List of top Mathematics Questions

The solution of the differential equation $ \frac{dy}{dx}=\frac{1}{x+{{y}^{2}}} $ is
If the equation $ (a+1){{x}^{2}}-(a+2)x+(a+3)=0 $ has roots equal in magnitude but opposite in signs, then the roots of the equation are
If $ (3,\,\,3) $ is a vertex of a triangle and $ (-3,\,\,6) $ and $ (9,\,\,6) $ are the mid points of the two sides through this vertex, then the centroid of the triangle is
If$\vec{a}+2\vec{b}+3\vec{c}=\vec{0}$ then $\vec{a} \times \vec{b}+\vec{b} \times \,\vec{c}+\vec{c} \times \vec{a} $ =
If $x$ is numerically so small so that $x^{2}$ and higher powers of $x$ can be neglected, then $\left(1+\frac{2 x}{3}\right)^{3 / 2} \cdot(32+5 x)^{-1 / 5}$ is approximately equal to
The coefficient of $x^{24}$ in the expansion of $\left(1+x^{2}\right)^{12}\left(1+x^{12}\right)\left(1+x^{24}\right)$ is
$\frac{1}{e^{3 x}}\left(e^{x}+e^{5 x}\right)=a_{0}+a_{1} x +a_{2} x^{2}+\ldots$ $\Rightarrow 2 a_{1}+2^{3} a_{3}+2^{5} a_{5}+\ldots$ is equal to
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
In the group $\{1, 2, 3, 4, 5, 6\}$ under multiplication mod $7, 2^{-1} \times 4 =$
The value of $\int \frac{10^{x/2}}{\sqrt{10^{-x} - 10^{x}}}dx$ is
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
The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is
$\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)} = $
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
$A$ 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