JEE MATHS UNIT 11
QUIZ NO 4
TOTAL QUESTIONS = 20


1. The equation of a plane parallel to the xz-plane is


2. The distance of the point (3, 4, 5) from the origin is


3. The equation of a sphere with center (2, -3, 4) and radius 5 is


4. The shortest distance between two parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is


5. The direction cosines of a line are related by the equation


6. The equation of the plane passing through the point (1, -2, 3) and perpendicular to the vector (2, 1, -3) is


7. The angle between two planes 3x - y + 2z = 5 and x + y - z = 3 is


8. The distance of the point (2, -1, 4) from the plane x + 2y - 3z + 5 = 0 is


9. The parametric equations of a line passing through (1, -2, 3) and parallel to (2, -1, 4) are


10. The vector equation of the plane passing through the point (2, 3, -4) and normal to (1, -1, 2) is


11. The length of the perpendicular from the point (1, 2, 3) to the plane x + 2y + 3z = 6 is


12. The equation of the plane passing through the points (1, 0, 0), (0, 1, 0), and (0, 0, 1) is


13. The line x = 1 + t, y = 2t, z = 3 - t intersects the plane x + y + z = 6 at


14. The equation of the sphere with center (0, 0, 0) and radius 7 is


15. The angle between the lines with direction ratios (3, -4, 5) and (-6, 8, 10) is


16. The coordinates of the centroid of a tetrahedron with vertices (1, 1, 1), (2, 0, 0), (0, 2, 0), and (0, 0, 2) are


17. The volume of a tetrahedron with vertices (1, 0, 0), (0, 1, 0), (0, 0, 1), and (2, 2, 2) is


18. The equation of the line passing through (3, -2, 4) and parallel to (1, -3, 2) is


19. The shortest distance between the lines x/1 = y/2 = z/3 and (x-1)/3 = (y+1)/2 = (z-2)/1 is


20. The vector perpendicular to both (1, -2, 3) and (-3, 4, -5) is



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