Mathematics questions
18011 published questions with worked solutions.
- _ x 0 e^ 2| x| - 2| x| - 1 x^2
- If f(x) = 4x+3 6x-4 , x ≠ 2/3 and (fof)(x) = g(x), where g : ℝ − 2/3 → ℝ − 2/3 , then (gogog)(4) is equal to
- The area of the region (x, y): y^2 4x, x < 4, xy(x-1)(x-2) (x-3)(x-4) > 0, x 3 is
- Let y = y(x) be the solution of the differential equation dy dx = ( x) + y x( x - x x) , x ∈ (0, π/2) satisfying the condition...
- Let g(x) be a linear function and f(x) = cases g(x), & x 0 ( 1+x 2+x )^ 1/x , & x > 0 cases , is continuous at x = 0. If f′(1) =...
- Let a⃗ = 3î + ĵ − 2k̂, b⃗ = 4î + ĵ + 7k̂ and c⃗ = î − 3ĵ + 4k̂ be three vectors. If a vector p⃗ satisfies p⃗ × b⃗ = c⃗ × b⃗ and...
- If one of the diameters of the circle x² + y² – 10x + 4y + 13 = 0 is a chord of another circle C, whose center is the point of...
- If the system of linear equations x − 2y + z = −4, 2x + αy + 3z = 5, 3x − y + βz = 3 has infinitely many solutions, then 12α +...
- The sum of the series 1 1 - 3 1^2 + 1^4 + 2 1 - 3 2^2 + 2^4 + 3 1 - 3 3^2 + 3^4 + up to 10-terms is
- Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being...
- Let S be the set of positive integral values of a for which ax^2 + 2(a+1)x + 9a + 4 x^2 - 8x + 32 < 0, ∀ x ∈ ℝ. Then, the number...
- Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten...
- Let S = (−1, ∞) and f : S → ℝ be define as f(x) = _ -1 ^x(e^t - 1)^ 11 (2t - 1)^5(t - 2)^7(t - 3)^ 12 (2t - 10)^ 61 dt. Let p =...
- If α denotes the number of solutions of |1 − i|ˣ = 2ˣ and = ( |z| (z) ), where z = 4(1 + i)^4 [ 1 - i + i + - i 1 + i ], i = √−1,...
- The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four...
- Let the foci and length of the latus rectum of an ellipse x²/a² + y²/b² = 1, a > b be (± 5, 0) and √50, respectively. Then, the...
- Let A = 1, 2, 3, 4 and R = (1, 2), (2, 3), (1, 4) be a relation on A. Let S be the equivalence relation on A such that R ⊂ S and...
- Let Q and R be the feet of perpendiculars from the point P(a, a, a) on the lines x = y, z = 1 and x = −y, z = −1 respectively. If...
- In the expansion of (1 + x)(1 - x^2) (1 + 3x + 3 x^2 + 1 x^3 )^5, x ≠ 0, the sum of the coefficients of x³ and x⁻¹³ is equal to...
- If the integral 525 _0^ /2 2x ^ 11 2 x (1 + ^ 52 x )^ 12 dx is equal to (n√2 − 64), then n is equal to ________.