JEE Main questions
34495 published questions with worked solutions.
- Let the set of all values of k∈ℝ such that the equation z( z+2+i)+k(2+3i)=0, z∈ℂ, has at least one solution, be the interval [α,...
- The value of 1³−2³+3³−…+15³ is:
- The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P....
- The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from...
- If the coefficients of the middle terms in the binomial expansions of (1+αx)²⁶ and (1−αx)²⁸, α≠0, are equal, then the value of α...
- If the eccentricity e of the hyperbola x^2 a^2 - y^2 b^2 =1, passing through (6, 4√3), satisfies 15(e²+1)=34e, then the length of...
- Let chord PQ of length 3√13 of the parabola y²=12x be such that the ordinates of points P and Q are in the ratio 1 : 2. If the...
- Let 0<α<1, β=1/(3α) and tan⁻¹(1−α)+tan⁻¹(1−β)=π/4. Then 6(α+β) is equal to:
- Let S= θ∈(−2π, 2π) : cosθ+1=√3 sinθ . Then _ S is equal to:Not in JEE Main syllabus
- Let the image of the point P(1, 6, a) in the line L: x1= y-1 2= z-a+1 b, b>0, be ( a3, 0, a+c ). If S(α, β, γ), α>0, is the point...
- Let a line L be perpendicular to both the lines L_1: x+1 3= y+3 5= z+5 7 and L_2: x-2 1= y-4 4= z-6 7. If θ is the acute angle...
- The value of _ x 0 ( x^2 ^2x x^2- ^2x ) is:
- The value of the integral _ - /4 ^ /4 ( 32 ^4x 1+e^ x )dx is:
- The area of the region (x,y) : 0≤y≤6−x, y²≥4x−3, x≥0 is:
- Let A= bmatrix -1&1&-1 1&0&1 0&0&1 bmatrix satisfy A²+α(adj(adj(A)))+β(adj(A))(adj(adj(A))) = bmatrix 2&-2&2 -2&0&-1 0&0&-1...
- Let the centre of the circle x²+y²+2gx+2fy+25=0 be in the first quadrant and lie on the line 2x−y=4. Let the area of an...
- If a= i+ j+ k, b= j- k and c are three vectors such that a c= b and a c=3, then c ( a-2 b) is equal to _______.
- For the functions f(θ)=α tan²θ+β cot²θ and g(θ)=α sin²θ+β cos²θ, α>β>0, let _ 0< < /2 f( )= _ 0< < g( ). If the first term of a...
- Let y=y(x) be the solution of the differential equation (x^2-x x^2-1 )dy+(y(x- x^2-1 )-x)dx=0, x≥1. If y(1)=1, then the greatest...
- The density ρ of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measured values of m, l...