JEE Main 2025 · 4 Apr 2025 Shift 1

Consider the sets A = {(x, y) ∈ R × R : x² + y² = 25}, B = {(x, y) ∈ R × R : x² + 9y² = 144}, C = {(x, y) ∈ Z × Z : x² + y² ≤ 4} and D = A ∩ B. The total number of one-one functions from the set D to the set C is:

1. A15120
2. B17160
3. C18290
4. D19320

Let f, g : (1, ∞) → R be defined as f(x) = (2x + 3)/(5x + 2) and g(x) = (2 − 3x)/(1 − x). If the range of the function f∘g : [2, 4] → R is [α, β], then 1/(β − α) is equal to

1. A2
2. B29
3. C56
4. D68

Consider the equation x² + 4x − n = 0, where n ∈ [20, 100] is a natural number. Then the number of all distinct values of n, for which the given equation has integral roots, is equal to

1. A5
2. B6
3. C7
4. D8

Let A = {1, 6, 11, 16, ...} and B = {9, 16, 23, 30, ....} be the sets consisting of the first 2025 terms of two arithmetic progressions. Then n(A ∪ B) is

1. A3814
2. B3761
3. C4027
4. D4003

1 + 3 + 5² + 7 + 9² +... upto 40 terms is equal to

1. A33980
2. B43890
3. C40870
4. D41880

For an integer n ≥ 2, if the arithmetic mean of all coefficients in the binomial expansion of (x + y)²ⁿ⁻³ is 16, then the distance of the point P (2n − 1, n² − 4n) from the line x + y = 8 is

1. A√2
2. B2√2
3. C3√2
4. D5√2

The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is

1. A129/182
2. B103/182
3. C17/26
4. D19/26

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is

1. A3/5
2. B11/15
3. C2/15
4. D28/75