Mathematics questions
18011 published questions with worked solutions.
- The number of functions f from 1, 2, 3, …, 20 onto 1, 2, 3, …, 20 such that f(k) is a multiple of 3, whenever k is a multiple of...
- Let z be a complex number such that |z| + z = 3 + i (where i = -1 ). Then |z| is equal to:
- Let α and β be the roots of the quadratic equation x^2 - x( + 1) + = 0 (0 < θ < 45º), and α < β. Then _ n=0 ^ ( ^n + (-1)^n ^n )...
- If vmatrix a - b - c & 2a & 2a 2b & b - c - a & 2b 2c & 2c & c - a - b vmatrix = (a + b + c)(x + a + b + c)^2, x ≠ 0 and a + b +...
- _ x 0 x (4x) ^2x ^2(2x) is equal to:
- Let (x + 10)^ 50 + (x - 10)^ 50 = a_0 + a_1x + a_2x^2 + + a_ 50 x^ 50 , for all x ∈ R; then a_2 a_0 is equal to:
- The area (in sq. units) in the first quadrant bounded by the parabola, y = x^2 + 1, the tangent to it at the point (2, 5) and the...
- Two lines x-3 1 = y+1 3 = z-6 -1 and x+5 7 = y-2 -6 = z-3 4 intersect at the point R. The reflection of R in the xy-plane has...
- Let A and B be two invertible matrices of order 3 × 3. If det(ABA^T) = 8 and det(AB^ -1 ) = 8, then det(BA^ -1 B^T) is equal to:
- If x + 1 2x - 1 dx = f(x) 2x - 1 + C, where C is a constant of integration, then f(x) is equal to:
- Contrapositive of the statement "If two numbers are not equal, then their squares are not equal." is:Not in JEE syllabus
- Let f(x) = x a^2 + x^2 - d - x b^2 + (d - x)^2 , x ∈ R, where a, b and d are non-zero real constants. Then:
- The integral _ /6 ^ /3 dx 2x( ^5x + ^5x) equals:
- Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance...
- If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the...
- Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression x^my^n (1 + x^ 2m )(1 + y^ 2n )...
- If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the...
- Let S_n = 1 + q + q^2 + + q^n and T_n = 1 + ( q+1 2 ) + ( q+1 2 )^2 + + ( q+1 2 )^n where q is a real number and q ≠ 1. If ^ 101...
- Let 3 i + j, i + 3 j and i + (1 - ) j respectively be the position vectors of the points A, B and C with respect to the origin O....
- All x satisfying the inequality ( ^ -1 x)^2 - 7( ^ -1 x) + 10 > 0, lie in the interval: