Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Three Dimensional Geometry

Long Answer Type

231.

Find the image of the point (1, 3, 4) in the plane x – y + z = 5.

90 Views

Short Answer Type

232. A variable plane passes through a fixed point (a, b, c) and meets the co– ordinate axes in A, B. C. Show that the locus of the point common to the planes through A. B, C parallel to the co-ordinate planes is

straight a over straight x plus straight b over straight y plus straight c over straight z equals 1.

96 Views

Long Answer Type

233. Establish by vector method the equation of the plane making intercepts a. b, c on the co-ordinate axes in the form of

straight x over straight a plus straight y over straight b plus straight z over straight c space equals space 1

78 Views

Multiple Choice Questions

234. The planes: 2x – y + 4 z = 5 and 5.x – 2.5 y + 10 z = 6 are

Perpendicular
Parallel
intersect y-axis
intersect y-axis

91 Views

Short Answer Type

235. Find the distance of the point (3, 4, 5) from the plane

straight r with rightwards arrow on top. space left parenthesis 2 space straight i with hat on top space minus space 5 space straight j with hat on top plus space 3 space straight k with hat on top right parenthesis space equals 13

90 Views

236. Find the distance from P (2, 1, – 1 ) to the plane x – 2 y + 4 z = 9.

92 Views

237. In the following cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(0, 0, 0) 3 x - 4 y+12 z = 3

91 Views

238. In the following cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(3, -2, 1) 2x - y + 2z + 3 = 0

The equation of plane is 2x –y + 2z + 3 = 0
Let p be length of perpendicular from (3, -2, 1) on plane.

therefore space space space space space space straight p space space equals space fraction numerator 2 left parenthesis 3 right parenthesis minus left parenthesis negative 2 right parenthesis space plus space 2 space left parenthesis 1 right parenthesis space plus space 3 over denominator square root of left parenthesis 2 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root end fraction space equals space fraction numerator 6 plus 2 plus 2 plus 3 over denominator square root of 4 plus 1 plus 4 end root end fraction space equals space fraction numerator 13 over denominator square root of 9 end fraction space equals 13 over 3

83 Views

239. In the following cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(2, 3, -5) x + 2y - 2z = 9

91 Views

240. In the following cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(–6, 0, 0) 2x - 3y + 6z - 2 = 0

93 Views