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were purer mereys, , ani wi, 1. For every point P (x, y, 2) on the xy-plane,, (a) x=0 (b) y=0 (G@iz—0 (d) x=y=z=0, 2. For every point P (x, y, Z) on the x-axis (except the origin),, (a) x = 0,y = 0,z#0 (b)x = 0,z = 0,y#0, , (c) y = 0,z = 0,x#0 Qh —2=0, by planes drawn through the points (5,7, 9) and, , 5. A rectangular parallelopiped is formed, (2, 3,7) parallel to the coordinate planes. The length of an edge of this rectangular, , parallelopiped is, (a) 2 (b) 3 (c) 4 (d) all of these, , 4A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9,7, parallel to the coordinate planes. The length of a diagonal of the parallelopiped is, , (a) 7 (b) ¥38 (c) V155 (d) none of these

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Ratio in which the xy-plane divides the join of (1, 2,3) and (2, é ie 1 externally, , (a) 3:1internally (b) 3:1externally (¢) 1:2 internally (d) Ay des PQ in the ratio, fP(3,2,~4),0.6,4,~6) and R (9, 8, —10) are collinear, then RAVI, , (a) 3:2internally (b) 3:2externally (c) 2: 1 internally De tee ly i, A(3, 2, 0), BG, 3, 2)andC (- 9, 6, ~ 3) are the vertices of a triangle BE, , ector of, , i ZABC meets BC at D, then coordinates of D are, (a) (19/8 ,57/16 , 17/16) () (-19/8, 57/16, 17/16), (c) (19/8 , 57/16 , 17/16) (d) none of these, 11. If O is the origin, OP = 3 with direction ratios proportion — to -1,2,-2 then the, coordinates of P are, (a) (-1,2,-2) — (®) 4,2, 2) (©) (-1/9, 2/9, - 2/9 (a) G, 6-9), 12. The angle between the two diagonals of a cube is, (a) 30° (b) 45° (0) cos”! (5) (a) cos”? (3), 33, If a line makes angles a,B,y,6 with four diagonals of a cube, then, , cos? a + cos” B+ cosy +cos* 8 is equal to, , Ht 2 4, as Ol Og, ot of the perpendicular drawn from the point (2, 5,7) on the x-axis, , 8, oe, , 14, The coordinates of the fo, are, (a) (2,0,0) (b) (0,5,0) (c) ©,0,7) (d) (0,5,7), (NCERT EXEMPLAR], , 15. Pisa point on the line segment joning the points (3, 2,-1) and (6, 2, -2). If x-coordinate of P, , is 5, then its y-coordinates is, , @2 (b) 1 () -1 (a) -2, {NCERT EXEMPLAR], 16. The distance of the point (a, B, y) from y-axis is ti, pele, () B (b) |B (©) [Bi+I yl (d) ya" +y, {NCERT EXEMPL AR], , t Ae, 7. The direction cosines of a line are k, k, k, then, , @) ko (b) 0<k<1 (c) k=1

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ee —™”_-—S—S—sSM$susMw—:—sSs—(— eeeeti‘_, , 1. ABC istriangle in a plane with vertices A (2, 3, 5), B(-I, 3; 2), andC (A, 5, 1). Ifthe median through A is equally inclined to, the coordinate axes, then the value of (3+ fe 5) se, , [Online April 10, 2016], (a) 1130 (b) 1348 (c) 1077 (d) 676, 2. Theangle between the lines whose direction cosines satisfy, , the equations /+m+n=0 and |? + m+n? is [2014], , (a) (b), , wla ala, Ala vila, , (c) (d), , 3. LetA(2,3,5),BC1, 3,2) and C (A, 5, 1) be the vertices ofa, AABC. if the median through A is equally inclined to the, , coordinate axes, then: [Online April 11, 2014], (a) 5A—Su=0 (b) 8A—S5p=0, (c) 10A—7p=0 (d) 7A—10pn=0, , 4. A line in the 3-dimensional space makes an angle 0, , 1, [0 <0 | with both the x and y axes. Then the set of all, , values of 9 is the interval: [Online April 9, 2014], , nt] Ea, ee, ies @ (372, , 5. Let ABC be a triangle with vertices at points A (2, 3, 5),, B(-l, 3,2) and C (A, 5, 1) in three dimensional space. If the, median through A is equally inclined with the axes, then, (A, |t) is equal to: [Online April 25, 2013], (a) (10,7) (b) (7.5) |, (cyan (7910) (d) (5,7)

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10., , il., , Ifthe projections ofa line segment on the x, y and z-axes;, 3-dimensional space are 2, 3 and 6 respectively, then i, length of the line segment is : [Online April 23, 213),, (a) 2 (b) 7 |, () 9 (d) 6, , The acute angle between two lines such that the direction, cosines /, m, 1 of each of them satisfy the equations, J+ m+n=Oand P+m?2-n°=0is :|Online April 22, 2013], (a) 15° (b) 30°, , (c) 6 (d) 45°, , Aline AB in three-dimensional space makes angles 45° and, 120° with the positive x-axis and the positive y-axis, respectively. If AB makes an acute angle 0 with the positive, , z-axis, then 9 equals [2010], (a) 45° (b) 60°, (c) 75° (d) 30°, , The projections of a yector on the three coordinate axis are 6,, _3, 2 respectively. The direction cosines of the vector are +, , [2009], 6-3 2 b 6 3 2, , a eas ON nT, , ( shee d) 6,-3.2, , Omi 7 (d) 6,-3,, , Ifa line makes an angle of «/4 with the positive directions, of each of x- axis and y- axis, then the angle that the line, makes with the positive direction of the zaxisis {2007\, , 1 1, @ 7 (b) 5, X a, , (c) 6 @ 3, , A line makes the same angle 8, with each of thex and zaxis, If the angle B, which it makes with y-axis, is such that, , sin? B= 3sin2 6, then cos20 equals (2004), 2 1, , @ = () 5, , 3 wy, © 3 Oe

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42. The number of distinct rea] values of), oO} A, , { ., al ¥-2 243 SF which the lines, , 2 22 and ——— >, , , , iT, , , , coplanar is : [0 : wee, nlin, ; |, @ 2 bg Pt0,20164, @ 3 @) 4, 13. The shortest distance between the lines = 22-2, nes —=1—, ss 227 and, x+2 mn y=4 7-5 |, i se lies in the interval - |, [Onli i, pone Gouc a April 9, 2016], (© [1,2) —@ 10, 14. Equation of the line of the shortest distance between the, 4 x Yo z x-l 1, lines = = and =— = =2 |;, qo ae 0 = 7, , [Online April 19, 2014], , , , , , @ *=-2-4 (ey ee avebe, 1 -1 -2 ] wi i}, x—-1_ytl z “4 yz, c a a — = =—, ee mena | => eT 52, cy ses, 15. Ifthe lines = and, , are coplanar, then k can have, , , , [2013], , (b) exactly one value, , (a) any value, exactly three values, , (c) exactly two values (d), 16. Iftwo lines Z, and L, in space, are defined by, , Ly ={x=viy+(Vi-1), z=(va-t)y+vi| and, I, ={x=yuy+(I-Ve), z=(I-vi) + ul, , for all non-negative reals 4, , is perpendicular to Ly», pa a [Online April 23, 2013), , and 1, such that :, , (a) Vi+Ju=! chee, , (d) A=H, , (c) A+H=0