Mathematics questions
18011 published questions with worked solutions.
- _ x 2 ( _ x^3 ^ ( /2)^3 ( (2t^ 1/3 ) + (t^ 1/3 ))dt (x - 2 )^2 ) is equal to :
- The sum of the coefficient of x^ 2/3 and x^ −2/5 in the binomial expansion of (x^ 2/3 + 12x^ -2/5 )^9 is :
- Let B = bmatrix 1&3 1&5 bmatrix and A be a 2 × 2 matrix such that AB⁻¹ = A⁻¹. If BCB⁻¹ = A and C⁴ + αC² + βI = O, then 2β − α is...
- If log_e y = 3 sin⁻¹x, then (1 − x²)y″ − xy′ at x = 1/2 is equal to :
- The integral _ 1/4 ^ 3/4 (2 ^ -1 1-x 1+x )dx is equal to :
- Let a, ar, ar², ........ be an infinite G.P. If _ n=0 ^ ar^n = 57 and _ n=0 ^ a^3r^ 3n = 9747, then a + 18r is equal to :
- The value of the integral _ -1 ^2 _e (x + x^2+1 )dx is :
- Let α, β; α > β, be the roots of the equation x² − √2x − √3 = 0. Let Pₙ = αⁿ − βⁿ, n ∈ ℕ. Then (11√3 − 10√2)P₁₀ + (11√2 + 10)P₁₁...
- Let a⃗ = 2î + αĵ + k̂, b⃗ = −î + k̂, c⃗ = β ĵ − k̂, where α and β are integers and αβ = −6. Let the values of the ordered pair...
- Consider the circle C : x² + y² = 4 and the parabola P : y² = 8x. If the set of all values of α, for which three chords of the...
- Let the set of all values of p, for which f(x) = (p² − 6p + 8)(sin²2x − cos²2x) + 2(2 − p)x + 7 does not have any critical point,...
- The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is ______.
- Let A, B and C be three points on the parabola y² = 6x and let the line segment AB meet the line L through C parallel to the...
- The square of the distance of the image of the point (6, 1, 5) in the line (x − 1)/3 = y/2 = (z − 2)/4, from the origin is ______.
- Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2 sin⁻¹x + 3 cos⁻¹x =...
- Consider the matrices : A = bmatrix 2&-5 3&m bmatrix , B = bmatrix 20 bmatrix and X = bmatrix x bmatrix . Let the set of all m,...
- Let the line L intersect the lines x − 2 = −y = z − 1, 2(x + 1) = 2(y − 1) = z + 1 and be parallel to the line x-2 3 = y-1 1 =...
- The parabola y² = 4x divides the area of the circle x² + y² = 5 in two parts. The area of the smaller part is equal to
- The solution curve, of the differential equation 2y dy dx + 3 = 5 dy dx , passing through the point (0, 1) is a conic, whose...
- A ray of light coming from the point P(1, 2) gets reflected from the point Q on the x-axis and then passes through the point R(4,...