List of top Mathematics Questions

If the ratio of corresponding sides of two similar triangles is 4: 9, then the ratio of areas of these triangles is

Let a = i + 2j -2k and b = 2i - j - 2k be two vectors. If the orthogonal projection vector of a on b is x and orthogonal projection vector of b on a is y then |x - y| =

In a triangle BC, if the mid points of sides AB, BC, CA are (3,0,0), (0,4,0),(0,0,5) respectively, then AB2 + BC2 + CA2 =

An enemy fighter jet is flying along the curve given by y = x2 + 2. A soldier is placed at (3, 2) wants to shoot down the jet when it is nearest to him. Then the nearest distance is
nth term of the series
\(1+\frac{3}{7}+\frac{5}{7^2}+\frac{1}{7^2}+...\) is
The function \(y=e^{kr}\) satisfies \((\frac{d^2y}{dx^2}+\frac{dy}{dx})(\frac{dy}{dx}-y)=y\frac{dy}{dx}\). It is valid for 
Let f(x)=πcosx+x2.The value of c∈(0,π) where f attains its local maximum/minumum is

Area of the Region bounded by the curve y=√49-x2 and x-axis is .

The number of solutions of tanx+secx=2cosx, n(0,2π) are?

\(f(x) = x^2 + 1\), \(g(x) = \frac{1}{x}\). Find \(f(g(g(f(x))))\) at \(x = 1\)
Considering only the principal value of an inverse function, the set: A= { x ≥ 0, tan-1x + tan-16x = \(\frac{\pi}{4}\)}, then A is... 
 

The differential equation dy/dx=√1-y2/y determines a family of circles with

General Solution of the differential equation:
\(cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0\) is:

If the line ax+by+c=0 is a normal to the curve xy=1, then 
 

The Points (1,3), (5,1) are Opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line y=2x+c, then one of the vertex on the other diagonal is? 
 

If nCr denotes the number of combinations of n distinct things taken r at a time, then the domain of the function g (x)= (16-x)C(2x-1)  is

Let F: R3 →R2 be the linear map defined by F(x, y, z) = (3x+2y-4z, x-5y+3z). The basis of R3 is S and basis of R2 is S', where S = {(1, 1, 1), (1, 1, 0), (1, 0, 0)} and S' = {(1, 3), (2, 5)}. Then the matrix of F in the bases of R3 and R2 is
For which toy category has there been a continuous increase in production over the years?
If A and B are events such that P(A)=\(\frac{1}{4}\), P(A/B)=\(\frac{1}{2}\) and P(B/A)=\(\frac{2}{3}\) then P(B) is
Let f(x)=[x2]sinπx, x>0. Then

The area (in square units) of the region bounded by the curve y = |sin2x| and the X-axis in [0,2π] is

\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} sin^2xcos^2x(sinx+cosx)dx=\)

\[\int_{-1}^{1} x|x| \,dx\]

\(∫\frac{dx}{(x-1)^{34} (x+2)^{\frac54}}=\)

\(∫\frac{dx}{(x2+1) (x2+4)} =\)