JEE Main questions
34568 published questions with worked solutions.
- The number of species from the following in which the central atom uses sp³ hybrid orbitals in its bonding is ________. NH₃, SO₂,...
- One Faraday of electricity liberates x × 10⁻¹ gram atom of copper from copper sulphate. x is ________.
- Consider the following reaction at 298 K. (3/2)O₂(g) ⇌ O₃(g), K_p = 2.47 × 10⁻²⁹. Δ_rG° for the reaction is ________ kJ. (Given R...
- CH₃CH₂Br + NaOH → (C₂H₅OH) → Product A; → (H₂O) → Product B. The total number of hydrogen atoms in product A and product B is...
- The solution curve of the differential equation y dx dy = x( _ex - _ey + 1), x > 0, y > 0 passing through the point (e, 1) is
- For 0 < c < b < a, let (a + b − 2c)x² + (b + c − 2a)x + (c + a − 2b) = 0 and α ≠ 1 be one of its root. Then, among the two...
- If f(x) = vmatrix x^3 & 2x^2 + 1 & 1 + 3x 3x^2 + 2 & 2x & x^3 + 6 x^3 - x & 4 & x^2 - 2 vmatrix for all x ∈ ℝ, then 2f(0) + f′(0)...
- _ x 0 e^ 2| x| - 2| x| - 1 x^2
- If f(x) = 4x+3 6x-4 , x ≠ 2/3 and (fof)(x) = g(x), where g : ℝ − 2/3 → ℝ − 2/3 , then (gogog)(4) is equal to
- The area of the region (x, y): y^2 4x, x < 4, xy(x-1)(x-2) (x-3)(x-4) > 0, x 3 is
- Let y = y(x) be the solution of the differential equation dy dx = ( x) + y x( x - x x) , x ∈ (0, π/2) satisfying the condition...
- Let g(x) be a linear function and f(x) = cases g(x), & x 0 ( 1+x 2+x )^ 1/x , & x > 0 cases , is continuous at x = 0. If f′(1) =...
- Let a⃗ = 3î + ĵ − 2k̂, b⃗ = 4î + ĵ + 7k̂ and c⃗ = î − 3ĵ + 4k̂ be three vectors. If a vector p⃗ satisfies p⃗ × b⃗ = c⃗ × b⃗ and...
- If one of the diameters of the circle x² + y² – 10x + 4y + 13 = 0 is a chord of another circle C, whose center is the point of...
- If the system of linear equations x − 2y + z = −4, 2x + αy + 3z = 5, 3x − y + βz = 3 has infinitely many solutions, then 12α +...
- The sum of the series 1 1 - 3 1^2 + 1^4 + 2 1 - 3 2^2 + 2^4 + 3 1 - 3 3^2 + 3^4 + up to 10-terms is
- Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being...
- Let S be the set of positive integral values of a for which ax^2 + 2(a+1)x + 9a + 4 x^2 - 8x + 32 < 0, ∀ x ∈ ℝ. Then, the number...
- Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten...
- Let S = (−1, ∞) and f : S → ℝ be define as f(x) = _ -1 ^x(e^t - 1)^ 11 (2t - 1)^5(t - 2)^7(t - 3)^ 12 (2t - 10)^ 61 dt. Let p =...