Mathematics questions
18011 published questions with worked solutions.
- A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times then the probability of...
- Let f, g : (0, ∞) → ℝ be two functions defined by f(x) = _ -x ^x(|t| - t^2)e^ -t^2 dt and g(x) = _0^ x^2 t^ 1/2 e^ -t dt. Then,...
- Let z₁ and z₂ be two complex numbers such that z₁ + z₂ = 5 and z₁³ + z₂³ = 20 + 15i. Then |z₁⁴ + z₂⁴| equals
- The number of solutions, of the equation e^ sin x − 2e^ −sin x = 2, isNot in JEE Main syllabus
- Let A(a, b), B(3, 4) and C(−6, −8) respectively denote the centroid, circumcentre and orthocenter of a triangle. Then, the...
- The temperature T(t) of a body at time t = 0 is 160°F and it decreases continuously as per the differential equation dT/dt = −K(T...
- Consider the function f : (0, ∞) → ℝ defined by f(x) = e^ -| _ex| . If m and n be respectively the number of points at which f is...
- Let A be a 3 × 3 matrix and det(A) = 2. If n = det(adj(adj(…(adj A)))) (adj taken 2024 times), then the remainder when n is...
- Let the coefficient of xʳ in the expansion of (x + 3)ⁿ⁻¹ + (x + 3)ⁿ⁻²(x + 2) + (x + 3)ⁿ⁻³(x + 2)² + ....... (x + 2)ⁿ⁻¹ be αᵣ. If...
- | 120 ^3 _0^ x^2 x x ^4x + ^4x dx | is equal to ________.
- Let y = y(x) be the solution of the differential equation sec²x dx + (e²ʸ tan²x + tan x)dy = 0, 0 < x < π/2, y(π/4) = 0. If...
- Let A = 1, 2, 3, …., 100 . Let R be a relation on A defined by (x, y) ∈ R if and only if 2x = 3y. Let R₁ be a symmetric relation...
- If _ x 0 ax^2e^x - b _e(1+x) + cxe^ -x x^2 x = 1, then 16(a² + b² + c²) is equal to ________.
- A line passes through A(4, −6, −2) and B(16, −2, 4). The point P(a, b, c), where a, b, c are non-negative integers, on the line...
- Let a, b, c be the lengths of three sides of a triangle satisfying the condition (a² + b²)x² − 2b(a + c)x + (b² + c²) = 0. If the...
- Let A(−2, −1), B(1, 0), C(α, β) and D(γ, δ) be the vertices of a parallelogram ABCD. If the point C lies on 2x − y = 5 and the...
- Let a⃗ = 3î + 2ĵ + k̂, b⃗ = 2î − ĵ + 3k̂ and c⃗ be a vector such that (a⃗ + b⃗) × c⃗ = 2(a⃗ × b⃗) + 24ĵ − 6k̂ and (a⃗ − b⃗ +...
- The solution curve of the differential equation y dx dy = x( _ex - _ey + 1), x > 0, y > 0 passing through the point (e, 1) is
- For 0 < c < b < a, let (a + b − 2c)x² + (b + c − 2a)x + (c + a − 2b) = 0 and α ≠ 1 be one of its root. Then, among the two...
- If f(x) = vmatrix x^3 & 2x^2 + 1 & 1 + 3x 3x^2 + 2 & 2x & x^3 + 6 x^3 - x & 4 & x^2 - 2 vmatrix for all x ∈ ℝ, then 2f(0) + f′(0)...