JEE Main questions
34495 published questions with worked solutions.
- 0.5 g of an organic compound on combustion gave 1.46 g of CO_2 and 0.9 g of H_2O. The percentage of carbon in the compound is...
- Consider the following reactions A + NaCl+H_2SO_4 (Little amount) CrO_2Cl_2 + Side Products CrO_2Cl_2(Vapour) + NaOH B + NaCl +...
- 1 + 3 + 5^2 + 7 + 9^2 + … upto 40 terms is equal to
- Considering the principal values of the inverse trigonometric functions, ^ -1 ( 3 2 x + 1 2 1-x^2 ), - 1 2 < x < 1 2 , is equal to
- Let A = 1, 6, 11, 16, … and B 9, 16, 23, 30, … be the sets consisting of the first 2025 terms of two arithmetic progressions....
- Consider two vectors u = 3 i - j and v = 2 i + j - k , λ > 0. The angle between them is given by ^ -1 ( 5 2 7 ). Let v = v_1 +...
- Let f, g : (1, ∞) → ℝ be defined as f(x) = 2x+3 5x+2 and g(x) = 2-3x 1-x . If the range of the function fog : [2, 4] → ℝ is [α,...
- In the expansion of ( [3] 2 + 1 [3] 3 )^n, n ∈ ℕ, if the ratio of 15th term from the beginning to the 15th term from the end is 1...
- The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers...
- If 10 ^4 + 15 ^4 = 6, then the value of 27 ^6 + 8 ^6 16 ^8 is
- Consider the equation x^2 + 4x – n = 0 where n ∈ [20, 100] is a natural number. Then the number of all distinct values of n, for...
- The value of _ -1 ^ 1 (1+ |x|-x )e^x + ( |x|-x )e^ -x e^x+e^ -x dx is equal to
- If _ x 1 (x-1)(6+ (x-1))+ (1-x) (x-1)^3 = -1, where λ, μ ∈ ℝ, then λ + μ is equal to
- For an integer n ≥ 2, if the arithmetic mean of all coefficients in the binomial expansion of (x+y)^ 2n-3 is 16, then the...
- Find the length of latus rectum of an ellipse, whose foci are (2, 5) and (2, –3) and the eccentricity of the ellipse is 4 5
- Let the shortest distance between the lines x-3 3 = y- -1 = z-3 1 and x+3 -3 = y+7 2 = z- 4 be 3 30 . Then the positive value of...
- Let A and B be two distinct points on the line L : x-6 3 = y-7 2 = z-7 -2 . Both A and B are at a distance 2 17 from the foot of...
- Let m and n be the number of points at which the function f(x) = x, x^3, x^5, …x^ 21 , x R , is not differentiable and not...
- Let A = z ∈ ℂ : |z − 2 − i| = 3 , B = z ∈ ℂ : Re(z − iz) = 2 and S = A∩B. Then _ z S |z|^2 is equal to _____.
- Let A = bmatrix & 0 & - 0 & 1 & 0 & 0 & bmatrix . If for some θ ∈ (0, π), A^2 = A^T, then the sum of the diagonal elements of the...