Mathematics questions
18011 published questions with worked solutions.
- Let _ x 2 ( (x-2))(rx^2+(p-2)x-2p) (x-2)^2 =5 for some r,p∈ℝ. If the set of all possible values of q, such that the roots of the...
- Let f : ℝ→ℝ be such that f(xy)=f(x)f(y), for all x,y∈ℝ and f(0)≠0. Let g : [1,∞)→ℝ be a differentiable function such that...
- The area of the region (x,y) : x²−8x≤y≤−x is:
- The value of the integral _ -1 ^ 1 ( x^3+|x|+1 x^2+2|x|+1 )dx is equal to:
- Let R= (x,y)∈ℕ×ℕ : log_e(x+y)≤2 . Then the minimum number of elements, required to be added in R to make it a transitive...
- Let the line x−y=4 intersect the circle C : (x−4)²+(y+3)²=9 at the points Q and R. If P(α,β) is a point on C such that PQ=PR,...
- Let the image of the point P(0,−5,0) in the line x-1 2= y1= z+1 -2 be the point R and the image of the point Q(0,−1/2,0) in the...
- Let f(x)= cases x^3+8, & x<0 x^2-4, & x 0 cases and g(x)= cases (x-8)^ 1/3 , & x<0 (x+4)^ 1/2 , & x 0 cases . Then the number of...
- 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