Mathematics questions
18011 published questions with worked solutions.
- The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at...
- Let f(x) = cases x^2 | x |, & x 0 0, & x = 0 cases , x R , then f is
- The function f : [0, 3] [1, 29], defined by f(x) = 2x^3 - 15x^2 + 36x + 1, is
- If _ x ( x^2 + x + 1 x + 1 - ax - b ) = 4, then
- Let z be a complex number such that the imaginary part of z is nonzero and a = z^2 + z + 1 is real. Then a **cannot** take the...
- The ellipse E_1 : x^2 9 + y^2 4 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another...
- Let P = [a_ ij ] be a 3×3 matrix and let Q = [b_ ij ], where b_ ij = 2^ i+j a_ ij for 1 i, j 3. If the determinant of P is 2,...
- The integral ^2x ( x + x)^ 9/2 ,dx equals (for some arbitrary constant K)
- The point P is the intersection of the straight line joining the points Q(2, 3, 5) and R(1, −1, 4) with the plane 5x − 4y − z =...
- The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x − 5y = 20 to the...
- Let θ, φ ∈ [0, 2π] be such that 2 (1 - ) = ^2 ( 2 + 2 ) - 1, (2 - ) > 0 and -1 < < - 3 2 . Then φ **cannot** satisfyNot in JEE Main syllabus
- Let S be the area of the region enclosed by y = e^ -x^2 , y = 0, x = 0, and x = 1. Then
- A ship is fitted with three engines E_1, E_2 and E_3. The engines function independently of each other with respective...
- Tangents are drawn to the hyperbola x^2 9 - y^2 4 = 1, parallel to the straight line 2x − y = 1. The points of contact of the...
- If y(x) satisfies the differential equation y' - y x = 2x x and y(0) = 0, then
- Let f : R R be defined as f(x) = |x| + |x^2 - 1|. The total number of points at which f attains either a local maximum or a local...
- The value of 6 + _ 3 2 ( 1 3 2 4 - 1 3 2 4 - 1 3 2 4 - 1 3 2 ) is
- Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and...
- If a, b and c are unit vectors satisfying | a - b|^2 + | b - c|^2 + | c - a|^2 = 9, then |2 a + 5 b + 5 c| is
- Let S be the focus of the parabola y^2 = 8x and let PQ be the common chord of the circle x^2 + y^2 - 2x - 4y = 0 and the given...