Mathematics questions
18011 published questions with worked solutions.
- Let P(α, β) be a point on the parabola y² = 4x. If P also lies on the chord of the parabola x² = 8y whose mid-point is (1, 5/4)....
- Let α, β be the roots of the equation x² – √6x + 3 = 0 such that Im(α) > Im(β). Let a, b be integers not divisible by 3 and n be...
- Let for any three distinct consecutive terms a, b, c of an A.P., the lines ax + by + c = 0 be concurrent at the point P and Q(α,...
- If the value of the integral _ - /2 ^ /2 ( x^2 x 1+ ^x + 1+ ^2x 1+e^ x^ 2003 )dx = 4( + a) - 2, then the value of a is-
- For x ∈ (−π/2, π/2), if y(x) = cosec ,x + x cosec ,x x + x ^2x dx, and _ x 2 y(x) = 0 then y ( 4 ) is equal to-
- In a ΔABC, suppose y = x is the equation of the bisector of the angle B and the equation of the side AC is 2x – y = 2. If 2AB =...
- _ x 2 ( 1 (x- 2 )^2 _ x^3 ^ ( 2 )^3 (t^ 1/3 )dt ) is equal to-
- Let PQR be a triangle with R(–1, 4, 2). Suppose M (2, 1, 2) is the mid-point of PQ. The distance of the centroid of ΔPQR from the...
- Let O be the origin and the position vectors of A and B be 2 i + 2 j + k and 2 i + 4 j + 4 k respectively. If the internal...
- A function y = f(x) satisfies f(x) sin 2x + sin x – (1 + cos²x) f ′(x) = 0 with condition f(0) = 0. Then, f(π/2) is equal to-
- If z = 1/2 – 2i is such that |z + 1| = αz + β(1 + i), i = √−1 and α, β ∈ ℝ, then α + β is equal to-
- Consider the function f : [1/2, 1] → ℝ defined by f(x) = 4√2x³ – 3√2x – 1. Consider the statements (I) The curve y = f(x)...
- In an A.P., the sixth term a₆ = 2. If the product a₁a₄a₅ is the greatest, then the common difference of the A.P. is equal to
- If α, −π/2 < α < π/2 is the solution of 4cosθ + 5sinθ = 1, then the value of tanα is-Not in JEE Main syllabus
- Let A = bmatrix 1&0&0 0& & 0& & bmatrix and |2A|³ = 2²¹ where α, β ∈ ℤ, then a value of α is-
- Let a, b and c be three non-zero vectors such that b and c are non-collinear. If a + 5 b is collinear with c, b + 6 c is...
- If f(x) = cases 2 + 2x, & -1 x < 0 1 - x3, & 0 x 3 cases ; g(x) = cases -x, & -3 x 0 x, & 0 < x 1 cases , then range of (fog)(x)...
- If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P. then the common ratio of the...
- Suppose f(x) = (2^x + 2^ -x ) x ^ -1 (x^2 - x + 1) (7x^2 + 3x + 1)^3 . Then the value of f′(0) is equal to-
- Let A be a square matrix such that AAᵀ = I. Then 12A [(A + A^T)^2 + (A - A^T)^2 ] is equal to-