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
Prove that root 2 is an irrational number Solution:- Let us assume that on the contrary that √2 is a rational number. Then there exist positive integers ‘a’ and ‘ b’ such that ⇒ Where and are coprime i.e. there HCF is 1 Squaring both side ⇒ ⇒ is divisible by 2 then also divisible … Read more
Question: Solution: Let —–(i) Let differentiate with respect to x Putting in eq (i) Divide by in numerator and denominator Let D.w.r. t.x Now OR We can do this question with another method —(i) Let Differentiate with respect to x Again taking Squaring both side Putting in (i) … Read more
f(x) = 5x^2+6x-9 prove that f is bijective. Question:- Consider given by prove that f is bijective. Solution:- To prove f is bijective,it is to prove f is one-one and onto Here, One-one: Let , such that i.e. f is one-one function. Onto:- Let f(x) = y Since, Obiviously, the value of Every value … Read more
Q:) Rahul had some bananas and he divided them into two lots A and B. He sold the first lot at the rate of ₹ 2 for 3 bananas and the second lot at the rate of ₹ 1 per banana and got a total of ₹400. If he had sold the first lot at … Read more
Q:) Ruhi invested a certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received ₹ 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have recieved ₹ 20 more … Read more