Mathematics questions for JEE Main

The value of cosec 10° − √3 sec 10° is equal to:

Let a₁ = 1 and for n ≥ 1, aₙ₊₁ = ½aₙ + (n² − 2n − 1)/(n²(n + 1)²). Then |Σ (n = 1 to ∞) (aₙ − 2/n²)| is equal to:

If the system of equations 3x + y + 4z = 3 2x + αy − z = −3 x + 2y + z = 4 has no solution, then the value of α is equal to:

If the domain of the function f(x) = sin⁻¹((5 − x)/(3 + 2x)) + 1/logₑ(10 − x) is (−∞, α] ∪ [β, γ) − {δ}, then 6(α + β + γ + δ) is equal to:

Let L be the line (x + 1)/2 = (y + 1)/3 = (z + 3)/6 and let S be the set of all points (a, b, c) on L, whose distance from the line (x + 1)/2 = (y + 1)/3 = (z − 9)/0 along the line L is 7. Then Σ_((a,b,c)∈S) (a + b + c) is equal to:

Let A = {−2, −1, 0, 1, 2, 3, 4}. Let R be a relation on A defined by xRy if and only if 2x + y ≤ 2. 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:

Let a circle of radius 4 pass through the origin O, the points A(−√3a, 0) and B(0, −√2b), where a and b are real parameters and ab ≠ 0. Then the locus of the centroid of ΔOAB is a circle of radius:

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