Mathematics questions
18011 published questions with worked solutions.
- Number of integral terms in the expansion of 7^ 12 + 11^ 16 ^ 824 is equal to ________.
- Let A = 1, 2, 3, …, 7 and let P(A) denote the power set of A. If the number of functions f : A → P(A) such that a ∈ f(a), ∀ a ∈ A...
- If d₁ is the shortest distance between the lines x + 1 = 2y = –12z, x = y + 2 = 6z – 6 and d₂ is the shortest distance between...
- If the function f(x) = cases 1 |x| , & |x| 2 ax^2 + 2b, & |x| < 2 cases is differentiable on ℝ, then 48(a + b) is equal to...
- Let the latus rectum of the hyperbola x^2 9 - y^2 b^2 = 1 subtend an angle of π/3 at the centre of the hyperbola. If b² is equal...
- Let y = y(x) be the solution of the differential equation (1 - x^2)dy = [xy + (x^3 + 2) 3(1 - x^2) ]dx, −1 < x < 1, y(0) = 0. If...
- Let α, β ∈ ℕ be roots of the equation x² – 70x + λ = 0. Where λ/2, λ/3 ∉ ℕ. If λ assumes the minimum possible value, then ( - 1 +...
- Let f : ℝ → (0, ∞) be a strictly increasing function such that _ x f(7x) f(x) = 1. Then, the value of _ x [ f(5x) f(x) - 1 ] is...
- If for some m, n: ⁶Cₘ + 2(⁶Cₘ₊₁) + ⁶Cₘ₊₂ > ⁸C₃ and ⁿ⁻¹P₃ : ⁿP₄ = 1 : 8, then ⁿP_ m+1 + ⁿ⁺¹Cₘ is equal to
- If the function f : (−∞, −1] → (a, b] defined by f(x) = e^ x^3 - 3x + 1 is one-one and onto, then the distance of the point P(2b...
- Let 2ⁿᵈ, 8ᵗʰ and 44ᵗʰ terms of a non-constant A.P. be respectively the 1ˢᵗ, 2ⁿᵈ and 3ʳᵈ terms of a G.P. If the first term of the...
- Let A be a 3 × 3 real matrix such that A pmatrix 1 0 1 pmatrix = 2 pmatrix 1 0 1 pmatrix , A pmatrix -1 0 1 pmatrix = 4 pmatrix...
- Let P be a parabola with vertex (2, 3) and directrix 2x + y = 6. Let an ellipse E : x²/a² + y²/b² = 1, a > b, of eccentricity...
- The shortest distance between lines L₁ and L₂, where L₁ : (x − 1)/2 = (y + 1)/(−3) = (z + 4)/2 and L₂ is the line, passing...
- The area of the region enclosed by the parabolas y = 4x − x² and 3y = (x − 4)² is equal to
- The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2...
- Let a variable line passing through the centre of the circle x² + y² − 16x − 4y = 0, meet the positive coordinate axes at the...
- Let the mean and the variance of 6 observations a, b, 68, 44, 48, 60 be 55 and 194, respectively. If a > b, then a + 3b is
- If a = sin⁻¹(sin(5)) and b = cos⁻¹(cos(5)), then a² + b² is equal to
- Let (α, β, γ) be the mirror image of the point (2, 3, 5) in the line (x − 1)/2 = (y − 2)/3 = (z − 3)/4. Then 2α + 3β + 4γ is...