JEE Main questions
34495 published questions with worked solutions.
- A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation...
- A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the...
- If 26 ( 2^3 3 12 2+ 2^5 5 12 4+ 2^7 7 12 6+ + 2^ 13 13 12 12 )=3^ 13 - , then α is equal to:
- A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so...
- If a straight line drawn through the point of intersection of the lines 4x + 3y − 1 = 0 and 3x + 4y − 1 = 0, meets the...
- Let O be the vertex of the parabola y² = 4x and its chords OP and OQ are perpendicular to each other. If the locus of the...
- Let α = 3 sin⁻¹(6/11) and β = 3 cos⁻¹(4/9), where inverse trigonometric functions take only the principal values. Given below are...
- For the function f(x) = e^ sin|x| − |x|, x ∈ ℝ, consider the following statements: Statement I: f is differentiable for all x ∈...
- Let a=4 i- j+3 k, b=10 i+2 j- k and a vector c be such that 2( a b)+3( b c)= 0. If a c=15, then c ( i+ j-3 k) is equal to:
- Let the foot of perpendicular from the point (λ, 2, 3) on the line x-4 1= y-9 2= z-5 1 be the point (1, μ, 2). Then the distance...
- Let y = y(x) be the solution of the differential equation x 1-x^2 ,dy+ (y 1-x^2 -x ^ -1 x )dx=0, x ∈ (0, 1), _ x 1^- y(x)=1. Then...
- Let f : (1, ∞) → ℝ be a function defined as f(x)= x-1 x+1 . Let fⁱ⁺¹(x) = f(fⁱ(x)), i = 1, 2, …, 25, where f¹(x) = f(x). If g(x)...
- Let f(x)= cases 13, & x /2 [2mm] b(1- x) ( -2x)^2 , & x> /2 cases . If f is continuous at x = π/2, then the value of _0^ 3b-6...
- Let x^2 f(a^2+7a+3) + y^2 f(3a+15) =1 represent an ellipse with major axis along y-axis, where f is a strictly decreasing...
- The sum of squares of all the real solutions of the equation _ (x+1) (2x^2+5x+3)=4- _ (2x+3) (x^2+2x+1) is equal to _______.
- Let a line L₁ pass through the origin and be perpendicular to the lines L₂ : r⃗ = (3 + t)î + (2t − 1)ĵ + (2t + 4)k̂ and L₃ : r⃗ =...
- Consider the circle C : x² + y² − 6x − 8y − 11 = 0. Let a variable chord AB of the circle C subtend a right angle at the origin....
- A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and...
- Consider the equation H= x^p ^qE^r t^s , where H = magnetic field; E = electric field, ε = permittivity, x = distance, t = time....
- A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car....