List of top Mathematics Questions

The roots of $(x-a)(x-a-1)+(x-a-1)(x-a-2) +(x-a)(x-a-2)=0, a \in R$ are always
If $A$ and $B$ are square matrices of the same order such that $(A + B) (A -B) = A^2-B^2$ then $(ABA^{-1} )^2=$
The negation of $p{\land}(q \to \sim r)$ is
If $'n '$ is a positive integer, then $n^3 + 2n$ is divisible by
On the set of integers $Z$. define $f: Z \to Z$ as $ f(n) = \begin{cases} n/2 & \quad \text{if } n \text{ is even}\\ 0 & \quad \text{if } n \text{ is odd}\\ \end{cases} $ then $'f'$ is
The value of $\int \frac{10^{x/2}}{\sqrt{10^{-x} - 10^{x}}}dx$ is
$\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} \cos^2 \frac{5 \pi}{12} = $
In the group $\{1, 2, 3, 4, 5, 6\}$ under multiplication mod $7, 2^{-1} \times 4 =$
The argument of the complex number $\sin\left(\frac{6\pi}{5}\right) + i\left(1 +\cos \frac{6\pi}{5}\right) $ is
If $A= \begin{bmatrix}1&2\\ 0&1\end{bmatrix} $, then $A^n$ is
The number of distinct real roots of $\begin{vmatrix}\sin x&\cos x&\cos x\\ \cos x&\sin x&\cos x\\ \cos x &\cos x&\sin x\end{vmatrix}$ in the interval $ \left[\frac{-\pi}{4}, \frac{\pi}{4}\right] $ is
If $\alpha , \beta , \gamma$ are the roots of the equation $x^3 + px + q = 0$, then the value of the determinant $\begin{vmatrix}\alpha&\beta&\gamma\\ \beta&\gamma&\alpha\\ \gamma&\alpha&\beta\end{vmatrix} = $
$\displaystyle\lim_{n\to\infty} \frac{\left(1^{2} +2^{2} + ....+n^{2}\right) \sqrt[n]{n}}{ \left(n+1\right)\left(n+10\right)\left(n+100\right)} = $
The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is
For a certain function $ u_x $ , given that $ u_0 = 3, u_1 = 12, u_2 = 81, u_3 = 200, u_4 = 100, u_5 = 8 $ , then $ \Delta ^{5}u_{x} $ is equal to
$ \lim\limits _{x\to 1 } \left(log \,ex\right)^{1/log\,x} $ is equal
The maximum value of $ z = 9x + 13y $ subject to $ 2x + 3y \le 18, 2x + y \le 10, x \ge 0, y \ge 0 $ is
A line through the point $A(2, 0)$ which makes an angle of $30^{\circ}$ with the positive direction of $x$-axis is rotated about $A$ in clockwise direction through an angle $15^{\circ}$. Then, the equation of the straight line in the new position is
The value of $\int\limits_{0}^{\infty} \frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)}$ is
For any two sets $A$ and $B$, $A-(A-B)$ equals
For what value of $m$, $\frac{a^{m+1}+b^{m+1}}{a^{m}+b^{m}}$ is the arithmetic mean of $�a�$ and $�b�$ ?
If $C_{0}, C_{1}, C_{2}, \ldots, C_{n}$ denote the coefficients in the expansion of $(1+x)^{n}$, then the value of $C_{1}+2C_{2}+3C_{3}+\ldots+nC_{n}$ is
If $\alpha, \beta $ be the roots of $x^{2}-a(x-1)+b=0$, then the value of $\frac{1}{\alpha^{2}-a\alpha}+\frac{1}{\beta^{2}-a\beta}+\frac{2}{a+b}$ is
The equation of the tangent to the conic $x^{2}-y^{2}-8x+2y+11=0$ at $(2,1)$ is
$A$ and $B$ are two independent events such that $P\left(A\cup B'\right)=0.8$, and $P\left(A\right)=0.3$ Then, $P(B)$ is