Mathematics questions
18011 published questions with worked solutions.
- Let O be the vertex of the parabola y² = 4x and its chords OP and OQ are perpendicular to each other. If the locus of the...
- Let α = 3 sin⁻¹(6/11) and β = 3 cos⁻¹(4/9), where inverse trigonometric functions take only the principal values. Given below are...
- For the function f(x) = e^ sin|x| − |x|, x ∈ ℝ, consider the following statements: Statement I: f is differentiable for all x ∈...
- Let a=4 i- j+3 k, b=10 i+2 j- k and a vector c be such that 2( a b)+3( b c)= 0. If a c=15, then c ( i+ j-3 k) is equal to:
- Let the foot of perpendicular from the point (λ, 2, 3) on the line x-4 1= y-9 2= z-5 1 be the point (1, μ, 2). Then the distance...
- Let y = y(x) be the solution of the differential equation x 1-x^2 ,dy+ (y 1-x^2 -x ^ -1 x )dx=0, x ∈ (0, 1), _ x 1^- y(x)=1. Then...
- Let f : (1, ∞) → ℝ be a function defined as f(x)= x-1 x+1 . Let fⁱ⁺¹(x) = f(fⁱ(x)), i = 1, 2, …, 25, where f¹(x) = f(x). If g(x)...
- Let f(x)= cases 13, & x /2 [2mm] b(1- x) ( -2x)^2 , & x> /2 cases . If f is continuous at x = π/2, then the value of _0^ 3b-6...
- Let x^2 f(a^2+7a+3) + y^2 f(3a+15) =1 represent an ellipse with major axis along y-axis, where f is a strictly decreasing...
- The sum of squares of all the real solutions of the equation _ (x+1) (2x^2+5x+3)=4- _ (2x+3) (x^2+2x+1) is equal to _______.
- Let a line L₁ pass through the origin and be perpendicular to the lines L₂ : r⃗ = (3 + t)î + (2t − 1)ĵ + (2t + 4)k̂ and L₃ : r⃗ =...
- Consider the circle C : x² + y² − 6x − 8y − 11 = 0. Let a variable chord AB of the circle C subtend a right angle at the origin....
- Consider the line L passing through the points (1, 2, 3) and (2, 3, 5). The distance of the point (11/3, 11/3, 19/3) from the...
- Let _0^x 1 - (y'(t))^2 dt = _0^xy(t)dt, 0 ≤ x ≤ 3, y ≥ 0, y(0) = 0. Then at x = 2, y″ + y + 1 is equal to :
- Let z be a complex number such that the real part of z - 2i z + 2i is zero. Then, the maximum value of |z − (6 + 8i)| is equal to...
- Let the foci of a hyperbola H coincide with the foci of the ellipse E : (x − 1)²/100 + (y − 1)²/75 = 1 and the eccentricity of...
- Two vertices of a triangle ABC are A(3, −1) and B(−2, 3), and its orthocentre is P(1, 1). If the coordinates of the point C are...Not in JEE syllabus
- If the variance of the frequency distribution is 160, then the value of c ∈ ℕ is | x | c | 2c | 3c | 4c | 5c | 6c |...
- Let the range of the function f(x) = 1 2 + 3x + 3x , x ∈ ℝ be [a, b]. If α and β are respectively the A.M. and the G.M. of a and...
- Between the following two statements : Statement-I : Let a⃗ = î + 2ĵ − 3k̂ and b⃗ = 2î + ĵ − k̂. Then the vector r⃗ satisfying a⃗...