Mathematics questions
18011 published questions with worked solutions.
- If ( 1+i 1-i )^ m/2 = ( 1+i i-1 )^ n/3 =1, (m, n ∈ N), then the greatest common divisor of the least values of m and n is...
- The value of k ∈ ℕ for which the integral I_n = _0^1(1 - x^k)^ndx, n ∈ ℕ, satisfies 147 I₂₀ = 148 I₂₁ is:
- The sum of all the solutions of the equation (8)²ˣ − 16·(8)ˣ + 48 = 0 is:
- Let the circles C₁ : (x − α)² + (y − β)² = r₁² and C₂ : (x − 8)² + (y - 15 2 )^2 = r₂² touch each other externally at the point...
- Let P(x, y, z) be a point in the first octant, whose projection in the xy-plane is the point Q. Let OP = γ; the angle between OQ...
- The number of critical points of the function f(x) = (x − 2)^ 2/3 (2x + 1) is:
- Let f(x) be a positive function such that the area bounded by y = f(x), y = 0 from x = 0 to x = a > 0 is e⁻ᵃ + 4a² + a − 1. Then...
- Let f(x) = 4cos³x + 3√3 sin²x − 10. The number of points of local maxima of f in interval (0, 2π) is:
- Let A = bmatrix 2 & a & 0 1 & 3 & 1 0 & 5 & b bmatrix . If A³ = 4A² − A − 21I, where I is the identity matrix of order 3 × 3,...
- If the shortest distance between the lines L₁ : r = (2 + λ)î + (1 − 3λ)ĵ + (3 + 4λ)k̂, λ ∈ R, L₂ : r = 2(1 + μ)î + 3(1 + μ)ĵ + (5...
- If sin x = − 35, where π < x < 3 2 , then 80(tan²x − cos x) is equal to:
- Let I(x) = 6 ^2x(1 - x)^2 dx. If I(0) = 3, then I ( 12 ) is equal to:
- The equations of two sides AB and AC of a triangle ABC are 4x + y = 14 and 3x − 2y = 5, respectively. The point (2, - 43 )...
- Let [t] be the greatest integer less than or equal to t. Let A be the set of all prime factors of 2310 and f : A → ℤ be the...
- Let z be a complex number such that |z + 2| = 1 and Im ( z + 1 z + 2 ) = 15. Then the value of |Re( z + 2 )| is:
- For the function f(x) = (cos x) − x + 1, x ∈ R, between the following two statements (S1) f(x) = 0 for only one value of x in [0,...
- The set of all α, for which the vector a = t i + 6 j - 3 k and b = t i - 2 j - 2 t k are inclined at an obtuse angle for all t ∈...
- Let H : -x^2 a^2 + y^2 b^2 = 1 be the hyperbola, whose eccentricity is √3 and the length of the latus rectum is 4√3. Suppose the...
- Let A = bmatrix 2 & -1 1 & 1 bmatrix . If the sum of the diagonal elements of A¹³ is 3ⁿ, then n is equal to ______.
- If the orthocentre of the triangle formed by the lines 2x + 3y − 1 = 0, x + 2y − 1 = 0 and ax + by − 1 = 0, is the centroid of...