List of top Mathematics Questions asked in AP EAPCET

In a triangle $ABC$, $C=90^\circ$. If $r$ is the inradius and $R$ is the circumradius of the triangle, then \[ 2(r+R)= \]

For $n\in\mathbb Z$, a set of values of $\theta$ satisfying \[ \sec\theta-1=(\sqrt2-1)\tan\theta \] is

Evaluate \[ \cos\frac{6\pi}{17}\cos\frac{10\pi}{17}\cos\frac{12\pi}{17}\cos\frac{14\pi}{17}. \]

The value of \[ \tan81^\circ-\tan63^\circ-\tan27^\circ+\tan9^\circ \] is

If \[ u=\log\tan\left(\frac{\pi}{4}+\frac{\theta}{2}\right), \] then \[ \tanh\frac{u}{2} = \]

The number of distinct real roots of \[ \begin{vmatrix} \sin x & \cos x & \cos x\\ \cos x & \sin x & \cos x\\ \cos x & \cos x & \sin x \end{vmatrix}=0 \] in the interval \[ \left(-\frac{\pi}{4},\frac{\pi}{4}\right) \] is

The number of real solutions of the equation \[ \tan^{-1}\sqrt{x(x+1)} + \sin^{-1}\sqrt{x^2+x+1} = \frac{\pi}{2} \] is

The number of different nine-digit numbers that can be formed by rearranging all the digits of the number $223355888$ so that odd digits always occupy even positions is

The value of $n$ for which the sum \[ \frac{{}^nC_0}{2^n} + 2\frac{{}^nC_1}{2^n} + 3\frac{{}^nC_2}{2^n} +\cdots+ (n+1)\frac{{}^nC_n}{2^n} =16 \] is

In the binomial expansion of $(x+a)^{15}$, if the eleventh term is the geometric mean of the eighth and twelfth terms, then the numerically greatest term in its expansion is

If all the letters of the word RANKS are permutated in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word RANKS is

If \[ \frac{x}{(x^2+1)^2(x-1)} = \frac{Ax+B}{x^2+1} + \frac{Cx+D}{(x^2+1)^2} + \frac{E}{x-1}, \] then \[ A+B-C+2D= \]

A student is allowed to select at most $n$ books from a collection of $2n+1$ books. If the total number of ways in which he can select at least one book is $255$, then the value of $n$ is

If $\alpha,\beta,\gamma$ are the roots of \[ x^3-10x^2+7x+8=0, \] match List-I with List-II and choose the correct option.

If the roots of the equation \[ x^3-px^2+qx-s=0 \] are in geometric progression, then

If $\alpha \neq \beta$ and $\alpha^2=5\alpha-3,\ \beta^2=5\beta-3$, then the equation whose roots are $\dfrac{\alpha}{\beta}$ and $\dfrac{\beta}{\alpha}$ is

If \[ \frac{3}{2+\cos\theta+i\sin\theta}=x+iy, \] then \[ (x-1)(x-3)= \]

If \[ y= \begin{vmatrix} \sin x & \cos x & \sin x\\ \cos x & -\sin x & \cos x\\ x & 1 & 1 \end{vmatrix}, \] then \[ \frac{dy}{dx}= \]

If $z_1,z_2$ are two roots of the equation \[ z^2+az+b=0 \] and on the Argand plane the points represented by $z_1,z_2$ and the origin form an equilateral triangle, then $a^2=$

If $\alpha,\beta$ are the roots of the equation \[ x^2-p(x+1)-c=0, \] then \[ \frac{\alpha^2+2\alpha+1}{\alpha^2+2\alpha+c} + \frac{\beta^2+2\beta+1}{\beta^2+2\beta+c} = \]

If \[ (1+\sin\alpha+i\cos\alpha)^8 = A(\cos\theta+i\sin\theta), \] then $A$ and $\theta$ are respectively

If \[ \frac34+\frac{15}{16}+\frac{63}{64}+\cdots+n \text{ terms} =\frac{939}{256}, \] then $5n=$

If $\alpha,\beta,\gamma$ are the roots of the equation $x^3+bx+c=0$, then \[ \begin{vmatrix} \alpha & \beta & \gamma\\ \beta & \gamma & \alpha\\ \gamma & \alpha & \beta \end{vmatrix} = \]

For a fixed positive integer $n$, if \[ D= \begin{vmatrix} n! & (n+1)! & (n+2)!\\ (n+1)! & (n+2)! & (n+3)!\\ (n+2)! & (n+3)! & (n+4)! \end{vmatrix}, \] then \[ \frac{D}{n!(n+1)!(n+2)!} = \]

Let $f$ be a function with domain $[0,7]$ and $g$ be a function defined by $g(x)=|2x+1|$. Then the domain of $(f\circ g)(x)$ is