Mathematics questions
18011 published questions with worked solutions.
- Let f : [−π/2, π/2] → ℝ be a differentiable function such that f(0) = 1/2. If _ x 0 x _0^xf(t)dt e^ x^2 - 1 = , then 8α² is equal...
- If 2sin³x + sin2xcosx + 4sinx – 4 = 0 has exactly 3 solutions in the interval [0, nπ/2], n ∈ ℕ, then the roots of the equation x²...Not in JEE Main syllabus
- If the domain of the function f(x) = ^ -1 ( 2 - |x| 4 ) + ( _e(3 - x) )^ -1 is [−α, β) − γ , then α + β + γ is equal to
- Let M denote the median of the following frequency distribution | Class | 0-4 | 4-8 | 8-12 | 12-16 | 16-20 |...
- Two integers x and y are chosen with replacement from the set 0, 1, 2, 3, …, 10 . Then the probability that |x – y| > 5, is:
- If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the...
- Let A(2, 3, 5) and C(–3, 4, –2) be opposite vertices of a parallelogram ABCD. If the diagonal BD = i + 2 j + 3 k, then the area...
- The value of _ n _ k=1 ^n n^3 (n^2 + k^2)(n^2 + 3k^2) is:
- Let Sₙ denote the sum of first n terms of an arithmetic progression. If S₂₀ = 790 and S₁₀ = 145, then S₁₅ – S₅ is:
- Consider the system of linear equation x + y + z = 4μ, x + 2y + 2λz = 10μ, x + 3y + 4λ²z = μ² + 15, where λ, μ ∈ ℝ. Which one of...
- Let g : ℝ → ℝ be a non constant twice differentiable function such that g′(1/2) = g′(3/2). If a real valued function f is defined...
- Let y = y(x) be the solution of the differential equation sec x dy + 2(1 – x)tan x + x(2 – x) dx = 0 such that y(0) = 2. Then...
- A line passing through the point A(9, 0) makes an angle of 30° with the positive direction of x-axis. If this line is rotated...
- If z = x + iy, xy ≠ 0, satisfies the equation z² + i z̄ = 0, then |z²| is equal to :
- Let a = a_1 i + a_2 j + a_3 k and b = b_1 i + b_2 j + b_3 k be two vectors such that |a⃗| = 1, a⃗·b⃗ = 2 and |b⃗| = 4. If c = 2(...
- The area (in square units) of the region bounded by the parabola y² = 4(x – 2) and the line y = 2x – 8, is:
- The maximum area of a triangle whose one vertex is at (0, 0) and the other two vertices lie on the curve y = –2x² + 54 at points...
- Let (α, β, γ) be the foot of perpendicular from the point (1, 2, 3) on the line x+3 5 = y-1 2 = z+4 3. Then 19(α + β + γ) is...
- A group of 40 students appeared in an examination of 3 subjects – Mathematics, Physics and Chemistry. It was found that all...
- The value of 9 _0^9 [ 10x x+1 ]dx, where [t] denotes the greatest integer less than or equal to t, is ________.