List of top Mathematics Questions

The function \(f(x) = \frac{x}{2} + \frac{2}{x}\) has a local minimum at:
If binomial coefficients of three consecutive terms of (1+x)ⁿ are in H.P., then the maximum value of n is
A line makes the same angle θ with each of the X and Z-axes. If the angle β, which it makes with Y-axis, is such that sin²β=3sin²θ, then cos²θ equals
If ρ=\(x,y)mid x²+y²=1; x,y∈R then ρ is
If in a binomial distribution n=4 and P(X=0)=dfrac1681, then P(X=4) equals
If complex numbers z₁,z₂,z₃ are vertices of an equilateral triangle, then z₁²+z₂²+z₃²-z₁z₂-z₂z₃-z₃z₁ is equal to
If (cos A)/(cos B)=n, (sin A)/(sin B)=m, then the value of (m²-n²)sin² B is
The degree of the differential equation √(1-x²)+√(1+y²)=a(x-y) is
Area of the circle in which a chord of length √(2) makes an angle π/2 at the centre is
If the lines p₁x+q₁y=1, p₂x+q₂y=1 and p₃x+q₃y=1 are concurrent, then the points (p₁,q₁), (p₂,q₂) and (p₃,q₃)
The domain of the function f(x)=fracsin⁻1(x-3)√(9-x²) is
Let f(x) be a polynomial of degree three satisfying f(0)=0, f(1)=0. Also, 0 is a stationary point and f(x) does not have any extremum at x=0. Then the value of int fracf(x)x³-1dx is
If limₓtₒᵢₙfty xsin((1)/(x))=A and limₓ\to0 xsin((1)/(x))=B, then which one of the following is correct?
The eccentricity of an ellipse, with its centre at the origin, is \dfrac12. If one of the directrices is x=4, then the equation of the ellipse is
If y=x+√(1+x²), then (1+x²)dfracd²ydx²+x(dy)/(dx) is
If \( 0 < x < \dfrac{\pi}{2} \), then
Tangents are drawn from the origin to the curve y=cos x. Their points of contact lie on
The slope of the tangent to the curve y=eˣcos x is minimum at x=α,0≤α\le2π. The value of α is
A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is
Let M be a 3×3 non-singular matrix with det(M)=α. If |M⁴operatornameadj(M)|=K, then the value of K is
The number of real roots of the equation eˣ-1+x-2=0 is
The line which is parallel to the X-axis and crosses the curve y=√(x) at an angle 45^∘, is
In a △ ABC, the lengths of the two larger sides are 10 and 9 units, respectively. If the angles are in A.P., then the length of the third side can be
The total number of 4-digit numbers in which the digits are in descending order, is
The arithmetic mean of the data 0,1,2,…,n with frequencies 1,1,1,…,1 is