3D-PART-III-05-ASSIGNMENT

253. The distance of the point (1, –2 3) from the plane measured parallel to the line , is (a) 1 (b) (c) (d) None of these 254. If line is parallel to the plane , t (a) (b) (c) (d) None of these 255. The angle between the line and the plane is (a) (b) 45° (c) 60° (d) 90° 256. The angle between the line and the plane i (a) 45° (b) 0° (c) (d) 90° 257. The angle between the line and the plane , is (a) 0° (b) 30° (c) 45° (d) 90° 258. The angle between the line and the plane , is (a) (b) (c) (d) None of these 259. A straight line passes through the point (2, –1, –1). It is parallel to the plane and is perpendicular to the line . The equation of the straight line are (a) (b) (c) (d) 260. The equations of the projection of the line on the plane are (a) (b) (c) (d) 261. If a plane passes through the point (1, 1, 1) and is perpendicular to the line , then its perpendicular distance from the origin is (a) (b) (c) (d) 1 262. The line intersects the curve if (a) (b) (c) (d) None of these 263. The points on the line distant from the point in which the line meets the plane are (a) (0, 0, 0), (2, –4, 6) (b) (0, 0, 0), (3, –4, –5) (c) (0, 0, 0), (2, 6, –4) (d) (2, 6, –4), (3, –4, –5) 264. The angle between the line and the normal to the plane is (a) (b) (c) (d) 265. Angle between the line and the plane is (a) (b) (c) (d) 266. The ratio in which the sphere divides the line segment AB joining the points and is given by (a) externally (b) internally (c) externally (d) None of these 267. The graph of the equation in three dimensional space is (a) x-axis (b) z-axis (c) y-axis (d) yz-plane 268. A point moves so that the sum of the squares of its distances from two given points remains constant. The locus of the point is (a) A line (b) A plane (c) A sphere (d) None of these 269. The locus of the equation is (a) An empty set (b) A sphere (c) A degenerate set (d) A pair of planes 270. Let (3, 4, –1) and (–1, 2, 3) are the end points of a diameter of sphere. Then the radius of the sphere is equal to (a) 1 (b) 2 (c) 3 (d) 9 271. The number of spheres of radius ‘a’ touching all the coordinate planes is (a) 4 (b) 8 (c) 1 (d) None of these 272. The equation of the sphere touching the three coordinate planes i (a) (b) (c) (d) 273. Equation represent, a sphere, if (a) (b) (c) (d) and 274. The centre of the sphere which passes through (a, 0, 0), (0, b, 0), (0, 0, 0) is (a) (b) (c) (d) 275. The equation represents a sphere if (a) (b) (c) (d) 276. The radius of the sphere (a) 7 (b) 5 (c) 2 (d) 15 277. Centre of the sphere is (a) (b) (c) (d) 278. The equation of the tangent plane at a point on the sphere is (a) (b) (c) (d) None of these 279. If two spheres of radii and cut orthogonally, then the radius of the common circle is (a) (b) (c) (d) 280. The equation of the sphere, concentric with the sphere and which passes through (0, 1, 0), is (a) (b) (c) (d) 281. The radius of the sphere which passes through the points (0, 0, 0), (1, 0, 0), (0, 1, 0) and (0, 0, 1) is (a) (b) 1 (c) (d) 282. The coordinates of the centre of the sphere are (a) (1, –1, 1) (b) (–1, 1, –1) (c) (2, –3, 2) (d) (–2, 3, –2) 283. Equation of the sphere with centre (1, –1, 1) and radius equal to that of sphere is (a) (b) (c) (d) None of these 284. The equation of the sphere concentric with the sphere and which passes through the origin is (a) (b) (c) (d) None of these 285. The equation of the sphere with centre at (2, 3, –4) and touching the plane is (a) (b) (c) (d) None of these 286. Spheres and (a) Intersect in a plane (b) Intersect in five points (c) Do not intersect (d) None of these 287. If r be position vector of any point on a sphere and a and b are respectively position vectors of the extremities of a diameter, then (a) (b) (c) (d) 288. The centre of the sphere is (a) (b) (c) (d) 289. The spheres and cut orthogonally (a) (b) (c) (d) 290. If a sphere of constant radius k passes through the origin and meets the axis in A, B, C then the centroid of the triangle ABC lies on (a) (b) (c) (d) 291. The smallest radius of the sphere passing through (1, 0, 0), (0, 1, 0) and (0, 0, 1) is (a) (b) (c) (d) 292. In order that bigger sphere (centre , radius R) may fully contain a smaller sphere (center , radius r), the correct relationship is (a) (b) (c) (d) 293. A sphere is cut by the plane . The radius of the circle so formed is (a) (b) (c) 3 (d) 6 294. The radius of the circle (a) 4 (b) (c) 5 (d) 7 295. The line cuts the surface in the point (a) (1, 1, 1) and (1, 2, 3) (b) (1, –1, 2) and (1, 2, 4) (c) (1, 2, 3) and (2, –3, 1) (d) None of these 296. The equation of the sphere circumscribing the tetrahedron whose faces are and is (a) (b) (c) (d) None of these 297. A plane passes through a fixed point (a, b, c). The locus of the foot of the perpendicular drawn to it from the origin is (a) (b) (c) (d) 298. The equation of the sphere passing through the point (1, 3, –2) and the circle and is (a) (b) (c) (d) 299. Radius of the circle , is (a) 2 (b) 3 (c) 4 (d) 5 300. The shortest distance from the point (1, 2, –1) to the surface of the sphere is (a) (b) (c) (d) 2

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