List of top Mathematics Questions

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
The function f(x)=dfracx2+(2)/(x) has a local minimum at
Two lines L₁:x=5, (y)/(3-α)=(z)/(-2) L₂:x=α, (y)/(-1)=(z)/(2-α) are coplanar. Then α can take value(s)
If y=x+√(1+x²), then (1+x²)dfracd²ydx²+x(dy)/(dx) is
If limₓtₒᵢₙfty xsin((1)/(x))=A and limₓ\to0 xsin((1)/(x))=B, then which one of the following is correct?
The number of real roots of the equation eˣ-1+x-2=0 is
Let M be a 3×3 non-singular matrix with det(M)=α. If |M⁴operatornameadj(M)|=K, then the value of K is
Minimise Z=sumᵢ=1ⁿsumj=1ᵐ cᵢjxᵢj Subject to sumᵢ=1ⁿ xᵢj=bj, j=1,2,…,m sumj=1ᵐ xᵢj=bᵢ, i=1,2,…,n is a LPP with number of constraints
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
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
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
Let S be the common focus of the circle x²+y²-2x-4y=0 and the parabola y²=8x. The area of quadrilateral APQS is
The mean square deviation of a set of n observations about points -2 and 2 are 18 and 10 respectively. The standard deviation of the set is
The total number of 4-digit numbers in which the digits are in descending order, is
The line which is parallel to the X-axis and crosses the curve y=√(x) at an angle 45^∘, is
The arithmetic mean of the data 0,1,2,…,n with frequencies 1,1,1,…,1 is
Let a, b, c be three vectors satisfying a × b = ( a × c), | a|=| c|=1, | b|=4 and | b × c|=√(15). If a · b = ?, then λ equals
Universal set, U=\xmid x⁵-6x⁴+11x³-6x²=0 A=\xmid x²-5x+6=0 B=\xmid x²-3x+2=0 What is (A∩ B)' equal to?
If cos⁻1x-cos⁻1(y)/(2)=α, then 4x²-4xycosα+y² is equal to
If fraceˣ+e⁵xe³x=a₀+a₁x+a₂x²+a₃x³+⋯ then the value of 2a₁+2³a₃+2⁵a₅+⋯ is
The area of the region R=\(x,y): |x|≤ |y| and x²+y²≤ 1 is
The value of
\( \dfrac{3}{4} + \dfrac{15}{16} + \dfrac{63}{64} + \cdots \)
up to \( n \) terms is
If φ(x) is a differentiable function, then the solution of the differential equation dy+yφ'(x)-φ(x)φ'(x)dx=0 is
If f(x)=(x)/(1+x)+(x)/((x+1)(2x+1))+(x)/((2x+1)(3x+1))+⋯ then at x=0, f(x)