Question 5:- Let f : R – {-4/3} → R be a function defined as f(x) = 4x/(3x+4). Show that, f:R – {-4/3} → Range of f, f is one-one and onto. [CBSE 2017(C)] Solution:- One-one: Let x, y ∈ R -{-4/3} Now, f(x) = … Read more
Question 6:- Let A = R – {3}, B = R – {1}. If f : A → B be defined by f(x) = {x – 2}/{x – 3}, ∀x ∈ A. Then, show that f is bijective. Solution:- Given that, A = R – {3}, B = R – {1}. f : A → … Read more
Question 7:- Let f : W → W, be defined as f(x) = x – 1, if x is odd and f(x) = x + 1, Show that f is bijective. Solution: One-one :- Case I : When x, y are even number Now, f(x) = f(y) ⇒ x + 1 = y + 1 … Read more
Question 4:- Consider → [4, ∞) given by f(x) = x² + 4. Show that f is invertible. [CBSE(AI) 2013] Solution:- One-one: Let x, y ∈ (Domain) such that f(x) = f(y) ⇒ x² + 4 = y² + 4 ⇒ x² = y² ⇒ x = y [∴ x, y are … Read more
Here we provide CBSE Class 12 math paper-2024 set-2 series QSS4R/4 for practice and student get more marks after understanding the question type in board exam. Case study question are in the paper of 12 marks. MATHEMATICS Cbse Class 12 math paper-2023 set-1 series-EF1GH/C CBSE Class … Read more
Question:1 There are 7 red and 8 white balls in the box. We get 5 balls without returning. What is the probability that exactly 4 balls will be red ? Solution: Number of Red balls = 7 Number of white balls = 8 Probability that exactly 4 balls will be Red = 4 balls Red … Read more
Question 3: show that the given differential equation is homogeneous and solve it. . Solution: . The given differential equation can be expressed as Now, Therefore, F(x, y) is a homogeneous function of degree zero. So, the given differential equation is a homogeneous differential equation . Put y = vx Putting the value of dy/dx … Read more
Question 2: Show that differential equation is homogeneous and find its particular solution, given that x = 0 when y = 1. [CBSE(North) 2016; (south) 2016, 2017] Solution: Given: Let, ∴ Hence, given differential equation is homogeneous. Now, … Read more
Question 1: Solve the following differential equation: x ≠ 0 Solution: It is a homogeneous differential equation. Put y = vx and We have, ………(i) On integrating both sides, we have Let Some other question Question 2: Show that differential equation is homogeneous and find its particular solution, given that x = 0 … Read more
Question 10: A sum of ₹ 4,250 is to be used to give 10 cash prizes to students of a school for their overall academic performance. If each prize is ₹ 50 less than its preceding prize, find the value of each of the prizes. [CBSE 2017] … Read more