Mathematics questions
18011 published questions with worked solutions.
- Let (5, a/4) be the circumcentre of a triangle with vertices A(a, –2), B(a, 6) and C(a/4, –2). Let α denote the circumradius, β...
- Let R be a relation on Z × Z defined by (a, b) R (c, d) if and only if ad – bc is divisible by 5. Then R is
- A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is-
- If ^ 11 C_1 2 + ^ 11 C_2 3 + + ^ 11 C_9 10 = nm with gcd(n, m) = 1, then n + m is equal to ________.
- Let α, β be the roots of the equation x² – x + 2 = 0 with Im(α) > Im(β). Then α⁶ + α⁴ + β⁴ – 5α² is equal to ______.
- A line with direction ratios 2, 1, 2 meets the lines x = y + 2 = z and x + 2 = 2y = 2z respectively at the points P and Q. If the...
- All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in...
- The area (in sq. units) of the part of the circle x² + y² = 169 which is below the line 5x – y = 13 is 2 - 65 2 + ^ -1 ( 12 13 ),...
- If the mean and variance of the data 65, 68, 58, 44, 48, 45, 60, α, β, 60 where α > β are 56 and 66.2 respectively, then α² + β²...
- If the solution curve y = y(x) of the differential equation (1 + y²)(1 + log_e x)dx + x dy = 0, x > 0 passes through the point...
- Equations of two diameters of a circle are 2x – 3y = 5 and 3x – 4y = 7. The line joining the points (–22/7, –4) and (–1/7, 3)...
- Let f(x) = 2ˣ – x², x ∈ ℝ. If m and n are respectively the number of points at which the curves y = f(x) and y = f ′(x) intersect...
- Let a⃗ and b⃗ be two vectors such that |b⃗| = 1 and |b⃗ × a⃗| = 2. Then |(b⃗ × a⃗) − b⃗|² is equal to
- Let A(α, 0) and B(0, β) be the points on the line 5x + 7y = 50. Let the point P divide the line segment AB internally in the...
- Let y = f(x) be a thrice differentiable function in (–5, 5). Let the tangents to the curve y = f(x) at (1, f(1)) and (3, f(3))...
- Let a and b be real constants such that the function f defined by f(x) = cases x^2 + 3x + a, & x 1 bx + 2, & x > 1 cases be...
- If the domain of the function f(x) = _e ( 2x+3 4x^2+x-3 ) + ^ -1 ( 2x-1 x+2 ) is (α, β], then the value of 5β – 4α is equal to
- Let a = i + j + k, α, β ∈ ℝ. Let a vector b⃗ be such that the angle between a⃗ and b⃗ is π/4 and |b⃗|² = 6. If a⃗·b⃗ = 3√2, then...
- Let f : ℝ → ℝ be a function defined by f(x) = x (1+x^4)^ 1/4 , and g(x) = f(f(f(f(x)))). Then 18 _0^ 2 5 x^2g(x)dx is equal to
- If z is a complex number, then the number of common roots of the equations z¹⁹⁸⁵ + z¹⁰⁰ + 1 = 0 and z³ + 2z² + 2z + 1 = 0, is...