List of top Mathematics Questions

If the third term of a $G.P.$ is $3$, then the product of its first $5$ terms is

The number of diagonals of a polygon of $20$ sides is

If $\alpha$ and $\beta$ are roots of the quadratic equation $ {{x}^{2}}+4x+3=0, $ then the equation whose roots are $ 2\alpha \,\text{+}\,\beta $ and $ \alpha \,\text{+2}\,\beta $ is

If $X$ and $Y$ are $ 2\times 2 $ matrices such that $ 2X+3Y=O $ and $ X+2Y=I, $ where $ O $ and $ I $ denote the $ 2\times 2 $ zero matrix and the $ 2\times 2 $ identity matrix, then $X$ is equal to

If $ f\,(x)=\underset{y\to x}{\mathop{lim}}\,\,\frac{{{\sin }^{2}}y-{{\sin }^{2}}x}{{{y}^{2}}-{{x}^{2}}}, $ then $ \int{4x\,\,f(x)\,\,dx} $ =

The value of $\begin{vmatrix} \log_5\,729 & \log_3\,5 \\[0.3em] \log_5\,27 & \log_9\,25 \end{vmatrix}.\begin{vmatrix} \log_3\,5 & \log_{27}\,5 \\[0.3em] \log_5\,9 & \log_5\,9 \end{vmatrix}=$

$x \in R : \frac{2x -1}{x^3 + 4x^2 + 3x} \in R$ Equals

If the sum to $2n$ terms of the $ A.P. \text{ }2,\text{ }5,\text{ }8,11,... $ is equal to the sum to $n$ terms of the $\text{ }57,\text{ }59,\text{ }61,\text{ }63,\text{ }...\text{ }, $ then $n$ =

In a boolean algebra $B$ with respect to $' +' $ and $'.',$ $ x' $ denotes the negation of $ x\in B $ . Then

The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is

The solution of the differential equation $ \frac{dy}{dx}=\frac{1}{x+{{y}^{2}}} $ is

The range of the function $ f(x)\frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1} $ where $ x\in R, $ 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

The value of $\int \frac{10^{x/2}}{\sqrt{10^{-x} - 10^{x}}}dx$ is