Mathematics questions
18011 published questions with worked solutions.
- Let the solution y = y(x) of the differential equation dy dx - y = 1 + 4 x satisfy y(π) = 1. Then y ( 2 ) + 10 is equal to ______...
- If the shortest distance between the lines x + 2 2 = y + 3 3 = z - 5 4 and x - 3 1 = y - 2 -3 = z + 4 2 is 38 3 5 k and...
- Let a = 1 + ^2C_2 3! + ^3C_2 4! + ^4C_2 5! + , b = 1 + ^1C_0 + ^1C_1 1! + ^2C_0 + ^2C_1 + ^2C_2 2! + ^3C_0 + ^3C_1 + ^3C_2 +...
- Let A be a 3 × 3 matrix of non-negative real elements such that A bmatrix 1 1 1 bmatrix = 3 bmatrix 1 1 1 bmatrix . Then the...
- Let the length of the focal chord PQ of the parabola y² = 12x be 15 units. If the distance of PQ from the origin is p, then 10p²...
- Let ABC be a triangle of area 15√2 and the vectors AB = i + 2 j - 7 k, BC = a i + b j + c k and AC = 6 i + d j - 2 k, d > 0. Then...
- Let d be the distance of the point of intersection of the lines x + 6 3 = y2 = z + 1 1 and x - 7 4 = y - 9 3 = z - 4 2 from the...
- Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on...
- If y = y(x) is the solution of the differential equation dy dx + 2y = (2x), y(0) = 34, then y ( 8 ) is equal to:
- For the function f(x) = x + 3x - 2 (x^2 + x), where x ∈ [0, 2 ]. Consider the following two statements: (I) f is increasing in...
- If the system of equations 11x + y + λz = −5, 2x + 3y + 5z = 3, 8x − 19y − 39z = μ has infinitely many solutions, then λ⁴ − μ is...
- If the function f(x) = 3x + x - 3x x^3 , x ∈ R, is continuous at x = 0, then f(0) is equal to:
- The coefficients a, b, c in the quadratic equation ax² + bx + c = 0 are chosen from the set 1, 2, 3, 4, 5, 6, 7, 8 . The...
- Let A and B be two square matrices of order 3 such that |A| = 3 and |B| = 2. Then |Aᵀ A (adj(2A))⁻¹ (adj(4B)) (adj(AB))⁻¹ A Aᵀ|...
- Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3, 2) and parallel to the...
- Let the line 2x + 3y − k = 0, k > 0, intersect the x-axis and y-axis at the points A and B, respectively. If the equation of the...
- Consider the following two statements: Statement I: For any two non-zero complex numbers z_1, z_2: (|z_1| + |z_2|) | z_1 |z_1| +...
- Suppose θ ∈ (0, 4 ) is a solution of 4 cos θ − 3 sin θ = 1. Then cos θ is equal to:Not in JEE Main syllabus
- If 1 1 + 2 + 1 2 + 3 + + 1 99 + 100 = m and 1 1 2 + 1 2 3 + + 1 99 100 = n, then the point (m, n) lies on the line
- Let f(x) = x⁵ + 2x³ + 3x + 1, x ∈ R, and g(x) be a function such that g(f(x)) = x for all x ∈ R. Then g(7) g'(7) is equal to: