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Let S = { z ∈ C : |(z − 6i)/(z − 2i)| = 1 and |(z − 8 + 2i)/(z + 2i)| = 3/5 }. Then ∑_{z∈S} |z|² is equal to

JEE Main Complex Numbers | Locus problem with modulus | Find Σ|z|² Q. Let $S={zinmathbb{C}:left|frac{z-6i}{z-2i}right|=1 text{ and } left|frac{z-8+2i}{z+2i}right|=frac{3}{5}}$. Then

The number of numbers greater than 5000, less than 9000 and divisible by 3, 73 that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits

The number of 3 × 2 matrices A, which can be formed using the elements of the set {−2, −1, 0, 1, 2} such that the sum of all the diagonal elements of AᵀA is 5, is

Let a differentiable function f satisfy the equation ∫₀³⁶ f(tx/36) dt = 4α f(x). If y = f(x) is a standard parabola passing through the points (2, 1) and (−4, β), then β^α is equal to ___.

The number of the real solutions of the equation: � is

Let 729, 81, 9, 1, … be a sequence and Pₙ denote the product of the first n terms of this sequence. If 2 ∑ₙ₌₁⁴⁰ (Pₙ)^(1/n) = (3^α − 1) / 3^β and gcd(α, β) = 1, then α + β is equal to

Let S = { z ∈ C : |(z − 6i)/(z − 2i)| = 1 and |(z − 8 + 2i)/(z + 2i)| = 3/5 }. Then ∑_{z∈S} |z|² is equal to

The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation α in this data is replaced by β, then the mean and variance become 10.1 and 1.99, respectively. Then α + β equals

Let a⃗ = 2î + ĵ − 2k̂, b⃗ = î + ĵ and c⃗ = a⃗ × b⃗. Let d⃗ be a vector such that |d⃗ − a⃗| = √11, |c⃗ × d⃗| = 3 and the angle between c⃗ and d⃗ is π/4. Then a⃗ · d⃗ is equal to

If the function f(x) = [ e^x ( e^{tan x − x − 1} ) + logₑ(sec x + tan x) − x ] / ( tan x − x ) is continuous at x = 0, then the value of f(0) is equal to