JEE Main 2026 · 8 Apr 2026 Shift 2

Consider the relation R on the set {−2, −1, 0, 1, 2} defined by (a, b) ∈ R if and only if 1 + ab > 0. Then, among the statements: I. The number of elements in R is 17 II. R is an equivalence relation

1. AOnly I is true
2. BOnly II is true
3. CBoth I and II are true
4. DNeither I nor II is true

The number of values of z ∈ C, satisfying the equations |z − (4 + 8i)| = √10 and |z − (3 + 5i)| + |z − (5 + 11i)| = 4√5, is:

1. A0
2. B2
3. C1
4. D4

If the system of linear equations: x + y + z = 6, x + 2y + 5z = 10, 2x + 3y + λz = μ has infinitely many solutions, then the value of λ + μ equals:

1. A12
2. B16
3. C22
4. D28

Let A = [α 1 2; 2 3 0; 0 4 5] and B = [1 0 0; 0 −5α 0; 0 4α −2α] + adj(A). If det(B) = 66, then det(adj(A)) equals:

1. A289
2. B361
3. C441
4. D529

Let α = 3 + 4 + 8 + 9 + 13 + 14 + ... up to 40 terms. If (tan β)^(α/1020) is a root of the equation x² + x − 2 = 0, β ∈ (0, π/2), then sin²β + 3cos²β is equal to:

1. A2
2. B7/4
3. C5/2
4. D3/2

A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are 2/5, 1/5 and 2/5. The probabilities that the candidate reaches late at the examination centre are 1/5, 1/3 and 1/4 if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is:

1. A11/37
2. B12/37
3. C13/37
4. D14/37

A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to:

1. A5.96
2. B6.14
3. C6.04
4. D6.24

If 26(2³/3 (¹²C₂) + 2⁵/5 (¹²C₄) + 2⁷/7 (¹²C₆) + ... + 2¹³/13 (¹²C₁₂)) = 3¹³ − α, then α is equal to:

1. A45
2. B48
3. C51
4. D54