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
Three friends go for coffee. They decide who will pay the bill, by each tossing a coin and and then letting the “odd person” pay. There is no odd person if all three tosses produce the same result. It there is no odd person in the first round , they make a second … Read more