List of top Mathematics Questions

Number of four digit numbers that can be formed using all the digits except zero such that every number has exactly \(2\) distinct digits in it is

The largest interval containing \(x\) for which \[ x^{12}-x^9+x^4-x+1\gt 0 \] is

Let \(a_n,a_{n-1},\ldots,a_1,a_0\in \mathbb{C}\) and \[ f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0 \] is a polynomial. If the polynomial \(f(x)\) is monic, then

The number of solutions of the equations \[ x+y+z=12,\quad x^2+y^2+z^2=50,\quad x^3+y^3+z^3=216 \] is

If \[ A= \begin{bmatrix} 1 & 1 & 3\\ 1 & 7 & 9\\ 2 & 3 & 7 \end{bmatrix} \] then \[ \mathrm{Tr}(A^2-A)= \] is equal to:

The number of distinct solutions of the equation \[ x^{11}-x^7+x^4-1=0 \] is

The number of complex numbers \(z\) satisfying \[ \overline{z}=iz^2 \] is

If \[ z=\cos\theta+i\sin\theta \] then \[ z^r+(\overline{z})^r= \] is equal to:

If \[ (x+iy)=\left(\frac{1+i}{1-i}\right)^3-\left(\frac{1-i}{1+i}\right)^3, \] then the true statement among the following is:

If \(f(x)=ax^2+bx+c\) satisfies \[ f(1)+2f(2)=0 \] and \[ 2f(1)+f(2)=0, \] then \(3a+b=\)

If \[ A=\begin{bmatrix} 3 & 4\\ 5 & 6 \end{bmatrix} \] and \[ B=\begin{bmatrix} x & 0\\ 0 & y \end{bmatrix}, \quad x,y\in \mathbb{N}, \] then:

If \(A\) and \(B\) are symmetric matrices of same order such that \[ AB+BA=X \] and \[ AB-BA=Y, \] then \((XY)^T=\)

If the ranks of the matrices \[ A= \begin{bmatrix} 1 & 0 & 1\\ 2 & 1 & 2\\ 1 & 0 & -1 \end{bmatrix} \] and \[ B= \begin{bmatrix} 1 & 2 & 3 & 4\\ 2 & 4 & 6 & -8 \end{bmatrix} \] are \(r_1\) and \(r_2\) respectively, then \(r_1-r_2=\)

Let \(f\) be a function defined by \[ f(xy)=\frac{f(x)}{y} \] for all positive real numbers \(x\) and \(y\). If \(f(30)=20\), then \(f(40)=\)

Let \(f:\mathbb{R}\to\mathbb{R}\) be defined by \[ f(x)=5^{x^4+2} \] Then:

By multiplying with \[ e^{\int Pdx} \] on both sides of the equation \[ \frac{dy}{dx}+P(x)y=Q(x), \] the left side of the equation turns in the form \[ \frac{d}{dx}\left(yf(x)\right), \] then \[ f(x)= \] is:

If the slope of the tangent at a point \((x,y)\) on a curve is \[ \frac{y-4}{x-3} \] and the curve passes through \((4,3)\), then the point where it cuts the line \[ y=x \] is:

The integrating factor of the linear differential equation \[ \frac{dy}{dx}+P(x)y=Q(x) \] is a solution of the differential equation:

\([\,.\,]\) represents a greatest integer function. If \[ \int_{\sqrt{3}}^{\sqrt{18}}[x]\,dx=a+b\sqrt{2}+c\sqrt{3}, \] then \[ a+b+c= \] is:

Evaluate \[ \int_{0}^{4}\frac{x+2}{\sqrt{4x-x^2}}\,dx \] is:

Evaluate \[ \int_{-\pi}^{\pi}\frac{2x(1+\sin x)}{1+\cos^2x}\,dx \] is:

Evaluate \[ \int_{-1}^{1}\frac{\sin x-x^2}{3-|x|}\,dx = \]

There exists \(\theta\) such that \[ a\gt |\sec\theta|, \] then \[ \int \frac{dx}{1+a\cos x} = \] is:

Evaluate \[ \int \frac{x^2}{x^3\sqrt{x^2-1}}\,dx = \]

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