Let Z1 Z2 and Z_3 be three complex numbers on the circle
Question 4:- Let and
be three complex numbers on the circle |Z| = 1 with
and
. If
, then the value of α² + β² is :
(1) 24 (2) 41
(3) 31 (4) 29 [JEE 22 JAN 2025]
Answer : (4) 29
Explanation:- Given, |z| = 1
⇒
⇒
⇒
= |√2 + i(1 – √2)|²
= (√2)² + (1 – √2)²
= 2 + 1 + 2 – 2√2 = 5 – 2√2 = α + β√2 (Compare)
α = 5, β = -2
⇒ α² + β² = (5)² + (-2)²
= 25 + 4 = 29
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) | 0 ≤ y ≤ f(ax), 0 ≤ x ≤ 2} is :
(i) (ii)
(iii) (iv)
[JEE 22 JAN 2025]
Solution:- See full solution
Question 3:- Let the triangle PQR be the image of the triangle with vertices (1, 3), (3, 1) and (2, 4) in the line x + 2y = 2. If the centroid of ΔPQR is the point (α, β), then 15(α – β) is equal to :
(1) 24 (2) 19
(3) 21 (4) 22 [JEE 22 JAN 2025]
Answer:- See full answer
Question 5:- Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of is :
(1) 24 π² (2) 18 π²
(3) 31 π² (4) 22 π² [JEE 22 JAN 2025]
Answer :- See full answer