This document contains 44 multiple choice questions about solid geometry and calculating the fraction of radiation intercepted by various geometric objects from a point source of light. The questions cover topics like solid angles subtended by spheres, cylinders, cones, and other objects, as well as the fraction of radiation intercepted by objects like toruses, planes, and shells based on their geometry and position relative to the point source.

1. Competitive Questions
Advanced Geometry by H.C. Rajpoot
Q.1.An electric bulb of 200 W is mounted onto the centre of one of the walls of a room of Find out the total radiation energy striking the floor area if the bulb emits radiation uniformly in all the directions.
(Neglect height of bulb from the centre of wall) Ans. 21.788 J/sec
Q.2.A uniform point-source of light is located at the centre of a torus having inner & outer radii 10cm & 18cm respectively. What will be the fraction of total radiation intercepted by the torus? Ans. ⁄
Q.3.A torus intercepts of the total radiation emitted by a uniform point- source located at the centre of torus. Find out ratio of outer to inner radii of torus. Ans. ⁄
Q.4.A solar-panel of is illuminated by a uniform point-source of light located at a normal height 15√√ from the centre of panel. Find out percentage of total radiation incident on panel. Ans.
Q.5. Find out the solid angle subtended by an infinitely long vertical cylindrical pole with a diameter D at a point lying in the plane of base at a normal distance 2D from the longitudinal axis. Ans. ⁄
Q.6.A torus having diameter 8cm intercepts of the total radiation emitted by a uniform point-source located at the centre of torus. Find out inner & outer radii of torus. Ans. 14cm & 6cm
Q.7.A uniform point-source of light is located at a normal height 8cm from the centre of an infinitely long rectangular plane having width 16cm. What will be the percentage of total radiation intercepted by the plane? Ans.
Q.8.Some identical spheres are arranged, touching one another, in a complete circular fashion such that each of them intercepts of total radiation emitted by a uniform point-source located at the centre of polygonal plane obtained by joining the centres of spheres. Find out number of spheres. Ans. 3

2. Q.9.A uniform point-source of 100 cd is located at the centre of a simple cubic cell. What will be total flux directly escaping the cell? Ans. 334.24 lm
Q.10. Solid angle subtended by an ellipsoid having major and minor axes respectively at any point lying on the major axis at a distance from the centre is given by ( √ ) ( √ ) ( √ )
Q.11.An ellipsoid with major axis unit & eccentricity √ ⁄ subtends a solid angle at a point lying on the major axis at a distance unit from the centre. The value of ⁄ √ √ √
Q.12.A sphere with radius R intercepts of total radiation emitted by a uniform point-source located at a distance from the centre. Then the value of ⁄ is equal to √ √ √
Q.13. Solid angle, subtended by an infinitely long circular cylinder with a radius 14cm at a point lying in the plane of one of the circular-ends at a normal distance 84cm from the longitudinal axis, is equal to
( ) ( ) ( ) ( )

3. Q.14.A uniform point-source of light is mounted at a normal height ‘ ’ from the centre of an infinitely long rectangular plane having width ‘ ’. If plane intercepts of total radiation emitted by the source then ⁄ equal to
Q.15.A circular plane intercepts of total radiation emitted by a uniform point-source located at a normal height from the centre. Then the area of circular plane is equal to
Q.16.A square plane intercepts fraction of total radiation emitted by a uniform point-source located at a normal height from one of the vertices. Then the area of square plane is equal to
Q.17.The angle between any two -bonds in molecule is given as ( √ ) ( √ ) (√ ) (√ )
Q.18. Solid angle (in sr.), subtended by a right pyramid having base as an equilateral triangle & angle between any two consecutive lateral edges at the vertex is equal to (√ ) (√ ) (√ ) (√ )
Q.19.A uniform point-source of light is located at a point in the space. Fraction of total radiation, intercepted by a plane bounded by the straight lines is

4. Q.20.A uniform point-source of 400cd is located at a point in the space. Total flux, intercepted by a plane bounded by the straight lines is
Q.21.A right circular cone with apex angle is thoroughly cut with a plane inclined at an angle with the longitudinal axis of cone. Eccentricity of generated elliptical-section is √ √ √ √
Q.22.A right circular cone with apex angle is thoroughly cut with a plane inclined at an angle with the longitudinal axis of cone. Angle, between the longitudinal axis & the line joining centre of elliptical-section to the apex-point of cone, is equal to ( ) ( ) ( ) ( ) Q.23.A uniform point-source of light is located at the centre of a torus. If ratio of inner to outer radii is ⁄ then the fraction of total radiation intercepted by the torus is equal to
Q.24. Total solid angle subtended by the identical spheres forming a tetrahedral void at the centre is equal to ( √ ) ( √ ) ( √ )
Q.25. Total solid angle subtended by the identical spheres forming an octahedral void at the centre is ( √ ) ( √ ) ( √ )

5. Q.26. Total solid angle subtended by the identical spheres forming a simple cubic unit-cell at the centre is ( √ ) ( √ ) ( √ )
Q.27.A uniform point-source of luminous intensity is located at the centre of hollow cylindrical shell with a radius & length Total flux intercepted by the shell is given by ( √ ) ( √ ) ( √ )
Q.28. Solid angle (in sr.), subtended by the largest sphere completely trapped in a tetrahedral void, at the centre of each of the identical spheres forming void is ( √√ ) ( √√ ) ( √√ ) ( √√ )
Q.29. Solid angle (in sr.), subtended by the largest sphere completely trapped in an octahedral void, at the centre of each of the identical spheres forming void is ( √ √ ) ( √ √ ) ( √ √ ) ( √ √ )

6. Q.30.A uniform point-source of luminous intensity is located at the centre of hollow conical shell with a radius & normal height Total flux intercepted by the shell is given by ( √ ) ( √ ) ( √ ) ( √ )
Q.31.A hollow cylindrical shell intercepts ⁄ of total radiation emitted by a uniform point-source of light located at the centre of shell. Ratio of length to diameter of the shell is √ √ √ √
Q.32.A hollow conical shell intercepts of total radiation emitted by a uniform point-source of light located at the centre of mass of shell. Ratio of radius to normal height of the shell is √ √ √ √
Q.33.A hollow cylindrical shell intercepts ⁄ of total radiation emitted by a uniform point-source of light located at the centre of shell. Ratio of diameter to length of the shell is √ √ √ √
Q.34. Solid angle (in sr.), subtended by the largest sphere completely trapped in a simple cubic cell, at the centre of each of the identical spheres forming S.C.C. is ( √ √ √ ) ( √ √ √ ) ( √ √ √ )

7. ( √ √ √ )
Q.35.A square plane intercepts ⁄ of total radiation emitted by a uniform point-source located at a normal height from one of the vertices then the area of plane is
Q.36.A square plane intercepts ⁄ of total radiation emitted by a uniform point-source located at a normal height from the centre then the area of plane is
37. Solid angle, subtended by a rectangular plane having length & width at a point lying at a normal height from one of the vertices of plane is ( √ ) ( √ ) ( √ ) ( √ )
Q.38.An equilateral-triangular plane intercepts of total radiation emitted by a uniform point-source located at a normal height from the centre then the area of plane is √ √ √
Q.39. Solid angle (in sr.) subtended by the solid generated by rotating the parabola, about -axis at a point is ( √ ) ( √ ) ( √ ) ( √ )
Q.40. Solid angle subtended by the plane bounded by the straight lines at a point is

8. Q.41. Solid angle subtended by the plane bounded by the straight lines at a point is ( ) ( ) ( ) ( )
Q.42. Solid angle subtended by the plane bounded by the straight lines at a point is (√ ) (√ ) (√ ) (√ )
Q.43. Solid angle subtended by the plane bounded by the straight lines at a point is ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
Q.44. Solid angle subtended by XY-plane, in the first quadrant, at a point is ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )