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
EXERCISE 7.6(Integration) Integrate the functions in Exercises 1 to 22.(Ex 7.6 integration ncert maths solution class 12) Question 1: Solution: Let Question 2: Solution: Let Question 3: Solution: Let Question 4: Solution: Let Question 5: Solution: Let Question 6: Solution: Let Question 7: Solution: Let Question 8: Solution: Let Question 9: Solution: Let Where, Substituting … Read more
EXERCISE 7.5(Integration) Integrate the rational functions in Exercises 1 to 21.(Ex 7.5 integration ncert maths solution class 12) Question 1: Solution: Let putting in (i) Again putting Now, Integrating Let Question 2: Solution: Let Let Now Integrating Question 3: Solution: Let Again Let Again let Putting the value of A, B and C in eq … 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
Exercise 7.4(Integration) Integrate the functions in Exercises 1 to 23.(Ex 7.4 integration ncert maths solution class 12) Question 1: Solution: Let Let Question 2: Solution: Let Let Using formula : Hence, Question 3: Solution: Let Let Using formula : Hence, Question 4: Solution: Let Let , Now, Question 5:- Solution: let Let , Now, Question … Read more
Chapter 3:Miscellaneous Exercise Prove that(Class 11 Chapter 3 Miscellaneous Exercise trigonometry ) Question 1: Solution: Given, Using formula Question 2: Solution: Taking Using formula: and Question 3: Solution: Taking Using formula: and ) Question 4: Solution: Taking Using formulae: and ) Question 5: Solution: Taking Using formulae: Again using formula: Question 6: Solution: Taking Using … 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 be the radius of the circular base and be the height of closed right circular cylinder. Formula for Total surface area –(i) Volume of cylinder Differentiating with respect … Read more
EXERCISE 3.4(Trigonometric function) Find the principal and general solutions of the following equations(Ex 3.4 Trigonomety ncert maths solution class 11) Question 1: Solution: Given, Since ‘‘ positive in Ist and IIIrd quadrant Then, Hence the principal solution are Given, Hence the general solution is Question 2: Solution: Given, Since ‘‘ positive in Ist and IVth … Read more
EXERCISE 7.3(Integration) Find the integrals of the functions in Exercises 1 to 22:(Ex 7.3 integration ncert maths solution class 12) Question 1: Solution: Let Using formula Question 2: Question: Let Question 3: Solution: Let Using the identity given expression can be written as Question 4: Solution: Let Let Substitute , Question 5: Solution: Let Let … 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