , with the point of intersection of the lines 4x+8y=12, and 3r+4y=12? (NDA 20111), (@)xty=1 O)x-y=1 (By=4r Mazy, Aline AB makes zero intercepts on x-axis and y-axis, and it is perpendicular to another line CD,, Sx + dy + 6= 0, The equation of line AB is, (a) y=4 (b) 4x- 3y+8=0, (©) ax-3y=0 (@) 4x 3y+6=0, 8. The equation of the line bisecting perpendicularly, the segment joining the points (4, 6) and (8, 8) is, (@) Gr+y-19=0, , , , form, , , , , , , , , , Oy, (@x+2y-7=0, , , , , , (© 6x +2y-19, , 9. Ifa tangent to the curve = Gr — x" is parallel to the, Tine 4x ~ 2 ~ 1 = 0, then the point of tangency on the, curve, , @2Z9 O82 O61) W4,2, 10. The line = — z = lcuts the x-axis at P. The equation of, , the line through P perpendicular to the given line is, , , , , , (ax+y=ab bet ysath, @ar+by=a® (a) by +ay= 8, , 11. What is the equation to the straight line joining the, origin to the point of intersection of the lines = +F=1, andt+2=1? (NDA 2010 1,, f@x+y=0 Gy xty+, (©) x-y=0 (rept, , The Straight Line, , 21, Consider the fallowine statements, i;, , , , 12,, , , , , | If the lines 3y+4x=1,, , NDA/NA Mathematics, , What is the image of the point (1, 2) on the line, Bx4 dy-1=0? (NDA 2010, , ofof, , , , A straight line through PQ,2) is such that its, intercept between the axes is bisected at P. Its, equation is, , , , , , , , , , , , @xty, (© x+2y=5 (art y=4, ‘The equation of the sides ofa triangle are x- 3y=0,, 4x + 3y = Sand 3x + y= O.The line 3x dy = Opasses, through, (@) the incentre (b) the centroid, (©) the orthocentre (@) the circumeentre, , ‘Two lines are drawn through (3, 4), each of which, makes angle of 45° with the line x— y = 2,then area, of the triangle formed by these lines is, , (a) 9 sq units (b) 9/2 sq unite, , (©) 2squnits (a) 2/9 sq units, , , , , , . Equation of a line passing through the line of, , intersection of lines 2x—3y+4=0, 3x+4y-5=0, and perpendicular to Gr-7y+3=0, then its, equation is, , (a) 119x + 102y + 125, (©) 119x— 102y = 125, , (b) 119x + 102y = 125, (@) None of these, =x+5 and Sy+br=3 are, concurrent, then what is the value of 6? (NDA 2010 1), , , , , , , , , , @)1 3 6 wo, If (5,4) divides the line segment between the, coordinate axes in the ratio 1:2, then what is its, equation? (NDA 2010 ), (a) 8r+ 5y+ (b) Be + 8y-7=0, , (©) 8x 5y+60= (a) 5x— 8y+57=0, , ‘The triangle formed by the lines x+y=0,, , Br y= dandx+3y=dis, (a) isosceles, (©) right angled, , (b) equilateral, (a) None of these, , Consider the following statements, , 1. The straight line 5x + 4y = 0 passes through the, , point of intersection of the straight lines, x+2y-10=0and 2r+y+5=0., , HL Only one straight line can be drawn through the, origin at equal distances from the points A (2, 2), and B(4, 0)., , III The product of the perpendiculars from the, points (V5 , 0), (- V5 , 0)to the straight line, , , , 2x cos 8 ~ By sin @ = 6 is independent of @, Which of the statements given above are correct?, (@) Land I, , (© Both II] and 1, , (b) Hand 1, (@ AUT, Hand 1

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8:04PMY @, , Co © Bll B Sal, , Mathematics NDA NA Guide Exam a, , , , The Straight Line, , 21. Consider the following statements, , 1. The points (2,5) and (-1,4) are equidistant, from the line x+y +5=0., , Il, If 2pis the length of the perpendicular from the, , origin to the lines ae 1, then a”, 8p”, bare, , , , in HP,, Which of the statements given above are correct?, (a) Only 1 (b) Only Il, , (©) Both I and (@) None of these, , (22. What is the product of the endiculars from the, two points (2{b*=a?,0) to the line, , , , ax cos+ by sing=ab? (NDA 2009 11), (a)a® a? (ab @alb, , 23, What is the foot of the perpendicular from the point, (2,3)on the line x+ y-11=0 (NDA 2009 1), @A10 G6 (6,5) @(7,4), , 24, The perpendicular segment from the origin to a line, is of length 4 units and is inclined to the positive, direction of x-axis at an angle of 30°. The equation of, the line is, (a) Vax+y=8, , , , (@x+Viy=8, , , , , , 26. The perpendicular distance between two parallel, , , , lines Sx+ dy — Gx+8y+7=, 1 nit 19 nite a2, @) Fumie) Bunits (@ TF units (a) 5 unit, , , , 27. Consider the following statements, 1. The equation toa straight line parallel to the axis, of ris, y=d, where d is a constant., IL. ‘The equation to the axis of xis x=0., Which of the statement(s) given above is/are correct?, (NDA 2009 1), (a) Only 1, (©) Both I and 11, , (b) Only I, (@) Neither I nor I, , 28, The coordinates of P and @ are (~8,4) and (2,1),, respectively. If PQ is extended to R such that, PR=2QR, then what are the coordinates of R?, , (@) (3,7), , (b) (2,4), @(7,-2), , (NDA 2007 11), , , , 29. If B is the acute angle between the lines, px+ ay = p+qand p(x— y)+ glx + y)= 2g,then the, value of sinB is, , , , 500, , 39. The straight line ax+ by+c=0 and the coordinate, axes from an isosceles triangle under which one of, , the following conditions? (NDA 2007 1), @lal=161 @)lal=lel, ©lol=lel (@) None of these, , 40., , :, @, 1X, , Gaana Music, 4.5% > Google Play, , @ <, , @), , 1 1, (es @, 5 ued, , 30. The line &x + 4y-24=0 cuts the x-axis at A and, y-axis at B. The incentre of the 4 OAB, where Ois the, origin, is at, @22 OB O43) G4), , 81. ‘The points (3, 4) and (2,— 6) lie on opposite sides of, which one of the following lines?, (a) 10r— y= 26, (©) 8x—4y=8 (@)x, 82. What is the acute angle between the lines, Ax+ By= A+ Band A(x y)+B(x+ y)=2B?, , (NDA 2007 1), , @)tan"| A, ror, B, (@) 60°, ate], , 33. In what ratio does the line y-x+2= 0 cut the line, , , , , , , , , , (a) 45°, , , , © tan, , joining (8-1) and (8. 9? (NDA 2007 1), 2:3 @)3:2 @3:-2 12, 34, What is the angle between the _ lines, , xcosa + ysina = pand xcosf + ysinB = p’,a>B?, (@a+B @a-B, oat @, , , , 2, 85. What are the coordinates of the centroid of the, , triangle whose, (a) (0, 0), , , , ides are x=0,y=O,x+ y=, (b) (0,2), , 22, @(=,, cof5-5), 36. What is the locus of a moving point equidistant from, , the straight lines x + y= Oand x— y=@, , (a) xy=0 (b) xy = constant, , ©x @y, 37, The intercepts of a straight line upon the coordinate, , axes area and b. Ifthe length of the perpendicular on, , this line from the origin be 1, then which one of the, , following relations is correct?, , (a) +e 2 ), , , , , , , , , , 1 1, ate Oy, 38. If phe the length of the perpendicular from the origin, , on the straight line ax+by= pand oo then what, is the angle between the perpendicular and the, , positive direction of x-axis? (NDA 2007 1), (30°) 45° GO" (@) 90°, NDA/NA Mathematics, , hg, a, b &, ay by, 43. Assertion (A) Distance between two parallel lines,, , , , , , , , Install

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8:04PMY @, , Co © B tl B Sal, , Mathematics NDA NA Guide Exam a, , , , 500, , 39. The straight line ax+by+c=0 and the coordinate, axes from an isosceles triangle under which one of, , the following conditions? (NDA 2007 1), @lal=16) ()lal=lel, (lbl=lel (@) None of these, , , , What is the locus of the point of intersection of the, straight line x cos@ + y sin = aand the straight line, x sin®— y cos@= 6?, , (@) Acircle (b) An ellipse, (©) A hyperbola (@)A parabola, 41, The bisector of the acute angle between the straight, , , , lines 8x—4y-3=0 and 12x+5y+6=0 passes, through which one of the following points?, , (a) 6,3) (b) (-3, 6), , 02D @ C14), , Directions (Q. Nos. 42-45) Bach of these, ‘questions contain tio statements, one is Assertion (A), and other is Reason (R). Each of these questions also has, four alternative choices, only one of which is the correct, answer. You have to select one of the codes (a), (b), (c)and, (@ given below., Codes, (@) Both A and R are individually true and Ris the, correct explanation of A., (b) Both A and R are individually true but R is not, the correct explanation of A., (©) Ais true but R is false., (@) Ais false but R is true., , 42, Assertion (A) ‘The lines ax+ by +e=0,, br+ey +a.= 0 and cx+ ay +6=0 are concurrent, if, a +B +6 = Babe., Reason (R) The lines ax+hy+=0,, ax+hy+e=0 and ax+hy+g=0 are, concurrent, if, , , , Level |, L@® 2@ 326 &@ 5, L® 2 2 Me 4, 1 2 @ BO 2 @ 3,, BL 8S, 4) @), , , , 2@ 8 @ © 5, za@ ww © 15., 22. (@) 38. (b) (a)., az (a) 38. (a) ) 8B., 2 @ 43. @) @ 45., , , , NDA/NA Mathematics, , , , 48. Assertion (A) Distance between two parallel lines, Br dy += Oand Gr + By +7= 0182, , Reason (R) Distance between two parallel lines, , , , ax+ by +c, = Oand ax + by + = Dis|, , , , 44, Assertion (A) Two lines 5x+3y+7=0 and, 15x+ Sy + 39= Oare parallel., , Reason (R) Two lines qx+by+e=0 and, ax + by +e = Oare parallel, if aby ~ ayb, = 0., 45. Assertion (A) The lines 2x+3y+4=0 and, , 3=Oare perpendicular., Reason (R) The lines ax+ by +e, Az By (60 Osre porpendiculas aA be, , , , , , , , and, , Directions (Q. Nos. 46-48) Suppose there are, two lines given by 3x— 4y+9=Oand 6x- 8y-15=0., , 46. Find the angle between two lines,, , (a) 0° (b) 45° (@) 60° (@) 90°, 47. The distance hetween two lines is, @)5 398 3 (@) 3310, , 48. Find the equation of a line passing through (2, - 5), and parallel to the line 6x~ 8y—15=0., (a) 2x—By+ (b) Br—4y—26=0, (©) ax+4y-25=0 (a) x+2y+3=0, , 49. The equation of line which is perpendicular to, Sx-4y+9=0 and passing through (0, 3) is, , , , , , , , (a) 4x~3y- ax 4y—, , (©) 4x+ 3y- (@) 3x + 4y +8), 6 © 2@ 8 © 10. (a), 16.) 17). by 20. (0), 26. tb) 2) BB.) 30., 36) AT) 8) 40.0), 6 «@ z@ 8 @ 10, (©), 6% 1 18 © 20.0, 2 @) =A) BB) 30. (a), 40. (a), , , , Hints & Solutions, , eg