Question: A line l passes through point (-1,3,-2) and is perpendicular to both the lines and . Find the vector equation of the line l. Hence, obtain its distance from origin. Solution: Point (-1, 3, -2) Equation of lines Let dr’s of the line l are (a, b, c) Equation of line passes through the … Read more
![A function f:[-4,4] → [0,4] is given by f(x) = √16 - x²](https://gmath.in/wp-content/uploads/2023/03/one-one.png)
Question: A function f:[-4,4] → [0,4] is given by f(x) = √16 – x². show that f is an onto function but not a one-one function. Further, find all possible values of ‘a’ for which f(a) = √7. Solution:- A function is given that One-one :- Let are lies in Therefore, But Thus the given … Read more
Question : Show that right circular cone of least curve surface and given volume has an altitude equal to √2 time the radius of the base Solution: Let ‘r’ be the radius of cone and ‘h’ be the height of cone Volume of cone –(i) Curve surface area of cone Squaring both side Differentiating with … Read more
Question: If 20 m of wire is available for fencing off a flower-bed in the form of a circular sector, then the maximum area(In sq m) of the flower bed is (a) 12.5 (b) 10 (c) 25 … Read more
Question: Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/27 of the volume of the sphere. Solution: Consider be the centre and be the radius of the given sphere, In ΔOBM, using pythagoras theorem BM is the radius of cone Volume of cone Differentiating … Read more
Question: A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum? Solution: Let … Read more
Question: Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base. Solution: Let r be the radius of the circular base and h be the height of closed right circular cylinder. Formula for Total surface area –(i) Volume of cylinder Differentiating … Read more
Question 3:- Show that of all the rectangles inscribed in a given fixed circle, the square has maximum area. Solution: LetPQRS be the rectangle inscribed in a given circle with centre and radius a. Let and be the length and breadth of the rectangle, that is, and In right angled ΔPQR, using Pythagoras theorem, –(i) … Read more
Question 2:- A rectangula sheet of tin 45 cm by 24 cmis to be made into a box without top, by cutting of square from each corner and folding up the flaps. What should be the side of square to be cutt of so that the volume of the box is maximum? Solution: Length and … Read more
Question 1:- A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box … Read more