List of top Mathematics Questions asked in EAMCET

If $\quad \tan \theta \cdot \tan \left(120^{\circ}-\theta\right) \tan \left(120^{\circ}+\theta\right)=\frac{1}{\sqrt{3}}$, then $\theta$ is equal to

If $f: R \rightarrow R, g: R \rightarrow R$ are defined by $f(x)=5\, x-3, g(x)=x^{2}+3$, then $g o f^{-1}(3)$ is equal to

The common roots of the equations $z^{3}+2 z^{2}+2 z+1=0, z^{2014}+z^{2015}+1=0$ are

If $\omega$ is a complex cube root of unity, then $\omega^{\left(\frac{1}{3}+\frac{2}{9}+\frac{4}{27}+\ldots \infty\right)}+\omega^{\left(\frac{1}{2}+\frac{3}{8}+\frac{9}{32}+\ldots \infty\right) \text { is equal to }}$

The system $2\,x+3 y+z=5,3\,x+y+5\,z=7$ and $x+4\,y-2\,z=3$ has

The value of the sum $1 \cdot 2 \cdot 3+2 \cdot 3 \cdot 4+3 \cdot 4 \cdot 5+\ldots$ upto $n$ terms is equal to

$\displaystyle \sum_{k=1}^{6}\left[\sin \frac{2 k \pi}{7}-i \cos \frac{2 k \pi}{7}\right]$ is equal to

The value of the determinant $\begin{vmatrix}b^{2}-a b & b-c & b c-a c \\ a b-a^{2} & a-b & b^{2}-a b \\ b c-a c & c-a & a b-a^{2}\end{vmatrix}$ is

If $A$ is a square matrix of order 3 , then | adj $\left(\operatorname{adj} A^{2}\right) \mid$ is equal to

If $A=\left\{x \in R / \frac{\pi}{4} \leq x \leq \frac{\pi}{3}\right\}$ and $f(x)=\sin x-x$, then $f(A)$ is equal to

If $a, b, c$ are distinct and the roots of $(b-c) x^{2}+(c-a) x+(a-b)=0 $ are equal, then $a, b$ and $c$ are in

If $\alpha, \beta, \gamma$ are the roots of $x^{3}+4 x+1=0$, then the equation whose roots are $\frac{\alpha^{2}}{\beta+\gamma}, \frac{\beta^{2}}{\gamma+\alpha},\,\frac{\gamma^{2}}{\alpha+\beta}$ is

For $|x|<1$, the constant term in the expansion of $\frac{1}{(x-1)^{2}(x-2)}$ is

The number of subsets of $\{1, 2, 3 ,............,9\}$ containing at least one odd number is

Match the following.

Let $f(x)=x^{2}+a x +b,$ where $a, b \in R .$ If $f(x)=0$ has all its roots imaginary, then the roots of $f(x)+f'(x)+f''(x)=0$ are

A binary sequence is an array of $0's$ and $1's$. The number of $n$ -digit binary sequences which contain even number of $0's$ is

$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is

The number of subsets of $\{1,2,3, \ldots, 9\}$ containing at least one odd number is

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