List of top Mathematics Questions

The set of all real values of x satisfying the inequation \( \frac{8x^2-14x-9}{3x^2-7x-6}>2 \) is
The number of solutions of the system of equations \(2x+y-z=7\), \(x-3y+2z=1\), \(x+4y-3z=5\) is
If \( x^6 = (\sqrt{3}-i)^5 \), then the product of all of its roots is
The points in the Argand plane represented by the complex numbers \(4\hat{i}+3\hat{j}\), \(6\hat{i}-2\hat{j}-3\hat{k}\) and \(\hat{i}-\hat{j}-3\hat{k}\) form
The set of all real values of \(x\) for which \(f(x) = \sqrt{\frac{|x|-2}{|x|-3}}\) is a well defined function is
\(f(x)\) is a quadratic polynomial satisfying the condition \( f(x) + f\left(\frac{1}{x}\right) = f(x)f\left(\frac{1}{x}\right) \). If \(f(-1)=0\), then the range of \(f\) is
If \( A = \begin{pmatrix} 1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6 \end{pmatrix} \) and \( |adj(adj(A))|(adj A)^{-1} = kA \), then k =
\( \sum_{k=1}^{n} k(k+1)(k+2)...(k+r-1) = \)
If the values \( x = \alpha, y = \beta, z = \gamma \) satisfy all the 3 equations \(x+2y+3z=4\), \(3x+y+z=3\) and \(x+3y+3z=2\), then \(3\alpha + \gamma = \)
If \( x \log_{10} x \frac{dy}{dx} + y = 2 \log_{10} x \) and \( y(e) = 0 \), then \( y(e^2) = \)
The number of turning points of the curve $f(x) = 2\cos x - \sin 2x$ in the interval $[-\pi, \pi]$ is
If $y = \tan^{-1}(\frac{3x - x^3}{1-3x^2}) + \tan^{-1}(\frac{7x}{1-12x^2})$, then at $x=0$, $\frac{dy}{dx} =$

If the probability distribution of a random variable X is as follows, then the mean of X is

X = xi-1012
P(X = xi)k32k3 + k4k - 10k24k - 1

The mean deviation about the mean for the following data is 
 

Class Interval0--22--44--66--88--10
Frequency13412
The number of solutions of the equation $\sqrt{3x^2 + x + 5} = x - 3$ is

$\left( 1 + \sqrt{5} + i \sqrt{10 - 2\sqrt{5}} \right)^5$

If $(\sqrt{3} - i)^n = 2^n$, $n \in \mathbb{N}$, then the least possible value of $n$ is
If the point $P$ denotes the complex number $z = x + iy$ in the Argand plane and $\frac{z - (2 - i)}{z + (1 + 2i)}$ is purely imaginary, then the locus of $P$ is
Consider two systems of 3 linear equations in 3 unknowns $AX = B$ and $CX = D$. If $AX = B$ has the unique solution $X = D$ and $CX = D$ has the unique solution $X = B$, then the solution of $(A - C^{-1})X = 0$ is
$f(x)$ is an $n^{th}$ degree polynomial satisfying $f(x) = \frac{1}{2}\left[f(x)f\left(\frac{1}{x}\right) + f\left(\frac{f(x)}{x}\right)\right]$. If $f(2) = 33$, then the value of $f(3)$ is
If $a$ is the determinant of the adjoint of the matrix $\begin{bmatrix} 1 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 3 \end{bmatrix}$ and $b$ is the determinant of the inverse of the matrix $\begin{bmatrix} 2 & 1 & 3 \\ 1 & -4 & -1 \\ 2 & 1 & 4 \end{bmatrix}$, then $\frac{b+1}{18b} = $
For all $n \in \mathbb{N}$, if $n(n^2+3)$ is divisible by $k$, then the maximum value of $k$ is
The domain of the function $f(x) = \ln\left(\frac{1}{\sqrt{x^2-4x+4}}\right) + \sin^{-1}(x^2-2)$ is
If \( f(t) = \int_0^t \tan^{2n-1}(x) \, dx \), \( n \in \mathbb{N} \), then \( f(t + \pi) =\)
\(\int_{-2\pi}^{2\pi} \sin^2(2x) \cos^4(2x) \, dx =\)