Mathematics questions
18011 published questions with worked solutions.
- If ( yx ) = _e|x| + 2 is the solution of the differential equation x ( yx ) dy dx = y ( yx ) + x and y(1) = 3, then α² is equal to
- The function f(x) = x x^2 - 6x - 16 , x ∈ ℝ − −2, 8
- Let P(3, 2, 3), Q(4, 6, 2) and R(7, 3, 2) be the vertices of ΔPQR. Then the angle ∠QPR isNot in JEE syllabus
- The sum of the solution x ∈ ℝ of the equation 3 2x + ^32x ^6x - ^6x = x^3 - x^2 + 6 isNot in JEE Main syllabus
- Let r and θ respectively be the modulus and amplitude of the complex number z = 2 - i (2 5 8 ), then (r, θ) is equal to
- An integer is chosen at random from the integers 1, 2, 3, ..., 50. The probability that the chosen integer is a multiple of...
- Let a unit vector u = x i + y j + z k make angles π/2, π/3 and 2π/3 with the vectors 1 2 i + 1 2 k, 1 2 j + 1 2 k and 1 2 i + 1 2...
- If each term of a geometric progression a₁, a₂, a₃, ..... with a₁ = 1/8 and a₂ ≠ a₁, is arithmetic mean of the next two terms,...
- Let A = bmatrix 2&1&2 6&2&11 3&3&2 bmatrix and P = bmatrix 1&2&0 5&0&2 7&1&5 bmatrix . The sum of the prime factors of |P⁻¹AP −...
- If the mean and variance of five observations are 24/5 and 194/25 respectively and the mean of the first four observations is...
- The function f(x) = 2x + 3x^ 2/3 , x ∈ ℝ, has
- Let y = _e ( 1 - x^2 1 + x^2 ), −1 < x < 1. Then at x = 1/2, the value of 225(y′ – y″) is equal to
- If ^ 3/2 x + ^ 3/2 x ^3x ^3x (x- ) dx = A x - + B - x + C, where C is the integration constant, then AB is equal to
- If R is the smallest equivalence relation on the set 1, 2, 3, 4 such that (1, 2), (1, 3) ⊂ R, then the number of elements in R is...
- Let the area of the region (x, y) : 0 ≤ x ≤ 3, 0 ≤ y ≤ min x² + 2, 2x + 2 be A. Then 12A is equal to ________.
- Let O be the origin, and M and N be the points on the lines x-5 4 = y-4 1 = z-5 3 and x+8 12 = y+2 5 = z+11 9 respectively such...
- If _ /6 ^ /3 1 - 2x ,dx = + 2 + 3, where α, β and γ are rational numbers, then 3α + 4β – γ is equal to ________.
- Remainder when 64³²³² is divided by 9 is equal to ________.
- Let the slope of the line 45x + 5y + 3 = 0 be 27r_1 + 9r_2 2 for some r₁, r₂ ∈ ℝ. Then _ x 3 ( _3^x 8t^2 3r_2x 2 - r_2x^2 -...
- Let f(x) = _ r x 2r^2[(f(r))^2 - f(x)f(r)] r^2 - x^2 - r^3e^ f(r) r be differentiable in (−∞, 0) ∪ (0, ∞) and f(1) = 1. Then the...