Mathematics questions
18011 published questions with worked solutions.
- Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for k equal to :
- If _0^1 1 3+x + 1+x dx = a + b 2 + c 3, where a, b, c are rational numbers, then 2a + 3b – 4c is equal to
- Let a = i + 2 j + k, b = 3( i - j + k). Let c be the vector such that a c = b and a c = 3. Then a (( c b) - b - c) is equal to :
- The number of common terms in the progressions 4, 9, 14, 19, ......, upto 25th term and 3, 6, 9, 12, ......, upto 37th term is :
- If (a, b) be the orthocentre of the triangle whose vertices are (1, 2), (2, 3) and (3, 1), and I_1 = _a^b x (4x - x^2)dx, I_2 =...
- If the shortest distance of the parabola y² = 4x from the centre of the circle x² + y² – 4x – 16y + 64 = 0 is d then, d² is
- Consider the function. f(x) = cases a(7x-12-x^2) b|x^2-7x+12| , & x<3 [2mm] 2^ (x-3) x-[x] , & x>3 [2mm] b, & x=3 cases Where [x]...
- If the shortest distance between the lines x-4 1 = y+1 2 = z -3 and x- 2 = y+1 4 = z-2 -5 is 6 5 , then the sum of all possible...
- The portion of the line 4x + 5y = 20 in the first quadrant is trisected by the lines L₁ and L₂ passing through the origin. The...
- If A denotes the sum of all the coefficients in the expansion of (1 - 3x + 10x^2)^n and B denotes the sum of all the coefficients...
- Let a₁, a₂, ... a₁₀ be 10 observations such that _ k=1 ^ 10 a_k = 50 and _ k<j a_ka_j = 1100. Then the standard deviation of a₁,...
- Let the area of region (x, y) : x – 2y + 4 ≥ 0, x + 2y² ≥ 0, x + 4y² ≤ 8, y ≥ 0 be mn, where m and n are coprime numbers. Then m...
- Let f(x) = x³ + x² f′(1) + x f″(2) + f‴(3), x ∈ R. Then f′(10) is equal to ______.
- Let the set of all a ∈ R such that the equation cos2x + a sinx = 2a – 7 has a solution be [p, q] and r = tan9° – tan27° – 1 63° +...Not in JEE Main syllabus
- If the solution of the differential equation (2x + 3y – 2)dx + (4x + 6y – 7)dy = 0, y(0) = 3, is αx + βy + 3log_e|2x + 3y – γ| =...
- A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required and let a = P(X = 3), b = P(X...
- The least positive integral value of α, for which the angle between the vectors i - 2 j + 2 k and i + 2 j - 2 k is acute, is...
- If α satisfies the equation x² + x + 1 = 0 and (1 + α)⁷ = A + Bα + Cα², A, B, C ≥ 0 then 5(3A – 2B – C) is equal to ______.
- Let for a differentiable function f : (0, ∞) → R, f(x) - f(y) _e ( xy ) + x - y, ∀ x, y ∈ (0, ∞). Then _ n=1 ^ 20 f' ( 1 n^2 ) is...
- Let A = bmatrix 2 & 0 & 1 1 & 1 & 0 1 & 0 & 1 bmatrix , B = [B₁, B₂, B₃], where B₁, B₂, B₃ are column matrices and AB_1 = bmatrix...