JEE Main 2025 · 3 Apr 2025 Shift 2

Let A = {−2, −1, 0, 1, 2, 3}. Let R be a relation on A defined by xRy if and only if y = max{x, 1}. Let l be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then l + m + n is equal to

1. A11
2. B12
3. C13
4. D14

Let f be a function such that f(x) + 3f (24/x) = 4x, x ≠ 0. Then f(3) + f(8) is equal to

1. A10
2. B11
3. C12
4. D13

Let the equation x(x + 2)(12 − k) = 2 have equal roots. Then the distance of the point (k, k/2) from the line 3x + 4y + 5 = 0 is

1. A5√3
2. B12
3. C15
4. D15√5

If z₁, z₂, z₃ ∈ C are the vertices of an equilateral triangle, whose centroid is z₀, then ∑ₖ₌₁³ (zₖ − z₀)² is equal to

1. A1
2. B0
3. Ci
4. D−i

The sum 1 + (1 + 3)/2! + (1 + 3 + 5)/3! + (1 + 3 + 5 + 7)/4! + ... upto ∞ terms, is equal to

1. A4e
2. B2e
3. C6e
4. D3e

Line L₁ of slope 2 and line L₂ of slope 1/2 intersect at the origin O. In the first quadrant, P₁, P₂,...,P₁₂ are 12 points on line L₁ and Q₁, Q₂,...,Q₉ are 9 points on line L₂. Then the total number of triangles, that can be formed having vertices at three of the 22 points O, P₁, P₂,...,P₁₂, Q₁, Q₂,...,Q₉, is:

1. A1026
2. B1080
3. C1134
4. D1188

If the probability that the random variable X takes the value x is given by P(X = x) = k(x + 1)3⁻ˣ, x = 0, 1, 2, 3,..., where k is a constant, then P(X ≥ 3) is equal to

1. A7/27
2. B8/27
3. C4/9
4. D1/9

Let the Mean and Variance of five observations x₁ = 1, x₂ = 3, x₃ = a, x₄ = 7 and x₅ = b, a > b, be 5 and 10 respectively. Then the Variance of the observations n + xₙ, n = 1,2,...,5 is

1. A16
2. B16.4
3. C17
4. D17.4