Mathematics questions
18011 published questions with worked solutions.
- Let f : (0, π) → ℝ be a function given by f(x) = cases ( 87 )^ 8x 7x , & 0 < x < 2 a - 8, & x = 2 (1 + | x|)^ ba| x| , & 2 < x <...
- Let A be a non-singular matrix of order 3. If det(3adj(2adj((det A)A))) = 3⁻¹³·2⁻¹⁰ and det(3adj(2A)) = 2ᵐ·3ⁿ, then |3m + 2n| is...
- Let the centre of a circle, passing through the point (0, 0), (1, 0) and touching the circle x² + y² = 9, be (h, k). Then for all...
- Let A = 2, 3, 6, 7 and B = 4, 5, 6, 8 . Let R be a relation defined on A × B by (a₁, b₁) R (a₂, b₂) if and only if a₁ + a₂ = b₁ +...
- Let e₁ be the eccentricity of the hyperbola x^2 16 - y^2 9 = 1 and e₂ be the eccentricity of the ellipse x^2 a^2 + y^2 b^2 = 1, a...
- The values of α, for which vmatrix 1 & 32 & + 32 1 & 13 & + 13 2 + 3 & 3 + 1 & 0 vmatrix = 0, lie in the interval
- Let R be the interior region between the lines 3x – y + 1 and x + 2y – 5 = 0 containing the origin. The set of all values of a,...
- The integral (x^8 - x^2)dx (x^ 12 + 3x^6 + 1) ^ -1 (x^3 + 1 x^3 ) is equal to:
- Consider the function f : (0, 2) → R defined by f(x) = x2 + 2x and the function g(x) defined by g(x) = cases f(t) , & 0 < t x and...
- Let the image of the point (1, 0, 7) in the line x1 = y-1 2 = z-2 3 be the point (α, β, γ). Then which one of the following...
- The 20ᵗʰ term from the end of the progression 20, 19 14, 18 12, 17 34, , -129 14 is :
- Let g(x) = 3f ( x3 ) + f(3 - x) and f″(x) > 0 for all x ∈ (0, 3). If g is decreasing in (0, α) and increasing in (α, 3), then 8α...
- The position vectors of the vertices A, B and C of a triangle are 2 i - 3 j + 3 k, 2 i + 2 j + 3 k, and - i + j + 3 k,...Not in JEE syllabus
- If _ x 0 3 + x + x + _e(1 - x) 3 ^2x = 13, then 2α – β is equal to:
- Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the...
- Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying...
- Let the position vectors of the vertices A, B and C of a triangle be 2 i + 2 j + k, i + 2 j + 2 k and 2 i + j + 2 k respectively....Not in JEE syllabus
- If y = y(x) is the solution curve of the differential equation (x² – 4)dy – (y² – 3y)dx = 0, x > 2, y(4) = 3/2 and the slope of...
- If 2tan²θ – 5secθ = 1 has exactly 7 solutions in the interval [0, n 2 ], for the least value of n ∈ N, then _ k=1 ^n k 2^k is...Not in JEE Main syllabus
- Let = (4!)! (4!)^ 3! and = (5!)! (5!)^ 4! . Then: