JEE Main questions
34568 published questions with worked solutions.
- r = k[A] for a reaction, 50% of A is decomposed in 120 minutes. The time taken for 90% decomposition of A is ________ minutes.
- A diatomic molecule has a dipole moment of 1.2 D. If the bond distance is 1 Å, then fractional charge on each atom is ________ ×...
- If 5 moles of an ideal gas expands from 10 L to a volume of 100 L at 300 K under isothermal and reversible condition then work,...
- In the reaction of potassium dichromate, potassium chloride and sulfuric acid (conc.), the oxidation state of the chromium in the...
- Number of moles of H⁺ ions required by 1 mole of MnO₄⁻ to oxidise oxalate ion to CO₂ is ________.
- Let f : ℝ → (0, ∞) be a strictly increasing function such that _ x f(7x) f(x) = 1. Then, the value of _ x [ f(5x) f(x) - 1 ] is...
- If for some m, n: ⁶Cₘ + 2(⁶Cₘ₊₁) + ⁶Cₘ₊₂ > ⁸C₃ and ⁿ⁻¹P₃ : ⁿP₄ = 1 : 8, then ⁿP_ m+1 + ⁿ⁺¹Cₘ is equal to
- If the function f : (−∞, −1] → (a, b] defined by f(x) = e^ x^3 - 3x + 1 is one-one and onto, then the distance of the point P(2b...
- Let 2ⁿᵈ, 8ᵗʰ and 44ᵗʰ terms of a non-constant A.P. be respectively the 1ˢᵗ, 2ⁿᵈ and 3ʳᵈ terms of a G.P. If the first term of the...
- Let A be a 3 × 3 real matrix such that A pmatrix 1 0 1 pmatrix = 2 pmatrix 1 0 1 pmatrix , A pmatrix -1 0 1 pmatrix = 4 pmatrix...
- Let P be a parabola with vertex (2, 3) and directrix 2x + y = 6. Let an ellipse E : x²/a² + y²/b² = 1, a > b, of eccentricity...
- The shortest distance between lines L₁ and L₂, where L₁ : (x − 1)/2 = (y + 1)/(−3) = (z + 4)/2 and L₂ is the line, passing...
- The area of the region enclosed by the parabolas y = 4x − x² and 3y = (x − 4)² is equal to
- The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2...
- Let a variable line passing through the centre of the circle x² + y² − 16x − 4y = 0, meet the positive coordinate axes at the...
- Let the mean and the variance of 6 observations a, b, 68, 44, 48, 60 be 55 and 194, respectively. If a > b, then a + 3b is
- If a = sin⁻¹(sin(5)) and b = cos⁻¹(cos(5)), then a² + b² is equal to
- Let (α, β, γ) be the mirror image of the point (2, 3, 5) in the line (x − 1)/2 = (y − 2)/3 = (z − 3)/4. Then 2α + 3β + 4γ is...
- A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times then the probability of...
- Let f, g : (0, ∞) → ℝ be two functions defined by f(x) = _ -x ^x(|t| - t^2)e^ -t^2 dt and g(x) = _0^ x^2 t^ 1/2 e^ -t dt. Then,...