JEE Main questions
34495 published questions with worked solutions.
- Let 3, a, b, c be in A.P. and 3, a − 1, b + 1, c + 9 be in G.P. Then, the arithmetic mean of a, b and c is:
- If 5f(x) + 4f ( 1x ) = x^2 - 2, ∀ x ≠ 0 and y = 9x²f(x), then y is strictly increasing in:
- Let a = -5 i + j - 3 k, b = i + 2 j - 4 k and c = ((( a b) i) i) i. Then c (- i + j + k) is equal to:
- If A = bmatrix 2 & 1 -1 & 2 bmatrix , B = bmatrix 1 & 0 1 & 1 bmatrix , C = ABA^T and X = A^TC^2A, then det X is equal to:
- The area enclosed by the curves xy + 4y = 16 and x + y = 6 is equal to:
- If the shortest distance between the lines x - -2 = y - 2 1 = z - 1 1 and x - 3 1 = y - 1 -2 = z - 2 1 is 1, then the sum of all...
- Let f : R → R be define as: f(x) = cases a - b 2x x^2 , & x < 0 x^2 + cx + 2, & 0 x 1 2x + 1, & x > 1 cases . If f is continuous...
- Let y = y(x) be the solution of the differential equation dy dx = 2x(x + y)^3 - x(x + y) - 1, y(0) = 1. Then ( 1 2 + y ( 1 2 )...
- Let C : x² + y² = 4 and C′ : x² + y² − 4λx + 9 = 0 be two circles. If the set of all values of λ so that the circles C and C′...
- If x = x(t) is the solution of the differential equation (t + 1)dx = (2x + (t + 1)^4)dt, x(0) = 2, then, x(1) equals _____.
- Let P = z ∈ C: |z + 2 − 3i| ≤ 1 and Q = z ∈ C: z(1 + i) + z(1 − i) ≤ −8 . Let in P ∩ Q, |z − 3 + 2i| be maximum and minimum at...
- The number of elements in the set S = (x, y, z) : x, y, z ∈ ℤ, x + 2y + 3z = 42, x, y, z ≥ 0 equal ______.
- Let 3, 7, 11, 15, …, 403 and 2, 5, 8, 11, …, 404 be two arithmetic progressions. Then the sum of the common terms in them, is...
- Let A = 1, 2, 3, …, 20 . Let R_1 and R_2 two relation on A such that R_1 = (a, b) : b is divisible by a , R_2 = (a, b) : a is an...
- If _ - /2 ^ /2 8 2 x ,dx (1 + e^ x )(1 + ^4x) = + _e(3 + 2 2) where α, β are integers, then α² + β² equals_____.
- If the coefficient of x^ 30 in the expansion of (1 + 1x )^6(1 + x^2)^7(1 - x^3)^8; x ≠ 0 is α, then |α| equals_______.
- Let the line L : 2x + y = pass through the point of the intersection P (in the first quadrant) of the circle x^2 + y^2 = 3 and...
- Let the line of the shortest distance between the lines L_1 : r = ( i + 2 j + 3 k) + ( i - j + k) and L_2 : r = (4 i + 5 j + 6 k)...
- The magnetic moment of a bar magnet is 0.5 Am^2. It is suspended in a uniform magnetic field of 8 × 10^ -2 T. The work done in...Not in JEE Advanced syllabus
- Arrange the following in the ascending order of wavelength: (A) Gamma rays (1) (B) x-ray (2) (C) Infrared waves (3) (D)...