Practice questions
90156 published questions with worked solutions.
- In a closed flask at 600 K, one mole of X₂Y₄(g) attains equilibrium as given below: X₂Y₄(g)⇌2XY₂(g). At equilibrium, 75% X₂Y₄(g)...
- Decomposition of a hydrocarbon follows the equation k=(5.5×10¹¹ s⁻¹)e^(−28000 K/T). The activation energy of reaction is _______...
- Let [·] denote the greatest integer function. If the domain of the function f(x)= ^ -1 ( x+[x] 3 ) is [α, β], then α²+β² is equal...
- Let one root of the quadratic equation in x: (k²−15k+27)x²+9(k−1)x+18=0 be twice the other. Then the length of the latus rectum...
- Let e₁ and e₂ be two distinct roots of the equation x²−ax+2=0. Let the sets a∈ℝ : e₁ and e₂ are the eccentricities of hyperbolas...
- 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...