Gmath

Question 2:- Let f : R → R be a twice differentiable function such that f(x + y) = f(x) f(y) for all x, y ∈ R. If f'(0) = 4a and f satisfies f”(x) – 3a f'(x) – f(x) = 0, a > 0, then the area of the region R = {(x, y) … Read more

Question 1:- The number of non-empty equivalence relations on the set {1, 2, 3} is : (i)  6                   (ii) 7 (iii) 5                  (iv) 4                        [JEE 22 JAN 2025] … Read more

Question 1:- For a positive integer n if the quadratic equation, x(x+1)+(x+1)(x+2) + . . . +[x+(n-1)][x+n] = 10n has two consecutive integral solution, then n is equal to (a) 12           (b) 9 (c) 10            (d) 11 Solution:- Given quadratic equation is x(x+1)+(x+1)(x+2) + . . … Read more

Question 5:- The region represented by {z = x + iy ∈ C : |z| – Re(z) ≤ 1} is also given by the inequality : (A) y² ≤ x + 1/2 (B) y² ≤ 2(x + 1/2) (C) y² ≥ x + 1 (D) y² ≥ 2(x + 1) Solution:- Given that, z = … Read more

Question 4:- If Re(z-1/2z+i) = 1, where z = x + iy, then the point (x, y) lies on a : (A) Straight line whose slope is -2/3 (B) Straight line whose slope 3/2 (C) Circle whose diameter is √5/2 (D) Circle whose centre is at (-1/2, -3/2) Solution:- Since, z = x + iy … Read more

Question 2:- Let complex numbers α and lies on circles and , respectively. If satisfies the equation , then |α| is equal to (2013 Adv.) Solution:- Intersection of circles, the basic concept is to equations simultaneously and using properties of modulus of complex numbers. We know that, and Here, and could be written as and … Read more