JEE Main questions
34495 published questions with worked solutions.
- For the function f(x) = (cos x) − x + 1, x ∈ R, between the following two statements (S1) f(x) = 0 for only one value of x in [0,...
- The set of all α, for which the vector a = t i + 6 j - 3 k and b = t i - 2 j - 2 t k are inclined at an obtuse angle for all t ∈...
- Let H : -x^2 a^2 + y^2 b^2 = 1 be the hyperbola, whose eccentricity is √3 and the length of the latus rectum is 4√3. Suppose the...
- Let A = bmatrix 2 & -1 1 & 1 bmatrix . If the sum of the diagonal elements of A¹³ is 3ⁿ, then n is equal to ______.
- If the orthocentre of the triangle formed by the lines 2x + 3y − 1 = 0, x + 2y − 1 = 0 and ax + by − 1 = 0, is the centroid of...
- Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively...
- The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which...
- If the range of f( ) = ^4 + 3 ^2 ^4 + ^2 , θ ∈ R is [α, β], then the sum of the infinite G.P., whose first term is 64 and the...
- Let = _ r=0 ^ n (4r^2 + 2r + 1) nr and = ( _ r=0 ^ n nr r + 1 ) + 1 n + 1 . If 140 < 2 < 281, then the value of n is ______.
- Let a = 9 i - 13 j + 25 k, b = 3 i + 7 j - 13 k and c = 17 i - 2 j + k be three given vectors. If r is a vector such that r a = (...
- Let the area of the region enclosed by the curve y = min sin x, cos x and the x-axis between x = −π to x = π be A. Then A² is...
- The value of _ x 0 2 ( 1 - x 2x [3] 3x [10] 10x x^2 ) is ________.
- In a hypothetical fission reaction ^ 236 _ 92 X → ^ 141 _ 56 Y + ^ 92 _ 36 Z + 3R. The identity of emitted particles (R) is:
- If ε₀ is the permittivity of free space and E is the electric field, then ε₀E² has the dimensions:
- A plane progressive wave is given by y = 2 cos 2π(330t − x) m. The frequency of the wave is:
- A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and...
- Given below are two statements: Statement (I): The mean free path of gas molecules is inversely proportional to square of...
- Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is 3v, the speed...
- The angle of projection for a projectile to have same horizontal range and maximum height is:
- Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating...